Publishing type：Research paper (scientific journal)   Publisher：Oxford University Press (OUP)  

Abstract

Since the discovery of the accelerated expansion of the present Universe, significant theoretical developments have been made in the area of modified gravity. In the meantime, cosmological observations have been providing more high-quality data, allowing us to explore gravity on cosmological scales. To bridge the recent theoretical developments and observations, we present an overview of a variety of modified theories of gravity and the cosmological observables in the cosmic microwave background and large-scale structure, supplemented with a summary of predictions for cosmological observables derived from cosmological perturbations and sophisticated numerical studies. We specifically consider scalar-tensor theories in the Horndeski and DHOST family, massive gravity/bigravity, vector-tensor theories, metric-affine gravity, and cuscuton/minimally-modified gravity, and discuss the current status of those theories with emphasis on their physical motivations, validity, appealing features, the level of maturity, and calculability. We conclude that the Horndeski theory is one of the most well-developed theories of modified gravity, although several remaining issues are left for future observations. The paper aims to help to develop strategies for testing gravity with ongoing and forthcoming cosmological observations.

DOI： 10.1093/ptep/ptad052

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Recently, a generalization of invertible disformal transformations containing
higher-order derivatives of a scalar field has been proposed in the context of
scalar-tensor theories of gravity. By applying this generalized disformal
transformation to the Horndeski theory, one can obtain the so-called
generalized disformal Horndeski theories which are more general healthy
scalar-tensor theories than ever. However, it is unclear whether or not the
generalized disformal Horndeski theories can be coupled consistently to matter
fields because introducing a matter field could break the degeneracy conditions
of higher-order scalar-tensor theories and hence yield the unwanted
Ostrogradsky ghost. We investigate this issue and explore the conditions under
which a minimal coupling to a matter field is consistent in the generalized
disformal Horndeski theories without relying on any particular gauge such as
the unitary gauge. We find that all the higher derivative terms in the
generalized disformal transformation are prohibited to avoid the appearance of
the Ostrogradsky ghost, leading to the conclusion that only the theories that
are related to the Horndeski theory through a conventional disformal
transformation remain ghost-free in the presence of minimally coupled matter
fields.

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Other Link： http://arxiv.org/pdf/2302.03418v1

We study the homogeneous and anisotropic dynamics of pseudoscalar inflation
coupled to an SU($N$) gauge field. To see how the initially anisotropic
universe is isotropized in such an inflation model, we derive the equations to
obtain axisymmetric SU($N$) gauge field configurations in Bianchi type-I
geometry and discuss a method to identify their isotropic subsets which are the
candidates of their late-time attractor. Each isotropic solution is
characterized by the corresponding SU(2) subalgebra of the SU($N$) algebra. It
is shown numerically that the isotropic universe is a universal late-time
attractor in the case of the SU(3) gauge field. Interestingly, we find that a
transition between the two distinct gauge-field configurations characterized by
different SU(2) subalgebras can occur during inflation. We clarify the
conditions for this to occur. This transition could leave an observable imprint
on the CMB and the primordial gravitational wave background.

DOI： 10.1103/PhysRevD.107.043508

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Other Link： http://arxiv.org/pdf/2211.09489v2

Publishing type：Research paper (scientific journal)   Publisher：IOP Publishing  

Abstract

We provide a cosmological test of modified gravity with two tensorial degrees of freedom and no extra propagating scalar mode. The theory of gravity we consider admits a cosmological model that is indistinguishable from the ΛCDM model at the level of the background evolution. The model has a single modified-gravity parameterβ, the effect of which can be seen in linear perturbations, though no extra scalar mode is propagating. Using the Boltzmann code modified to incorporate the present model, we derive the constraints -0.047 <β< -0.028 at 68% confidence from Planck CMB data. Since our modified gravity model can hardly be constrained by the Solar System tests and gravitational-wave propagation, our result offers the first observational test on the model.

DOI： 10.1088/1475-7516/2022/07/040

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Other Link： https://iopscience.iop.org/article/10.1088/1475-7516/2022/07/040/pdf

We consider spatially covariant modified gravity in which the would-be scalar
degree of freedom is made non-dynamical and hence there are just two tensorial
degrees of freedom, i.e., the same number of dynamical degrees of freedom as in
general relativity. Focusing on a class of such modified gravity theories
characterized by three functions of time, we discuss how modified gravity with
two tensorial degrees of freedom can be distinguished observationally or
phenomenologically from general relativity. It is checked that the theory gives
the same predictions as general relativity for weak gravitational fields and
the propagation speed of gravitational waves. We also find that there is no
modification to asymptotically flat black hole solutions. Due to a large degree
of freedom to choose the time-dependent functions in the theory, the
homogeneous and isotropic cosmological dynamics can be made close to or even
identical to that of the $\Lambda$CDM model. We investigate the behavior of
cosmological perturbations in the long and short wavelength limits and show
that in both limits the effects of modified gravity appear only through the
modification of the background evolution. Finally, it is remarked that in the
presence of a galileon field in the matter sector, the scalar degree of freedom
is revived, ruining the essential feature of the theory.

DOI： 10.1103/PhysRevD.104.124020

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Other Link： http://arxiv.org/pdf/2109.10615v1

We investigate static and spherically symmetric stars disformally coupled to
a scalar field. The scalar field is assumed to be shift symmetric, and hence
the conformal and disformal factors of the metric coupled to matter are
dependent only on the kinetic term of the scalar field. Assuming that the
scalar field is linearly dependent on time, we consider a general
shift-symmetric scalar-tensor theory and a general form of the matter
energy-momentum tensor that allows for the anisotropic pressure and the heat
flux in the radial direction. This is a natural starting point in light of how
the gravitational field equations and the energy-momentum tensor transform
under a disformal transformation. By inspecting the structure of the
hydrostatic equilibrium equation in the presence of the derivative-dependent
conformal and disformal factors, we show that the energy density and tangential
pressure must vanish at the surface of a star. This fact is used to prove the
disformal invariance of the surface of a star, which was previously subtle and
unclear. We then focus on the shift-symmetric k-essence disformally coupled to
matter, and study the interior and exterior metric functions and scalar-field
profile in more detail. It is found that there are two branches of the solution
depending on the velocity of the scalar field. The disformally-related metric
functions of the exterior spacetime are also discussed.

DOI： 10.1103/PhysRevD.104.104009

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Other Link： http://arxiv.org/pdf/2107.13804v1

We study the dynamics of a homogeneous, isotropic, and positively curved
universe in the presence of a SU(2) gauge field or a triplet of mutually
orthogonal vector fields. In the SU(2) case we use the previously known ansatz
for the gauge-field configuration, but the case without non-abelian symmetries
is more nontrivial and we develop a new ansatz. We in particular consider
axion-SU(2) inflation and inflation with vector fields having
U(1)$\times$U(1)$\times$U(1) symmetry, and analyze their dynamics in detail
numerically. Novel effects of the spatial curvature come into play through
vector fields, which causes unconventional pre-inflationary dynamics. It is
found that the closed universe with vector fields is slightly more stable
against collapse than that filled solely with an inflaton field.

DOI： 10.1103/PhysRevD.104.083514

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Other Link： http://arxiv.org/pdf/2107.07199v2

SU(2) gauge fields coupled to an axion field can acquire an isotropic
background solution during inflation. We study homogeneous but anisotropic
inflationary solutions in the presence of such (massless) gauge fields. A gauge
field in the cosmological background may pose a threat to spatial isotropy. We
show, however, that such models $\textit{generally}$ isotropize in Bianchi
type-I geometry, and the isotropic solution is the attractor. Restricting the
setup by adding an axial symmetry, we revisited the numerical analysis
presented in Wolfson et.al (2020). We find that the reported numerical
breakdown in the previous analysis is an artifact of parametrization
singularity. We use a new parametrization that is well-defined all over the
phase space. We show that the system respects the cosmic no-hair conjecture and
the anisotropies always dilute away within a few e-folds.

DOI： 10.1088/1475-7516/2021/09/031

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Other Link： http://arxiv.org/pdf/2105.06259v3

Publishing type：Research paper (scientific journal)  

We derive the solutions of gravitational waves in the future (F) expanding and past (P) shrinking Kasner spacetimes, as well as in the left (L) and right (R) Rindler wedges in the Regge-Wheeler gauge. The solutions for all metric components are obtained in an analytic form in each region. We identify the master variables, which are equivalent to massless scalar fields, to describe the gravitational degrees of freedom for the odd-parity and even-parity modes under the transformation in the two-dimensional plane-symmetric space. Then, the master variables are quantized, and we develop the quantum field theory of the gravitational waves in the F, P, L, and R regions. We demonstrate that the mode functions of the quantized gravitational waves in the left and right Rindler wedges are obtained by an analytic continuation of the left-moving and right-moving wave modes in Kasner spacetime. On the basis of these analyses, we discuss the Unruh effect of the quantized gravitational waves for an observer in a uniformly accelerated motion in Minkowski spacetime in an explicit manner for the first time.

DOI： 10.1103/PhysRevD.103.083503

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We study odd parity perturbations of spherically symmetric black holes with
time-dependent scalar hair in shift-symmetric higher-order scalar-tensor
theories. The analysis is performed in a general way without assuming the
degeneracy conditions. Nevertheless, we end up with second-order equations for
a single master variable, similarly to cosmological tensor modes. We thus
identify the general form of the quadratic Lagrangian for the odd parity
perturbations, leading to a generalization of the Regge-Wheeler equation. We
also investigate the structure of the effective metric for the master variable
and refine the stability conditions. As an application of our generalized
Regge-Wheeler equation, we compute the quasi-normal modes of a certain
nontrivial black hole solution. Finally, our result is extended to include the
matter energy-momentum tensor as a source term.

DOI： 10.1103/PhysRevD.103.084041

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Other Link： http://arxiv.org/pdf/2101.03790v1

Publishing type：Research paper (scientific journal)   Publisher：American Physical Society (APS)  

DOI： 10.1103/physrevd.102.103505

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Other Link： http://harvest.aps.org/v2/journals/articles/10.1103/PhysRevD.102.103505/fulltext

We study nanohertz gravitational waves relevant to pulsar timing array
experiments from quantum fluctuations in the early universe with null energy
condition (NEC) violation. The NEC violation admits accelerated expansion with
the scale factor $a\propto (-t)^{-p}$ ($p>0$), which gives the tensor spectral
index $n_t=2/(p+1)>0$. To evade the constraint from Big Bang nucleosynthesis
(BBN), we connect the NEC-violating phase to a subsequent short slow-roll
inflationary phase which ends with standard reheating, and thereby reduce the
high frequency part of the spectrum. An explicit model is constructed within
the cubic Horndeski theory which allows for stable violation of the NEC. We
present numerical examples of the background evolution having the different
maximal Hubble parameters (which determine the peak amplitude of gravitational
waves), the different inflationary Hubble parameters (which determine the
amplitudes of high frequency gravitational waves), and different durations of
the inflationary phase (which essentially determine the peak frequency of the
spectrum). We display the spectra with $n_t=0.8$, $0.9$, and $0.95$ for
$f\lesssim 1/{\rm yr}$, which are consistent with the recent NANOGrav result.
We also check that they do not contradict the BBN constraint. We discuss how
the nearly scale-invariant spectrum of curvature perturbations is produced in
the NEC-violating phase.

DOI： 10.1103/PhysRevD.102.123533

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Other Link： http://arxiv.org/pdf/2011.01605v2

Publishing type：Research paper (scientific journal)   Publisher：American Physical Society (APS)  

It has been found that the primordial non-Gaussianity of the curvature
perturbation in the case of non-Bunch-Davies initial states can be enhanced
compared with those in the case of the Bunch-Davies one due to the interactions
among the perturbations on subhorizon scales. The purpose of the present paper
is to investigate whether tensor non-Gaussianities can also be enhanced or not
by the same mechanism. We consider general gravity theory in the presence of an
inflaton, and evaluate the tensor auto-bispectrum and the cross-bispectrum
involving one tensor and two scalar modes with the non-Bunch-Davies initial
states for tensor modes. The crucial difference from the case of the scalar
auto-bispectrum is that the tensor three-point function vanishes at the
flattened momentum triangles. We point out that the cross-bispectrum can
potentially be enhanced at non-trivial triangle shapes due to the
non-Bunch-Davies initial states.

DOI： 10.1103/physrevd.102.023513

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Other Link： http://harvest.aps.org/v2/journals/articles/10.1103/PhysRevD.102.023513/fulltext

Publishing type：Research paper (scientific journal)   Publisher：IOP Publishing  

Late-time cosmology in the extended cuscuton theory is studied, in which
gravity is modified while one still has no extra dynamical degrees of freedom
other than two tensor modes. We present a simple example admitting analytic
solutions for the cosmological background evolution that mimics $\Lambda$CDM
cosmology. We argue that the extended cuscuton as dark energy can be
constrained, like usual scalar-tensor theories, by the growth history of matter
density perturbations and the time variation of Newton's constant.

DOI： 10.1088/1475-7516/2020/07/004

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Other Link： https://iopscience.iop.org/article/10.1088/1475-7516/2020/07/004

We construct a model of higher dimensional cosmology in which extra
dimensions are frozen by virtue of the cubic-order Lovelock gravity throughout
the cosmic history from inflation to the present with radiation and
matter-dominated regimes in between.

DOI： 10.1016/j.physletb.2020.135857

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Other Link： http://arxiv.org/pdf/2005.14481v1

We reformulate the recently proposed regularized version of Lovelock gravity
in four dimensions as a scalar-tensor theory. By promoting the warp factor of
the internal space to a scalar degree of freedom by means of Kaluza-Klein
reduction, we show that regularized Lovelock gravity can be described
effectively by a certain subclass of the Horndeski theory. Cosmological aspects
of this particular scalar-tensor theory are studied. It is found that the
background with a scalar charge is generically allowed. The consequences of
this scalar charge are briefly discussed.

DOI： 10.1088/1475-7516/2020/07/013

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Other Link： http://arxiv.org/pdf/2003.12771v2

Publishing type：Research paper (scientific journal)   Publisher：American Physical Society (APS)  

DOI： 10.1103/physrevd.101.043529

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Other Link： http://harvest.aps.org/v2/journals/articles/10.1103/PhysRevD.101.043529/fulltext

We explore the possibility of a blue-tilted gravitational wave spectrum from
potential-driven slow-roll inflation in the Horndeski theory. In Kamada et al.
(2012), it was claimed that a blue gravitational wave spectrum cannot be
obtained from stable potential-driven slow-roll inflation within the Horndeski
framework. However, it has been demonstrated that the spectrum of primordial
gravitational waves can be blue in inflation with the Gauss-Bonnet term, where
the potential term is dominant and slow-roll conditions as well as the
stability conditions are satisfied. To fill in this gap, we clarify where the
discrepancy is coming from. We extend the formulation of Kamada et al. (2012)
and show that a blue gravitational wave spectrum can certainly be generated
from stable slow-roll inflation if some of the conditions previously imposed on
the form of the free functions in the Lagrangian are relaxed.

DOI： 10.1103/PhysRevD.101.043536

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Other Link： http://arxiv.org/pdf/1911.02143v2

We study relativistic stars in Hordenski theories that evade the
gravitational wave constraints and exhibit the Vainshtein mechanism, focusing
on a model based on the cubic Galileon Lagrangian. We derive the scalar field
profile for static spherically symmetric objects in asymptotically de Sitter
space-time with a linear time dependence. The exterior solution matches to the
black hole solution found in the literature. Due to the Vainshtein mechanism,
the stellar structure is indistinguishable from that of General Relativity with
the same central density as long as the radius of the star is shorter than the
Vainshtein radius. On the other hand, the scalar field is not suppressed beyond
the Vainshtein radius. These solutions have an additional integration constant
in addition to the mass of the star.

DOI： 10.1103/PhysRevD.101.024026

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Language：English   Publishing type：Research paper (scientific journal)  

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Language：English   Publishing type：Research paper (scientific journal)  

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Publishing type：Research paper (scientific journal)   Publisher：American Physical Society (APS)  

We consider a subclass of degenerate higher-order scalar-tensor (DHOST) theories in which gravitational waves propagate at the speed of light and do not decay into scalar fluctuations. The screening mechanism in DHOST theories evading these two gravitational wave constraints operates very differently from that in generic DHOST theories. We derive a spherically symmetric solution in the presence of nonrelativistic matter. General relativity is recovered in the vacuum exterior region provided that functions in the Lagrangian satisfy a certain condition, implying that fine-tuning is required. Gravity in the matter interior exhibits novel features: although the gravitational potentials still obey the standard inverse power law, the effective gravitational constant is different from its exterior value, and the two metric potentials do not coincide. We discuss possible observational constraints on this subclass of DHOST theories, and argue that the tightest bound comes from the Hulse-Taylor pulsar.

DOI： 10.1103/PhysRevD.99.104073

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Publishing type：Research paper (scientific journal)   Publisher：American Physical Society (APS)  

We investigate the potential of cosmological observations, such as galaxy surveys, for constraining degenerate higher-order scalar-tensor (DHOST) theories, focusing in particular on the linear growth of the matter density fluctuations. We develop a formalism to describe the evolution of the matter density fluctuations during the matter dominated era and in the early stage of the dark energy dominated era in DHOST theories, and give an approximate expression for the gravitational growth index in terms of several parameters characterizing the theory and the background solution under consideration. By employing the current observational constraints on the growth index, we obtain a new constraint on a parameter space of DHOST theories. Combining our result with other constraints obtained from the Newtonian stellar structure, we show that the degeneracy between the effective parameters of DHOST theories can be broken without using the Hulse-Taylor pulsar constraint.

DOI： 10.1103/PhysRevD.99.104051

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Publishing type：Research paper (scientific journal)  

This article is intended to review the recent developments in the Horndeski theory and its generalization, which provide us with a systematic understanding of scalar-tensor theories of gravity as well as a powerful tool to explore astrophysics and cosmology beyond general relativity. This review covers the generalized Galileons, (the rediscovery of) the Horndeski theory, cosmological perturbations in the Horndeski theory, cosmology with a violation of the null energy condition, degenerate higher-order scalar-tensor theories and their status after GW170817, the Vainshtein mechanism in the Horndeski theory and beyond, and hairy black hole solutions.

DOI： 10.1088/1361-6633/ab2429

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Publishing type：Research paper (scientific journal)   Publisher：IOP Publishing  

We show explicitly that the nonminimal coupling between the scalar field and the Ricci scalar in 2D dilaton gravity can be recast in the form of kinetic gravity braiding (KGB). This is as it should be, because KGB is the 2D version of the Horndeski theory. We also determine all the static solutions with a linearly time-dependent scalar configuration in the shift-symmetric KGB theories in 2D.

DOI： 10.1088/1361-6382/ab1355

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Publishing type：Research paper (scientific journal)  

Our Universe is nearly spatially flat, but this does not mean that it is exactly spatially flat. In this paper we derive general quadratic actions for cosmological perturbations in non-flat models from the Horndeski theory. This allows us to study how the spatial curvature influences the behavior of cosmological perturbations in the early universe described by some general scalar-tensor theory. We show that a tiny spatial curvature at the onset of inflation is unlikely to yield large (or ${\cal O}(1)$) effects on the primordial spectra even if one modifies gravity. We also argue that non-singular cosmological solutions in the Horndeski theory are unstable in spatially open cases as well as in flat cases.

DOI： 10.1103/PhysRevD.99.043522

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Publishing type：Research paper (scientific journal)   Publisher：IOP Publishing  

Among single-field scalar-tensor theories, there is a special class called "cuscuton," which is represented as some limiting case of k-essence in general relativity. This theory has a remarkable feature that the number of propagating degrees of freedom is only two in the unitary gauge in contrast to ordinary scalar-tensor theories with three degrees of freedom. We specify a general class of theories with the same property as the cuscuton in the context of the beyond Horndeski theory, which we dub as the extended cuscuton. We also study cosmological perturbations in the presence of matter in these extended cuscuton theories.

DOI： 10.1088/1475-7516/2018/12/002

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Publishing type：Research paper (scientific journal)  

We consider gravitational waves (GWs) in generic parity-violating gravity including recently proposed ghost-free theories with parity violation as well as Chern-Simons (CS) modified gravity, and study the implications of observational constraints from GW170817/GRB 170817A. Whereas GWs propagate at the speed of light, c, in CS gravity, we point out that this is specific to CS gravity and the GW propagation speed deviates from c, in general, in parity-violating gravity. Therefore, contrary to the previous literature in which only CS gravity is studied as a concrete example, we show that GW170817/GRB 170817A can, in fact, be used to limit gravitational parity violation. Our argument implies that the constraint on the propagation speed of GWs can pin down the parity-violating sector, if any, to CS gravity.

DOI： 10.1103/PhysRevD.98.124018

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Publishing type：Research paper (scientific journal)  

As opposed to Wald's cosmic no-hair theorem in general relativity, it is shown that the Horndeski theory (and its generalization) admits anisotropic inflationary attractors if the Lagrangian depends cubically on the second derivatives of the scalar field. We dub such a solution as a self-anisotropizing inflationary universe because anisotropic inflation can occur without introducing any anisotropic matter fields such as a vector field. As a concrete example of self-anisotropization we present the dynamics of a Bianchi type-I universe in the Horndeski theory.

DOI： 10.1088/1475-7516/2018/07/058

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：American Physical Society  

We study relativistic stars in degenerate higher-order scalar-tensor theories that evade the constraint on the speed of gravitational waves imposed by GW170817. It is shown that the exterior metric is given by the usual Schwarzschild solution if the lower order Horndeski terms are ignored in the Lagrangian and a shift symmetry is assumed. However, this class of theories exhibits partial breaking of Vainshtein screening in the stellar interior and thus modifies the structure of a star. Employing a simple concrete model, we show that for high-density stars the mass-radius relation is altered significantly even if the parameters are chosen so that only a tiny correction is expected in the Newtonian regime. We also find that, depending on the parameters, there is a maximum central density above which solutions cease to exist.

DOI： 10.1103/PhysRevD.97.104012

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Publishing type：Research paper (scientific journal)  

The Vainshtein mechanism is known as an efficient way of screening the fifth force around a matter source in modified gravity. This has been verified mainly in highly symmetric matter configurations. To study how the Vainshtein mechanism works in a less symmetric setup, we numerically solve the scalar field equation around a disk with a hole at its center in the cubic Galileon theory. We find, surprisingly, that the Galileon force is enhanced, rather than suppressed, in the vicinity of the hole. This anti-screening effect is larger for a thinner, less massive disk with a smaller hole. At this stage our setup is only of academic interest and its astrophysical consequences are unclear, but this result implies that the Vainshtein screening mechanism around less symmetric matter configurations is quite nontrivial.

DOI： 10.1142/S0217732319500135

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：American Physical Society  

The Horndeski scalar-tensor theory and its recent extensions allow nonlinear derivative interactions of the scalar degree of freedom. We study the matter bispectrum of large scale structure as a probe of these modified gravity theories, focusing in particular on the effect of the terms that newly appear in the so-called "beyond Horndeski" theories. We derive the second-order solution for the matter density perturbations and find that the interactions beyond Horndeski lead to a new time-dependent coefficient in the second-order kernel which differs in general from the standard value of general relativity and the Horndeski theory. This can deform the matter bispectrum at the folded triangle configurations ($k_1+k_2=k_3$), while it is never possible within the Horndeski theory.

DOI： 10.1103/PhysRevD.97.103517

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Language：English   Publisher：AMER PHYSICAL SOC  

DOI： 10.1103/PhysRevD.96.109903

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：IOP PUBLISHING LTD  

We propose a novel class of degenerate higher-order scalar-tensor theories as an extension of mimetic gravity. By performing a noninvertible conformal transformation on "seed" scalar-tensor theories which may be nondegenerate, we can generate a large class of theories with at most three physical degrees of freedom. We identify a general seed theory for which this is possible. Cosmological perturbations in these extended mimetic theories are also studied. It is shown that either of tensor or scalar perturbations is plagued with gradient instabilities, except for a special case where the scalar perturbations are presumably strongly coupled, or otherwise there appear ghost instabilities.

DOI： 10.1088/1475-7516/2017/11/038

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：IOP PUBLISHING LTD  

We study the stability of a recently proposed model of scalar-field matter called mimetic dark matter or imperfect dark matter. It has been known that mimetic matter with higher derivative terms suffers from gradient instabilities in scalar perturbations. To seek for an instability-free extension of imperfect dark matter, we develop an effective theory of cosmological perturbations subject to the constraint on the scalar field's kinetic term. This is done by using the unifying framework of general scalar-tensor theories based on the ADM formalism. We demonstrate that it is indeed possible to construct a model of imperfect dark matter which is free from ghost and gradient instabilities. As a side remark, we also show that mimetic $F({\cal R})$ theory is plagued with the Ostrogradsky instability.

DOI： 10.1088/1475-7516/2017/07/009

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

An invertible field transformation is such that the old field variables correspond one-to-one to the new variables. As such, one may think that two systems that are related by an invertible transformation are physically equivalent. However, if the transformation depends on field derivatives, the equivalence between the two systems is nontrivial due to the appearance of higher derivative terms in the equations of motion. To address this problem, we prove the following theorem on the relation between an invertible transformation and Euler-Lagrange equations: If the field transformation is invertible, then any solution of the original set of Euler-Lagrange equations is mapped to a solution of the new set of Euler-Lagrange equations, and vice versa. We also present applications of the theorem to scalar-tensor theories.

DOI： 10.1103/PhysRevD.95.084053

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

It has been pointed out that non-singular cosmological solutions in second-order scalar-tensor theories generically suffer from gradient instabilities. We extend this no-go result to second-order gravitational theories with an arbitrary number of interacting scalar fields. Our proof follows directly from the action of generalized multi-Galileons, and thus is different from and complementary to that based on the effective field theory approach. Several new terms for generalized multi-Galileons on a flat background were proposed recently. We find a covariant completion of them and confirm that they do not participate in the no-go argument.

DOI： 10.1103/PhysRevD.95.064011

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Publishing type：Research paper (international conference proceedings)  

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

We propose a novel branch of the Galilean Genesis scenario as an alternative to inflation, in which the universe starts expanding from Minkowski in the asymptotic past with a gross violation of the null energy condition (NEC). This variant, described by several functions and parameters within the Horndeski scalar-tensor theory, shares the same background dynamics with the existing Genesis models, but the nature of primordial quantum fluctuations is quite distinct. In some cases, tensor perturbations grow on superhorizon scales. The tensor power spectrum can be red, blue, or scale invariant, depending on the model, while scalar perturbations are nearly scale invariant. This is in sharp contrast to typical NEC-violating cosmologies, in which a blue tensor tilt is generated. Though the primordial tensor and scalar spectra are both nearly scale invariant as in the inflationary scenario, the consistency relation in our variant of Galilean Genesis is non-standard.

DOI： 10.1103/PhysRevD.95.064001

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

The null energy condition can be violated stably in generalized Galileon theories, which gives rise to the possibilities of healthy non-singular cosmologies. However, it has been reported that in many cases cosmological solutions are plagued with instabilities or have some pathologies somewhere in the whole history of the universe. Recently, this was shown to be generically true in a certain subclass of the Horndeski theory. In this short paper, we extend this no-go argument to the full Horndeski theory, and show that non-singular models (with flat spatial sections) in general suffer either from gradient instabilities or some kind of pathology in the tensor sector. This implies that one must go beyond the Horndeski theory to implement healthy non-singular cosmologies.

DOI： 10.1103/PhysRevD.94.043511

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

The conventional slow-roll approximation is broken in the so-called "ultra slow-roll" models of inflation, for which the inflaton potential is exactly (or extremely) flat. The interesting nature of (canonical) ultra slow-roll inflation is that the curvature perturbation grows on superhorizon scales, but has a scale-invariant power spectrum. We study the ultra slow-roll inflationary dynamics in the presence of non-canonical kinetic terms of the scalar field, namely ultra slow-roll G-inflation. We compute the evolution of the curvature perturbation and show that the primordial power spectrum follows a broken power law with an oscillation feature. It is demonstrated that this could explain the lack of large-scale power in the cosmic microwave background temperature anisotropies. We also point out that the violation of the null energy condition is prohibited in ultra slow-roll G-inflation and hence a blue tensor tilt is impossible as long as inflation is driven by the potential. This statement is, however, not true if the energy density is dominated by the kinetic energy of the scalar field.

DOI： 10.1103/PhysRevD.94.103515

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：IOP PUBLISHING LTD  

Galilean genesis is an alternative to inflation, in which the universe starts expanding from Minkowski with the stable violation of the null energy condition. In this paper, we discuss how the early universe is reheated through the gravitational particle production at the trasition from the genesis phase to the subsequent phase where the kinetic energy of the scalar field is dominant. We then study the consequences of gravitational reheating after Galilean genesis on the spectrum of primordial gravitational waves. The resultant spectrum is strongly blue, and at high frequencies $\Omega_{\rm gw}\propto f^3$ in terms of the energy density per unit logarithmic frequency. Though this cannot be detected in existing detctors, the amplitude can be as large as $\Omega_{\rm gw}\sim 10^{-12}$ at $f\sim 100\,$MHz, providing a future test of the genesis scenario. The analysis is performed within the framework of generalized Galilean genesis based on the Horndeski theory, which enables us to derive generic formulas.

DOI： 10.1088/1475-7516/2016/04/018

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Language：Japanese   Publisher：The Physical Society of Japan (JPS)  

DOI： 10.11316/jpsgaiyo.71.1.0_470

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

We clarify the features of primordial non-Gaussianities of tensor perturbations in Gao's unifying framework of scalar-tensor theories. The general Lagrangian is given in terms of the ADM variables so that the framework maintains spatial covariance and includes the Horndeski theory and Gleyzes-Langlois-Piazza-Vernizzi (GLPV) generalization as specific cases. It is shown that the GLPV generalization does not give rise to any new terms in the cubic action compared to the case of the Horndeski theory, but four new terms appear in more general theories beyond GLPV. We compute the tensor 3-point correlation functions analytically by treating the modification to the dispersion relation as a perturbation. The relative change in the 3-point functions due to the modified dispersion relation is only mildly configuration-dependent. When the effect of the modified dispersion relation is small, there is only a single cubic term generating squeezed non-Gaussianity, which is the only term present in general relativity. The corresponding non-Gaussian amplitude has a fixed and universal feature, and hence offers a "consistency relation" for primordial tensor modes in a quite wide class of single-field inflation models. All the other cubic interactions are found to give peaks at equilateral shapes.

DOI： 10.1103/PhysRevD.93.043519

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

We analyze spherically symmetric black hole solutions with time-dependent scalar hair in a class of Lovelock-Galileon theories, which are the scalar-tensor theories with second-order field equations in arbitrary dimensions. We first show that known black hole solutions in five dimensions are always plagued by the ghost/gradient instability in the vicinity of the horizon. We then generalize such black hole solutions to higher dimensions and show that the same instability found in five dimensions appears universally in any number of dimensions.

DOI： 10.1103/PhysRevD.93.064068

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：American Physical Society  

We address the question of how one can modify the inflationary tensor spectrum without changing at all the successful predictions on the curvature perturbation. We show that this is indeed possible, and determine the two quadratic curvature corrections that are free from instabilities and affect only the tensor sector at the level of linear cosmological perturbations. Both of the two corrections can reduce the tensor amplitude, though one of them generates large non-Gaussianity of the curvature perturbation. It turns out that the other one corresponds to so-called Lorentz-violating Weyl gravity. In this latter case one can obtain as small as 65% of the standard tensor amplitude. Utilizing this effect we demonstrate that even power-law inflation can be within the 2σ contour of the Planck results.

DOI： 10.1103/PhysRevD.92.103503

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

Recently it was pointed out that in shift-symmetric scalar-tensor theories a black hole can have nontrivial scalar hair which depends linearly on time. We develop black hole perturbation theory for such solutions and compute the quadratic action of odd-parity perturbations. We show that around all the solutions known so far with such time-dependent scalar hair the perturbations trigger instabilities or are presumably strongly coupled.

DOI： 10.1103/PhysRevD.93.064078

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Publishing type：Research paper (scientific journal)  

We investigate perturbations of a class of spherically symmetric solutions in massive gravity and bi-gravity. The background equations of motion for the particular class of solutions we are interested in reduce to a set of the Einstein equations with a cosmological constant. Thus, the solutions in this class include all the spherically symmetric solutions in general relativity, such as the Friedmann-Lema\^{i}tre-Robertson-Walker solution and the Schwarzschild (-de Sitter) solution, though the one-parameter family of two parameters of the theory admits such a class of solutions. We find that the equations of motion for the perturbations of this class of solutions also reduce to the perturbed Einstein equations at first and second order. Therefore, the stability of the solutions coincides with that of the corresponding solutions in general relativity. In particular, these solutions do not suffer from non-linear instabilities which often appear in the other cosmological solutions in massive gravity and bi-gravity.

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

We address the question of how one can modify the inflationary tensor spectrum without changing at all the successful predictions on the curvature perturbation. We show that this is indeed possible, and determine the two quadratic curvature corrections that are free from instabilities and affect only the tensor sector at the level of linear cosmological perturbations. Both of the two corrections can reduce the tensor amplitude, though one of them generates large non-Gaussianity of the curvature perturbation. It turns out that the other one corresponds to so-called Lorentz-violating Weyl gravity. In this latter case one can obtain as small as 65% of the standard tensor amplitude. Utilizing this effect we demonstrate that even power-law inflation can be within the 2$\sigma$ contour of the Planck results.

DOI： 10.1103/PhysRevD.92.103503

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：WORLD SCIENTIFIC PUBL CO PTE LTD  

Recently it was argued that gravity with the squire of the Ricci tensor can be stabilized by adding constraints to the theory. This was so far demonstrated for fluctuations on the Minkowski/de Sitter background. We show that the same scheme works equally well for removing Ostrogradski's ghost from fluctuations on a cosmological background in generic $f(R,R_{\mu\nu}^2,C_{\mu\nu\rho\sigma}^2)$-type theories of gravity. We also derive the general formula for the spectrum of primordial tensor perturbations from the stabilized theory.

DOI： 10.1142/S021773231650067X

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Publishing type：Research paper (scientific journal)  

The Horndeski theory is known as the most general scalar-tensor theory with second-order field equations. In this paper, we explore the bi-scalar extension of the Horndeski theory. Following Horndeski's approach, we determine all the possible terms appearing in the second-order field equations of the bi-scalar-tensor theory. We compare the field equations with those of the generalized multi-Galileons, and confirm that our theory contains new terms that are not included in the latter theory. We also discuss the construction of the Lagrangian leading to our most general field equations.

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：IOP PUBLISHING LTD  

It has been pointed out that the null energy condition can be violated stably in some non-canonical scalar-field theories. This allows us to consider the Galilean Genesis scenario in which the universe starts expanding from Minkowski spacetime and hence is free from the initial singularity. We use this scenario to study the early-time completion of inflation, pushing forward the recent idea of Pirtskhalava et al. We present a generic form of the Lagrangian governing the background and perturbation dynamics in the Genesis phase, the subsequent inflationary phase, and the graceful exit from inflation, as opposed to employing the effective field theory approach. Our Lagrangian belongs to a more general class of scalar-tensor theories than the Horndeski theory and Gleyzes-Langlois-Piazza-Vernizzi generalization, but still has the same number of the propagating degrees of freedom, and thus can avoid Ostrogradski instabilities. We investigate the generation and evolution of primordial perturbations in this scenario and show that one can indeed construct a stable model of inflation preceded by (generalized) Galilean Genesis.

DOI： 10.1088/1475-7516/2015/07/017

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：IOP PUBLISHING LTD  

The galilean genesis scenario is an alternative to inflation in which the universe starts expanding from Minkowski in the asymptotic past by violating the null energy condition stably. Several concrete models of galilean genesis have been constructed so far within the context of galileon-type scalar-field theories. We give a generic, unified description of the galilean genesis scenario in terms of the Horndeski theory, i.e., the most general scalar-tensor theory with second-order field equations. In doing so we generalize the previous models to have a new parameter (denoted by {\alpha}) which results in controlling the evolution of the Hubble rate. The background dynamics is investigated to show that the generalized galilean genesis solution is an attractor, similarly to the original model. We also study the nature of primordial perturbations in the generalized galilean genesis scenario. In all the models described by our generalized genesis Lagrangian, amplification of tensor perturbations does not occur as opposed to what happens in quasi-de Sitter inflation. We show that the spectral index of curvature perturbations is determined solely from the parameter {\alpha} and does not depend on the other details of the model. In contrast to the original model, a nearly scale-invariant spectrum of curvature perturbations is obtained for a specific choice of {\alpha}.

DOI： 10.1088/1475-7516/2015/03/057

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Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：Kyoto University, Yukawa Institute for Theoretical Physics  

We consider USR k- and G-inflation driven by potential. In certain Lagrangian cases, we can construct the models which explain large scale suppression of Cl .

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Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：World Scientific  

We study linear perturbations around static, spherically-symmetric spacetimes in f(R, C) theory, the nondynamical and dynamical Chern-Simons theory, and the most general scalar-tensor theory with second-order field equations. By explicitly constructing the second order action, we have derived the no-ghost condition and the no-tachyon condition, and the propagation speed for each mode.

DOI： 10.1142/9789814623995_0152

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：American Physical Society  

The Stückelberg analysis of nonlinear massive gravity in the presence of a general fiducial metric is investigated. We develop a "covariant" formalism for the Stückelberg expansion by working with a local inertial frame, through which helicity modes can be characterized correctly. Within this covariant approach, an extended Λ3 decoupling limit analysis can be consistently performed, which keeps R¯μνρσ/m2 fixed with R¯μνρσ the Riemann tensor of the fiducial metric. In this extended decoupling limit, the scalar mode π acquires self-interactions due to the presence of the curvature of the fiducial metric. However, the equation of motion for π remains of second order in derivatives, which extends the understanding of the absence of the Boulware Deser ghost in the case of a flat fiducial metric.

DOI： 10.1103/PhysRevD.90.124073

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

The Horndeski theory of gravity is known as the most general scalar-tensor theory with second-order field equations. Recently, it was demonstrated by Gleyzes et al. that the Horndeski theory can further be generalized in such a way that although field equations are of third order, the number of propagating degrees of freedom remains the same. We study small-scale gravity in the generalized Horndeski theory, focusing in particular on an impact of the new derivative interaction beyond Horndeski on the Vainshtein screening mechanism. In the absence of the quintic galileon term and its generalization, we show that the new interaction does not change the qualitative behavior of gravity outside and near the source: the two metric potentials coincide, $\Phi = \Psi \;(\sim r^{-1})$, while the gravitational coupling is given by the cosmological one and hence is time-dependent in general. We find, however, that the gravitational field inside the source shows a novel behavior due to the interaction beyond Horndeski: the gravitational attraction is not determined solely from the enclosed mass and two potentials do not coincide, indicating breaking of the screening mechanism.

DOI： 10.1103/PhysRevD.91.064013

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

The St\"uckelberg analysis of nonlinear massive gravity in the presence of a general fiducial metric is investigated. We develop a "covariant" formalism for the St\"uckelberg expansion by working with a local inertial frame, through which helicity modes can be characterized correctly. Within this covariant approach, an extended $\Lambda_3$ decoupling limit analysis can be consistently performed, which keeps $\bar{R}_{\mu\nu\rho\sigma}/m^2$ fixed with $\bar{R}_{\mu\nu\rho\sigma}$ the Riemann tensor of the fiducial metric. In this extended decoupling limit, the scalar mode $\pi$ acquires self-interactions due to the presence of the curvature of the fiducial metric. However, the equation of motion for $\pi$ remains of second order in derivatives, which extends the understanding of the absence of the Boulware Deser ghost in the case of a flat fiducial metric.

DOI： 10.1103/PhysRevD.90.124073

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：American Physical Society  

We perform a fully relativistic analysis of even-parity linear perturbations around a static and spherically symmetric solution in the most general scalar-tensor theory with second-order field equations. This paper is a sequel to Kobayashi et al. [Phys. Rev. D 85, 084025 (2012)], in which the linear perturbation analysis for the odd-parity modes is presented. Expanding the Horndeski action to second order in perturbations and eliminating auxiliary variables, we derive the quadratic action for even-parity perturbations written solely in terms of two dynamical variables. The two perturbations can be interpreted as the gravitational and scalar waves. Correspondingly, we obtain two conditions to evade ghosts and two conditions for the absence of gradient instabilities. Only one in each pair of conditions yields a new stability criterion, as the conditions derived from the stability of the gravitational-wave degree of freedom coincide with those in the odd-parity sector. Similarly, the propagation speed of one of the two modes is the same as that for the odd-parity mode, while the other differs in general from them. Our result is applicable to all the theories of gravitation with an extra single scalar degree of freedom such as the Brans-Dicke theory, f(R) models, and Galileon gravity. © 2014 American Physical Society.

DOI： 10.1103/PhysRevD.89.165424

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：American Physical Society  

We perform a fully relativistic analysis of even-parity linear perturbations around a static and spherically symmetric solution in the most general scalar-tensor theory with second-order field equations. This paper is a sequel to Kobayashi et al. [Phys. Rev. D 85, 084025 (2012)], in which the linear perturbation analysis for the odd-parity modes is presented. Expanding the Horndeski action to second order in perturbations and eliminating auxiliary variables, we derive the quadratic action for even-parity perturbations written solely in terms of two dynamical variables. The two perturbations can be interpreted as the gravitational and scalar waves. Correspondingly, we obtain two conditions to evade ghosts and two conditions for the absence of gradient instabilities. Only one in each pair of conditions yields a new stability criterion, as the conditions derived from the stability of the gravitational-wave degree of freedom coincide with those in the odd-parity sector. Similarly, the propagation speed of one of the two modes is the same as that for the odd-parity mode, while the other differs in general from them. Our result is applicable to all the theories of gravitation with an extra single scalar degree of freedom such as the Brans-Dicke theory, f(R) models, and Galileon gravity. © 2014 American Physical Society.

DOI： 10.1103/PhysRevB.89.165427

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：American Physical Society  

We perform a fully relativistic analysis of even-parity linear perturbations around a static and spherically symmetric solution in the most general scalar-tensor theory with second-order field equations. This paper is a sequel to Kobayashi et al. [Phys. Rev. D 85, 084025 (2012)], in which the linear perturbation analysis for the odd-parity modes is presented. Expanding the Horndeski action to second order in perturbations and eliminating auxiliary variables, we derive the quadratic action for even-parity perturbations written solely in terms of two dynamical variables. The two perturbations can be interpreted as the gravitational and scalar waves. Correspondingly, we obtain two conditions to evade ghosts and two conditions for the absence of gradient instabilities. Only one in each pair of conditions yields a new stability criterion, as the conditions derived from the stability of the gravitational-wave degree of freedom coincide with those in the odd-parity sector. Similarly, the propagation speed of one of the two modes is the same as that for the odd-parity mode, while the other differs in general from them. Our result is applicable to all the theories of gravitation with an extra single scalar degree of freedom such as the Brans-Dicke theory, f(R) models, and Galileon gravity. © 2014 American Physical Society.

DOI： 10.1103/PhysRevD.89.084042

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：OXFORD UNIV PRESS INC  

We derive a variety of exact black hole solutions in a subclass of Horndeski's scalar-tensor theory possessing shift symmetry, $\phi\to\phi+c$, and reflection symmetry, $\phi\to-\phi$. The theory admits two arbitrary functions of $X:=-(\partial\phi)^2/2$, and our solutions are constructed without specifying the concrete form of the two functions, implying that black hole solutions in specific scalar-tensor theories found in the literature can be extended to a more general class of theories with shift symmetry. Our solutions include a black hole in the presence of an effective cosmological constant, the Nariai spacetime, the Lifshitz black hole, and other nontrivial solutions, all of which exhibit nonconstant scalar-field profile.

DOI： 10.1093/ptep/ptu096

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

We perform a fully relativistic analysis of even-parity linear perturbations around a static and spherically symmetric solution in the most general scalar-tensor theory with second-order field equations. This paper is a sequel to Kobayashi {\em et al.} (2012), in which the linear perturbation analysis for the odd-parity modes is presented. Expanding the Horndeski action to second order in perturbations and eliminating auxiliary variables, we derive the quadratic action for even-parity perturbations written solely in terms of two dynamical variables. The two perturbations can be interpreted as the gravitational and scalar waves. Correspondingly, we obtain two conditions to evade ghosts and two conditions for the absence of gradient instabilities. Only one in each pair of conditions yields a new stability criterion, as the conditions derived from the stability of the gravitational-wave degree of freedom coincide with those in the odd-parity sector. Similarly, the propagation speed of one of the two modes is the same as that for the odd-parity mode, while the other differs in general from them. Our result is applicable to all the theories of gravitation with an extra single scalar degree of freedom such as the Brans-Dicke theory, $f(R)$ models, and Galileon gravity.

DOI： 10.1103/PhysRevD.89.084042

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：IOP PUBLISHING LTD  

We derive the cosmological matching conditions for the homogeneous and isotropic background and for linear perturbations in Horndeski's most general second-order scalar-tensor theory. In general relativity, the matching is done in such a way that the extrinsic curvature is continuous across the transition hypersurface. This procedure is generalized so as to incorporate the mixing of scalar and gravity kinetic terms in the field equations of Horndeski's theory. Our matching conditions have a wide range of applications including the galilean genesis and the bounce scenarios, in which stable, null energy condition violating solutions play a central role. We demonstrate how our matching conditions are used in the galilean genesis scenario. In doing so, we extend the previous genesis models and provide a unified description of the theory admitting the solution that starts expanding from the Minkowski spacetime.

DOI： 10.1088/1475-7516/2014/03/008

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Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：University of Tokyo, Kavli Institute for Physics and Mathematics of the Universe, KIPMU  

BH perturbation in the Horndeski framework was formulated (Both for odd parity and even parity perturbations). Healthy conditions such as no-ghost condition are obtained. Master equations are derived. This formulation can be applied to a wide range of modified gravity theories such as f(R), Galileon gravity, kinetic braiding gravity, etc. Dynamical degrees of freedom: 1 for odd parity and 2 for even parity. Gravitational odd and even parity perturbations propagate at the same speed. But the scalar wave propagates at different speed in general. They are independent of the multipole L.

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Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：ELSEVIER SCIENCE BV  

In this talk, we have presented new and simple cosmological solutions with flat, open, and closed spatial geometries, recently found by the present authors. The metric and the Stuckelberg fields are given explicitly, showing nontrivial configurations of the Stuckelberg in the usual Friedmann-Lemaitre-Robertson-Walker coordinates. The solutions exhibit self-acceleration, while being free from ghost instabilities. Our solutions can be extended to include inhomogeneous dust collapse represented by the Lemaitre-Tolman-Bondi metric as well. Thus, our results can be used not only to describe homogeneous and isotropic cosmology but also to study gravitational collapse in massive gravity.

DOI： 10.1016/j.nuclphysbps.2013.10.068

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：American Physical Society  

Higgs G inflation is a Higgs inflation model with a generalized Galileon term added to the standard model Higgs field, which realizes inflation compatible with observations. Recently, it was claimed that the generalized Galileon term induces instabilities during the oscillation phase and that the simplest Higgs G-inflation model inevitably suffers from this problem. In this paper, we extend the original Higgs G-inflation Lagrangian to a more general form, namely introducing a higher-order kinetic term and generalizing the form of the Galileon term, so that the Higgs field can oscillate after inflation without encountering instabilities. Moreover, it accommodates a large region of the ns-r plane, most of which is consistent with current observations, leading us to expect the detection of B-mode polarization in the cosmic microwave background in the near future. © 2013 American Physical Society.

DOI： 10.1103/PhysRevD.88.123518

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Language：English   Publishing type：Research paper (scientific journal)  

We propose a multifield extension of (generalized) G inflation, based on covariant multi-Galileons and their generalization preserving second-order field equations. We compute the quadratic action for cosmological perturbations. By comparing the formulas for cosmological perturbations, it is highlighted that multifield Dirac-Born-Infield Galileon inflation is not included in the multifield version of generalized G inflation. Our result indicates that the generalized covariant multi-Galileon theory is not the most general multi-scalar-tensor theory with second-order field equations. © 2013 American Physical Society.

DOI： 10.1103/PhysRevD.88.083504

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

Higgs G-inflation is a Higgs inflation model with a generalized Galileon term added to the standard model Higgs field, which realizes inflation compatible with observations. Recently, it was claimed that the generalized Galileon term induces instabilities during the oscillation phase, and that the simplest Higgs G-inflation model inevitably suffers from this problem. In this paper, we extend the original Higgs G-inflation Lagrangian to a more general form, namely introducing a higher-order kinetic term and generalizing the form of the Galileon term, so that the Higgs field can oscillate after inflation without encountering instabilities. Moreover, it accommodates a large region of the n_s - r plane, most of which is consistent with current observations, leading us to expect the detection of B-mode polarization in the cosmic microwave background in the near future.

DOI： 10.1103/PhysRevD.88.123518

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

We propose a multi-field extension of (generalized) G-inflation, based on covariant multi-galileons and their generalization preserving second-order field equations. We compute the quadratic action for cosmological perturbations. By comparing the formulas for cosmological perturbations, it is highlighted that multi-field DBI galileon inflation is not included in the multi-field version of generalized G-inflation. Our result indicates that the generalized covariant multi-galileon theory is not the most general multi-scalar-tensor theory with second-order field equations.

DOI： 10.1103/PhysRevD.88.083504

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

We explore the possibility of testing modified gravity exhibiting the Vainshtein mechanism against observations of cluster lensing. We work in the most general scalar-tensor theory with second-order field equations (Horndeski's theory), and derive static and spherically symmetric solutions, for which the scalar field is screened below a certain radius. It is found that the essential structure of the problem in the most general case can be captured by the program of classifying Vainshtein solutions out of different solutions to a quintic equation, as has been performed in the context of massive gravity. The key effect on gravitational lensing is that the second derivative of the scalar field can substantially be large at the transition from screened to unscreened regions, leaving a dip in the convergence. This allows us to put observational constraints on parameters characterizing the general scalar-tensor modification of gravity. We demonstrate how this occurs in massive gravity as an example, and discuss its observational signatures in cluster lensing.

DOI： 10.1103/PhysRevD.87.124006

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：OXFORD UNIV PRESS INC  

We develop a theory of nonlinear cosmological perturbations on superhorizon scales for generic single-field inflation. Our inflaton is described by the Lagrangian of the form $W(X,\phi)-G(X,\phi)\Box\phi$ with $X=-\partial^{\mu}\phi\partial_{\mu}\phi/2$, which is no longer equivalent to a perfect fluid. This model is more general than k-inflation, and is called G-inflation. A general nonlinear solution for the metric and the scalar field is obtained at second order in gradient expansion. We derive a simple master equation governing the large-scale evolution of the nonlinear curvature perturbation. It turns out that the nonlinear evolution equation is deduced as a straightforward extension of the corresponding linear equation for the curvature perturbation on uniform $\phi$ hypersurfaces.

DOI： 10.1093/ptep/ptt033

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Publishing type：Research paper (international conference proceedings)  

• Instabilities in Higgs G-inflation avoided by adding a higher order kinetic term • New class of Higgs inflation models, consistent throughout inflation and reheating • (Typically) a large tensor-to-scalar ratio →Would be detected by Planck.

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Publishing type：Research paper (scientific journal)  

We compute the full bispectra, namely both auto- and cross- bispectra, of primordial curvature and tensor perturbations in the most general single-field inflation model whose scalar and gravitational equations of motion are of second order. The formulae in the limits of k-inflation and potential-driven inflation are also given. These expressions are useful for estimating the full bispectra of temperature and polarization anisotropies of the cosmic microwave background radiation.

DOI： 10.1093/PTEP/PTT031

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

We find new, simple cosmological solutions with flat, open, and closed spatial geometries, contrary to the previous wisdom that only the open model is allowed. The metric and the St\"{u}ckelberg fields are given explicitly, showing nontrivial configurations of the St\"{u}ckelberg in the usual Friedmann-Lema\^{i}tre-Robertson-Walker coordinates. The solutions exhibit self-acceleration, while being free from ghost instabilities. Our solutions can accommodate inhomogeneous dust collapse represented by the Lema\^{i}tre-Tolman-Bondi metric as well. Thus, our results can be used not only to describe homogeneous and isotropic cosmology but also to study gravitational collapse in massive gravity.

DOI： 10.1103/PhysRevD.86.061505

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

We study Higgs inflation in the context of generalized G-inflation, i.e. the most general single-field inflation model with second-order field equations. The four variants of Higgs inflation proposed so far in the literature can be accommodated at one time in our framework. We also propose yet another class of Higgs inflation, the running Einstein inflation model, that can naturally arise from the generalized G-inflation framework. As a result, five Higgs inflation models in all should be discussed on an equal footing. Concise formulas for primordial fluctuations in these generalized Higgs inflation models are provided, which will be helpful to determine which model is favored from the future experiments and observations such as the Large Hadron Collider and the Planck satellite.

DOI： 10.1103/PhysRevD.86.023504

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

We perform a fully relativistic analysis of odd-type linear perturbations around a static and spherically symmetric solution in the most general scalar-tensor theory with second-order field equations in four-dimensional spacetime. It is shown that, as in the case of general relativity, the quadratic action for the perturbations reduces to the one having only a single dynamical variable, from which concise formulas for no-ghost and no-gradient instability conditions are derived. Our result is applicable to all the theories of gravity with an extra scalar degree of freedom. We demonstrate how the generic formulas can be applied to some particular examples such as the Brans-Dicke theory, $f(R)$ models, and Galileon gravity.

DOI： 10.1103/PhysRevD.85.084025

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

A generic second-order scalar-tensor theory contains a nonlinear derivative self-interaction of the scalar degree of freedom $\phi$ \`{a} la Galileon models, which allows for the Vainshtein screening mechanism. We investigate this effect on subhorizon scales in a cosmological background, based on the most general second-order scalar-tensor theory. Our analysis takes into account all the relevant nonlinear terms and the effect of metric perturbations consistently. We derive an explicit form of Newton's constant, which in general is time-dependent and hence is constrained from observations, as suggested earlier. It is argued that in the most general case the inverse-square law cannot be reproduced on the smallest scales. Some applications of our results are also presented.

DOI： 10.1103/PhysRevD.85.024023

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

The cross-correlation between the integrated Sachs-Wolfe (ISW) effect and the large scale structure (LSS) is a powerful tool to constrain dark energy and alternative theories of gravity. In this paper, we obtain observational constraints on kinetic gravity braiding from the ISW-LSS cross-correlation. We find that the late-time ISW effect in the kinetic gravity braiding model anti-correlates with large scale structures in a wide range of parameters, which clearly demonstrates how one can distinguish modified gravity theories from the LCDM model using the ISW effect. In addition to the analysis based on a concrete model, we investigate a future prospect of the ISW-LSS cross-correlation by using a phenomenological parameterization of modified gravity models.

DOI： 10.1103/PhysRevD.85.123503

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：ELSEVIER SCIENCE BV  

In the Horndeski's most general scalar-tensor theories the equations of scalar density perturbations are derived in the presence of non-relativistic matter minimally coupled to gravity. Under a quasi-static approximation on sub-horizon scales we obtain the effective gravitational coupling $G_{eff}$ associated with the growth rate of matter perturbations as well as the effective gravitational potential $\Phi_{eff}$ relevant to the deviation of light rays. We then apply our formulas to a number of modified gravitational models of dark energy--such as those based on f(R) theories, Brans-Dicke theories, kinetic gravity braidings, covariant Galileons, and field derivative couplings with the Einstein tensor. Our results are useful to test the large-distance modification of gravity from the future high-precision observations of large-scale structure, weak lensing, and cosmic microwave background.

DOI： 10.1016/j.physletb.2011.11.028

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

We completely clarify the feature of primordial non-Gaussianities of tensor perturbations in generalized G-inflation, i.e., the most general single-field inflation model with second order field equations. It is shown that the most general cubic action for the tensor perturbation (gravitational wave) $h_{ij}$ is composed only of two contributions, one with two spacial derivatives and the other with one time derivative on each $h_{ij}$. The former is essentially identical to the cubic term that appears in Einstein gravity and predicts a squeezed shape, while the latter newly appears in the presence of the kinetic coupling to the Einstein tensor and predicts an equilateral shape. Thus, only two shapes appear in the graviton bispectrum of the most general single-field inflation model, which could open a new clue to the identification of inflationary gravitational waves in observations of cosmic microwave background anisotropies as well as direct gravitational wave detection experiments.

DOI： 10.1103/PhysRevLett.107.211301

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：WORLD SCIENTIFIC PUBL CO PTE LTD  

We study generalized Galileons as a framework to develop the most general single-field inflation models ever, Generalized G-inflation, containing yet further generalization of G-inflation, as well as previous examples such as k-inflation, extended inflation, and new Higgs inflation as special cases. We investigate the background and perturbation evolution in this model, calculating the most general quadratic actions for tensor and scalar cosmological perturbations to give the stability criteria and the power spectra of primordial fluctuations. It is pointed out in the Appendix that the Horndeski theory and the generalized Galileons are equivalent. In particular, even the non-minimal coupling to the Gauss-Bonnet term is included in the generalized Galileons in a non-trivial manner.

DOI： 10.1143/PTP.126.511

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Language：English   Publishing type：Research paper (scientific journal)  

We present a comprehensive study of primordial fluctuations generated from G inflation, in which the inflaton Lagrangian is of the form K(•,X)-G(•,X) • with X=-(-•)2/2. The Lagrangian still gives rise to second-order gravitational and scalar field equations, and thus offers a more generic class of single-field inflation than ever studied, with a richer phenomenology. We compute the power spectrum and the bispectrum, and clarify how the non-Gaussian amplitude depends upon parameters such as the sound speed. In so doing we try to keep as great generality as possible, allowing for non slow-roll and deviation from the exact scale invariance. © 2011 American Physical Society.

DOI： 10.1103/PhysRevD.83.103524

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

We study a vacuum Bianchi IX universe in the context of Ho\v{r}ava-Lifshitz (HL) gravity. In particular, we focus on the classical dynamics of the universe and analyze how anisotropy changes the history of the universe. For small anisotropy, we find an oscillating universe as well as a bounce universe just as the case of the Friedmann-Lemaitre-Robertson-Walker (FLRW) spacetime. However, if the initial anisotropy is large, we find the universe which ends up with a big crunch after oscillations if a cosmological constant $\Lambda$ is zero or negative. For $\Lambda>0$, we find a variety of histories of the universe, that is de Sitter expanding universe after oscillations in addition to the oscillating solution and the previous big crunch solution. This fate of the universe shows sensitive dependence of initial conditions, which is one of the typical properties of a chaotic system. If the initial anisotropy is near the upper bound, we find the universe starting from a big bang and ending up with a big crunch for $\Lambda\leq 0$, while de Sitter expanding universe starting from a big bang for $\Lambda>0$.

DOI： 10.1103/PhysRevD.84.064030

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Language：English   Publishing type：Research paper (scientific journal)  

A new class of inflation models within the context of G inflation is proposed, in which the standard model Higgs boson can act as an inflaton thanks to Galileon-like nonlinear derivative interaction. The generated primordial density perturbation is shown to be consistent with the present observational data. We also make a general discussion on potential-driven G-inflation models, and find a new consistency relation between the tensor-to-scalar ratio r and the tensor spectral index nT, r = -326nT/9, which is crucial in discriminating the present models from standard inflation with a canonical kinetic term. © 2011 American Physical Society.

DOI： 10.1103/PhysRevD.83.083515

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

We study how the dynamical vector degree of freedom in modified gravity affects the CMB B-mode polarization in terms of the Einstein-aether theory. In this theory, vector perturbations can be generated from inflation, which can grow on superhorizon scales in the subsequent epochs and thereby leaves imprints on the CMB B-mode polarization. We derive the linear perturbation equations in a covariant formalism, and compute the CMB B-mode polarization using the CAMB code modified so as to incorporate the effect of the aether vector field. We find that the amplitude of the B-mode signal from the aether field can surpass the contribution from the inflationary gravitational waves for a viable range of model parameters. We also give an analytic argument explaining the shape of the spectrum based on the tight coupling approximation.

DOI： 10.1103/PhysRevD.84.084051

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

We present a comprehensive study of primordial fluctuations generated from G-inflation, in which the inflaton Lagrangian is of the form $K(\phi, X)-G(\phi, X)\Box\phi$ with $X=-(\partial\phi)^2/2$. The Lagrangian still gives rise to second-order gravitational and scalar field equations, and thus offers a more generic class of single-field inflation than ever studied, with a richer phenomenology. We compute the power spectrum and the bispectrum, and clarify how the non-Gaussian amplitude depends upon parameters such as the sound speed. In so doing we try to keep as great generality as possible, allowing for non slow-roll and deviation from the exact scale-invariance.

DOI： 10.1103/PhysRevD.83.103524

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Publishing type：Research paper (scientific journal)  

We study the impact of modifying the vector sector of gravity on the CMB polarization. We employ the Einstein-aether theory as a concrete example. The Einstein-aether theory admits dynamical vector perturbations generated during inflation, leaving imprints on the CMB polarization. We derive the perturbation equations of the aether vector field in covariant formalism and compute the CMB B-mode polarization using the modified CAMB code. It is found that the amplitude of the B-mode signal from the aether field can surpass the one from the inflationary gravitational waves. The shape of the spectrum is clearly understood in an analytic way using the tight coupling approximation.

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

A new class of inflation models within the context of G-inflation is proposed, in which the standard model Higgs boson can act as an inflaton thanks to Galileon-like non-linear derivative interaction. The generated primordial density perturbation is shown to be consistent with the present observational data. We also make a general discussion on potential-driven G-inflation models, and find a new consistency relation between the tensor-to-scalar ratio $r$ and the tensor spectral index $n_T$, $r = -32 \sqrt{6}n_T / 9$, which is crucial in discriminating the present models from standard inflation with a canonical kinetic term.

DOI： 10.1103/PhysRevD.83.083515

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

We propose a new class of inflation model, G-inflation, which has a Galileon-like nonlinear derivative interaction of the form $G(\phi, (\nabla\phi)^2)\Box\phi$ in the Lagrangian with the resultant equations of motion being of second order. It is shown that (almost) scale-invariant curvature fluctuations can be generated even in the exactly de Sitter background and that the tensor-to-scalar ratio can take a significantly larger value than in the standard inflation models, violating the standard consistency relation. Furthermore, violation of the null energy condition can occur without any instabilities. As a result, the spectral index of tensor modes can be blue, which makes it easier to observe quantum gravitational waves from inflation by the planned gravitational-wave experiments such as LISA and DECIGO as well as by the upcoming CMB experiments such as Planck and CMBpol.

DOI： 10.1103/PhysRevLett.105.231302

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

We study the dynamics of isotropic and homogeneous universes in the generalized Ho\v{r}ava-Lifshitz gravity, and classify all possible evolutions of vacuum spacetime. In the case without the detailed balance condition, we find a variety of phase structures of vacuum spacetimes depending on the coupling constants as well as the spatial curvature $K$ and a cosmological constant $\Lambda$. A bounce universe solution is obtained for $\Lambda> 0, K=\pm 1$ or $\Lambda= 0, K=- 1$, while an oscillation spacetime is found for $\Lambda\geq 0, K=1$, or $\Lambda< 0, K=\pm 1$. We also propose a quantum tunneling scenario from an oscillating spacetime to an inflationary universe, resulting in a macroscopic cyclic universe.

DOI： 10.1103/PhysRevD.82.064024

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

We study models of late-time cosmic acceleration in terms of scalar-tensor theories generalized to include a certain class of non-linear derivative interaction of the scalar field. The non-linear effect suppress the scalar-mediated force at short distances to pass solar-system tests of gravity. It is found that the expansion history until today is almost indistinguishable from that of the $\Lambda$CDM model or some (phantom) dark energy models, but the fate of the universe depends clearly on the model parameter. The growth index of matter density perturbations is computed to show that its past asymptotic value is given by 9/16, while the value today is as small as 0.4.

DOI： 10.1103/PhysRevD.81.103533

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：IOP PUBLISHING LTD  

In Horava's theory of gravity, Lorentz symmetry is broken in exchange for renormalizability, but the original theory has been argued to be plagued with problems associated with a new scalar mode stemming from the very breaking of Lorentz symmetry. Recently, Blas, Pujolas, and Sibiryakov have proposed a healthy extension of Horava gravity, in which the behavior of the scalar mode is improved. In this paper, we study scalar modes of cosmological perturbations in extended Horava gravity. The evolution of metric and density perturbations is addressed analytically and numerically. It is shown that for vanishing non-adiabatic pressure of matter the large scale evolution of cosmological perturbations converges to that described by a single constant, $\zeta$, which is an analog of a curvature perturbation on the uniform-density slicing commonly used in usual gravitational theories. The subsequent evolution is thus determined completely by the value of $\zeta$.

DOI： 10.1088/1475-7516/2010/04/025

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

A scalar-tensor theory of gravity can be made not only to account for the current cosmic acceleration, but also to satisfy solar-system and laboratory constraints, by introducing a non-linear derivative interaction for the scalar field. Such an additional scalar degree of freedom is called "Galileon". The basic idea is inspired by the DGP braneworld, but one can construct a ghost-free model that admits a self-accelerating solution. We perform a fully relativistic analysis of linear perturbations in Galileon cosmology. Although the Galileon model can mimic the background evolution of standard $\Lambda$CDM cosmology, the behavior of perturbation is quite different. It is shown that there exists a super-horizon growing mode in the metric and Galileon perturbations at early times, suggesting that the background is unstable. A fine-tuning of the initial condition for the Galileon fluctuation is thus required in order to promote a desirable evolution of perturbations at early times. Assuming the safe initial condition, we then compute the late-time evolution of perturbations and discuss observational implications in Galileon cosmology. In particular, we find anticorrelations in the cross-correlation of the integrated Sachs-Wolfe effect and large scale structure, similar to the normal branch of the DGP model.

DOI： 10.1103/PhysRevD.81.063513

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：IOP PUBLISHING LTD  

In the non-relativistic theory of gravity recently proposed by Horava, the Hamiltonian constraint is not satisfied locally at each point in space. The absence of the local Hamiltonian constraint allows the system to have an extra dark-matter-like component as an integration constant. We discuss consequences of this fact in the context of cosmological perturbations, paying a particular attention to the large scale evolution of the curvature perturbation. The curvature perturbation is defined in a gauge invariant manner with this ``dark matter'' taken into account. We then clarify the conditions under which the curvature perturbation is conserved on large scales. This is done by using the evolution equations.

DOI： 10.1088/1475-7516/2009/11/015

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

We study the spectral tilt of primordial perturbations in Horava-Lifshitz cosmology. The uniform approximation, which is a generalization of the familiar Wentzel-Kramers-Brillouin (WKB) method, is employed to compute the spectral index both numerically and analytically in a closed form. We clarify how the spectral index depends on the inflation model and parameters in the modified dispersion relation.

DOI： 10.1103/PhysRevD.80.063514

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：IOP PUBLISHING LTD  

We explore the possibility that the dark matter and dark energy are mimicked by a single fluid or by a single $k$-essence-like scalar field. The so called Chaplygin gas unified dark matter models can reproduce the observed matter power spectrum by adding a baryon component. It has been argued that the evolution of the baryon fluctuations is particularly favoured for the "superluminal" case where the sound speed of the Chaplygin gas exceeds the speed of light at late times, as well as for the models with the negligibly small sound speed. In this note we compute the integrated Sachs-Wolfe signal in the Chaplygin gas models, focusing on the superluminal case which has not been investigated before because of the premature understanding of causality. It is shown that the superluminal model leads to large enhancement of the integrated Sachs-Wolfe effect, which is inconsistent with the CMB measurements.

DOI： 10.1088/1475-7516/2010/07/027

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：OXFORD UNIV PRESS  

We investigate the effect of modified gravity on cluster abundance and the Sunyaev-Zel'dovich angular power spectrum. Our modified gravity is based on a phenomenological extension of the Dvali-Gabadadze-Porrati model which includes two free parameters characterizing deviation from Lambda-CDM cosmology. Assuming that Birkhoff's theorem gives a reasonable approximation, we study the spherical collapse model of structure formation and show that while the growth function changes to some extent, modified gravity gives rise to no significant change in the linear density contrast at collapse time. The growth function is enhanced in the so called normal branch, while in the "self-accelerating" branch it is suppressed. The Sunyaev-Zel'dovich angular power spectrum is computed in the normal branch, which turns out to be amplified compared to the Lambda-CDM case. This allows us to put observational constraints on the parameters of the modified gravity model using small scale CMB observation data.

DOI： 10.1111/j.1365-2966.2009.15168.x

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：IOP PUBLISHING LTD  

Recently it was shown that an inflationary background can be realized by any $p$-form field non-minimally coupled to gravity. In this paper, we study gravitational waves generated during p-form inflation. Even though the background evolution is identical to that in conventional scalar field inflation, the behavior of gravitational waves is different in p-form inflation. In particular, we find that the propagation speed of gravitational waves differs from unity in 2- and 3-form inflationary models. We point out that the squared speed becomes negative in the large field models. The small field models are free from pathologies and the correction to the spectrum of gravitational waves turns out to be very small.

DOI： 10.1088/1475-7516/2009/05/004

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Language：English   Publishing type：Research paper (scientific journal)  

Although f(R) modified gravity models can be made to satisfy solar system and cosmological constraints, it has been shown that they have the serious drawback of the nonexistence of stars with strong gravitational fields. In this paper, we discuss whether or not higher curvature corrections can remedy the nonexistence consistently. The following problems are shown to arise as the costs one must pay for the f(R) models that allow for neutrons stars: (i) the leading correction must be fine-tuned to have the typical energy scale μ 10-19GeV, which essentially comes from the free fall time of a relativistic star
(ii) the leading correction must be further fine-tuned so that it is not given by the quadratic curvature term. The second problem is caused because there appears an intermediate curvature scale, and laboratory experiments of gravity will be under the influence of higher curvature corrections. Our analysis thus implies that it is a challenge to construct viable f(R) models without very careful and unnatural fine-tuning. © 2009 The American Physical Society.

DOI： 10.1103/PhysRevD.79.024009

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

Although $f(R)$ modified gravity models can be made to satisfy solar system and cosmological constraints, it has been shown that they have the serious drawback of the nonexistence of stars with strong gravitational fields. In this paper, we discuss whether or not higher curvature corrections can remedy the nonexistence consistently. The following problems are shown to arise as the costs one must pay for the $f(R)$ models that allow for neutrons stars: (i) the leading correction must be fine-tuned to have the typical energy scale $\mu \lesssim 10^{-19}$ GeV, which essentially comes from the free fall time of a relativistic star; (ii) the leading correction must be further fine-tuned so that it is not given by the quadratic curvature term. The second problem is caused because there appears an intermediate curvature scale and laboratory experiments of gravity will be under the influence of higher curvature corrections. Our analysis thus implies that it is a challenge to construct viable $f(R)$ models without very careful and unnatural fine-tuning.

DOI： 10.1103/PhysRevD.79.024009

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Language：English   Publishing type：Research paper (scientific journal)  

Several f(R) modified gravity models have been proposed which realize the correct cosmological evolution and satisfy solar system and laboratory tests. Although nonrelativistic stellar configurations can be constructed, we argue that relativistic stars cannot be present in such f(R) theories. This problem appears due to the dynamics of the effective scalar degree of freedom in the strong gravity regime. Our claim thus raises doubts on the viability of f(R) models. © 2008 The American Physical Society.

DOI： 10.1103/PhysRevD.78.064019

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We investigate conformal scalar, electromagnetic, and massless Dirac quasinormal modes of a brane-localized black hole. The background solution is the four-dimensional black hole on a 2-brane that has been constructed by Emparan, Horowitz, and Myers in the context of a lower-dimensional version of the Randall-Sundrum model. The conformally transformed metric admits a Killing tensor, allowing us to obtain separable field equations. We find that the radial equations take the same form as in the four-dimensional braneless Schwarzschild black hole. The angular equations are, however, different from the standard ones, leading to a different prediction for quasinormal frequencies. © 2008 The American Physical Society.

DOI： 10.1103/PhysRevD.78.064006

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

Several f(R) modified gravity models have been proposed which realize the correct cosmological evolution and satisfy solar system and laboratory tests. Although nonrelativistic stellar configurations can be constructed, we argue that relativistic stars cannot be present in such f(R) theories. This problem appears due to the dynamics of the effective scalar degree of freedom in the strong gravity regime. Our claim thus raises doubts on the viability of f(R) models.

DOI： 10.1103/PhysRevD.78.064019

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

In the context of six-dimensional conical braneworlds we consider a simple and explicit model that incorporates long distance modification of gravity and regularization of codimension-2 singularities. To resolve the conical singularities we replace the codimension-2 branes with ring-like codimension-1 branes, filling in the interiors with regular caps. The six-dimensional Planck scale in the cap is assumed to be much greater than the bulk Planck scale, which gives rise to the effect analogous to brane-induced gravity. Weak gravity on the regularized brane is studied in the case of a sharp conical bulk. We show by a linear analysis that gravity at short distances is effectively described by the four-dimensional Brans-Dicke theory, while the higher dimensional nature of gravity emerges at long distances. The linear analysis breaks down at some intermediate scale, below which four-dimensional Einstein gravity is shown to be recovered thanks to the second-order effects of the brane bending.

DOI： 10.1103/PhysRevD.78.084018

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：IOP PUBLISHING LTD  

We explore the possibility of generating large-scale magnetic fields from second-order cosmological perturbations during the pre-recombination era. The key process for this is Thomson scattering between the photons and the charged particles within the cosmic plasma. To tame the multi-component interacting fluid system, we employ the tight coupling approximation. It is shown that the source term for the magnetic field is given by the vorticity, which signals the intrinsically second-order quantities, and the product of the first order perturbations. The vorticity itself is sourced by the product of the first-order quantities in the vorticity evolution equation. The magnetic fields generated by this process are estimated to be $\sim 10^{-29} $Gauss on the horizon scale at the recombination epoch. Although our rough estimate suggests that the current generation mechanism can work even on smaller scales, more careful investigation is needed to make clear whether it indeed works in a wide range of spatial scales.

DOI： 10.1088/0264-9381/26/13/135014

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

We investigate conformal scalar, electromagnetic, and massless Dirac quasinormal modes of a brane-localized black hole. The background solution is the four-dimensional black hole on a 2-brane that has been constructed by Emparan, Horowitz, and Myers in the context of a lower dimensional version of the Randall-Sundrum model. The conformally transformed metric admits a Killing tensor, allowing us to obtain separable field equations. We find that the radial equations take the same form as in the four-dimensional "braneless" Schwarzschild black hole. The angular equations are, however, different from the standard ones, leading to a different prediction for quasinormal frequencies.

DOI： 10.1103/PhysRevD.78.064006

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Language：English   Publishing type：Research paper (scientific journal)  

We study the emission of scalar fields into the bulk from a six-dimensional rotating black hole pierced by a 3-brane. We determine the angular eigenvalues in the presence of finite brane tension by using the continued fraction method. The radial equation is integrated numerically, giving the absorption probability (graybody factor) in a wider frequency range than in the preexisting literature. We then compute the power and angular momentum emission spectra for different values of the rotation parameter and brane tension, and compare their relative behavior in detail. As is expected from the earlier result for a nonrotating black hole, the finite brane tension suppresses the emission rates. As the rotation parameter increases, the power spectra are reduced at low frequencies due to the smaller Hawking temperature and are enhanced at high frequencies due to superradiance. The angular momentum spectra are enhanced over the whole frequency range as the rotation parameter increases. The spectra and the amounts of energy and angular momentum radiated away into the bulk are thus determined by the interplay of these effects. © 2008 The American Physical Society.

DOI： 10.1103/PhysRevD.77.044022

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

We study the effective gravitational theory on a brane in a six-dimensional Einstein-Maxwell model of flux compactification, regularizing a conical defect as a codimension-one brane. We employ the gradient expansion technique valid at low energies. A lowest order analysis showed that standard four-dimensional Einstein gravity is reproduced on the brane. We extend this study to include second order corrections in the effective equations, and show that the correction term is given by a quadratic energy-momentum tensor. Taking the thin-brane limit where the regularized brane shrinks to the pole, we find that the second order metric diverges logarithmically on the brane, giving rise to divergences in the brane effective action. Away from the branes, the effective action is however well-defined.

DOI： 10.1103/PhysRevD.77.124012

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

We study the emission of scalar fields into the bulk from a six-dimensional rotating black hole pierced by a 3-brane. We determine the angular eigenvalues in the presence of finite brane tension by using the continued fraction method. The radial equation is integrated numerically, giving the absorption probability (graybody factor) in a wider frequency range than in the preexisting literature. We then compute the power and angular momentum emission spectra for different values of the rotation parameter and brane tension, and compare their relative behavior in detail. As is expected from the earlier result for a nonrotating black hole, the finite brane tension suppresses the emission rates. As the rotation parameter increases, the power spectra are reduced at low frequencies due to the smaller Hawking temperature and are enhanced at high frequencies due to superradiance. The angular momentum spectra are enhanced over the whole frequency range as the rotation parameter increases. The spectra and the amounts of energy and angular momentum radiated away into the bulk are thus determined by the interplay of these effects.

DOI： 10.1103/PhysRevD.77.044022

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：IOP PUBLISHING LTD  

We derive the low energy effective theory on a brane in six-dimensional chiral supergravity. The conical 3-brane singularities are resolved by introducing cylindrical codimension one 4-branes whose interiors are capped by a regular spacetime. The effective theory is described by the Brans-Dicke (BD) theory with the BD parameter given by $\omega_{\rm BD}=1/2$. The BD field is originated from a modulus which is associated with the scaling symmetry of the system. If the dilaton potentials on the branes preserve the scaling symmetry, the scalar field has an exponential potential in the Einstein frame. We show that the time dependent solutions driven by the modulus in the four-dimensional effective theory can be lifted up to the six-dimensional exact solutions found in the literature. Based on the effective theory, we discuss a possible way to stabilize the modulus to recover standard cosmology and also study the implication for the cosmological constant problem.

DOI： 10.1088/1475-7516/2007/12/006

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

Conical brane singularities in six-dimensional flux compactification models can be resolved by introducing cylindrical codimension-one branes with regular caps instead of 3-branes (a la Kaluza-Klein braneworlds with fluxes). In this paper, we consider such a regularized braneworld with axial symmetry in six-dimensional Einstein-Maxwell theory. We derive a low energy effective theory on the regularized brane by employing the gradient expansion approach, and show that standard four-dimensional Einstein gravity is recovered at low energies. Our effective equations extend to the nonlinear gravity regime, implying that conventional cosmology can be reproduced in the regularized braneworld.

DOI： 10.1103/PhysRevD.76.104052

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：IOP PUBLISHING LTD  

We consider a six-dimensional axisymmetric Einstein-Maxwell model of warped braneworlds. The bulk is bounded by two branes, one of which is a conical 3-brane and the other is a 4-brane wrapped around the axis of symmetry. The latter brane is assumed to be our universe. If the tension of the 3-brane is fine-tuned, it folds the internal two-dimensional space in a narrow cone, making sufficiently small the Kaluza-Klein circle of the 4-brane. An arbitrary energy-momentum tensor can be accommodated on this ring-like 4-brane. We study linear perturbations sourced by matter on the brane, and show that weak gravity is apparently described by a four-dimensional scalar-tensor theory. The extra scalar degree of freedom can be interpreted as the fluctuation of the internal space volume (or that of the circumference of the ring), the effect of which turns out to be suppressed at long distances. Consequently, four-dimensional Einstein gravity is reproduced on the brane. We point out that as in the Randall-Sundrum model, the brane bending mode is crucial for recovering the four-dimensional tensor structure in this setup.

DOI： 10.1088/0264-9381/25/1/015007

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：IOP PUBLISHING LTD  

We study cosmology on a conical brane in the six-dimensional Einstein-Maxwell-dilaton system, where the extra dimensions are compactified by a magnetic flux. We systematically construct exact cosmological solutions using the fact that the system is equivalently described by (6+n)-dimensional pure Einstein-Maxwell theory via dimensional reduction. In particular, we find a power-law inflationary solution for a general dilatonic coupling. When the dilatonic coupling is given by that of Nishino-Sezgin chiral supergravity, this reduces to the known solution which is not inflating. The power-law solution is shown to be the late-time attractor. We also investigate cosmological tensor perturbations in this model using the (6+n)-dimensional description. We obtain the separable equation of motion and find that there always exist a zero mode, while tachyonic modes are absent in the spectrum. The mass spectrum of Kaluza-Klein modes is obtained numerically.

DOI： 10.1088/1475-7516/2007/07/016

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMERICAN PHYSICAL SOC  

We study linearized gravity in a six-dimensional Einstein-Maxwell model of warped braneworlds, where the extra dimensions are compactified by a magnetic flux. It is difficult to construct a strict codimension two braneworld with matter sources other than pure tension. To overcome this problem we replace the codimension two defect by an extended brane, with one spatial dimension compactified on a Kaluza-Klein circle. Our background is composed of a warped, axisymmetric bulk and one or two branes. We find that weak gravity sourced by arbitrary matter on the brane(s) is described by a four-dimensional scalar-tensor theory. We show, however, that the scalar mode is suppressed at long distances and hence four-dimensional Einstein gravity is reproduced on the brane.

DOI： 10.1103/PhysRevD.75.104013

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMERICAN PHYSICAL SOC  

In the standard cosmological model, magnetic fields and vorticity are generated during the radiation era via second-order density perturbations. In order to clarify the complicated physics of this second-order magnetogenesis, we use a covariant approach and present the electromagneto-dynamical equations in the nonlinear regime. We use the tight-coupling approximation to analyze Thomson and Coulomb scattering. At the zero-order limit of exact tight-coupling, we show that the vorticity is zero and no magnetogenesis takes place at any nonlinear order. We show that magnetogenesis also fails at all orders if either protons or electrons have the same velocity as the radiation, and momentum transfer is neglected. Then we prove a key no-go result: at first-order in the tight-coupling approximation, magnetic fields and vorticity still cannot be generated even via nonlinear effects. The tight-coupling approximation must be broken at first order, for the generation of vorticity and magnetic fields, and we derive a closed set of nonlinear evolution equations that governs this generation. We estimate that the amplitude of the magnetic field at recombination on the horizon scale is $\sim 10^{-27} $G.

DOI： 10.1103/PhysRevD.75.103501

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：IOP PUBLISHING LTD  

We study scalar cosmological perturbations in a braneworld model with a bulk Gauss-Bonnet term. For an anti-de Sitter bulk, the five-dimensional perturbation equations share the same form as in the Randall-Sundrum model, which allows us to obtain metric perturbations in terms of a master variable. We derive the boundary conditions for the master variable from the generalized junction conditions on the brane. We then investigate several limiting cases in which the junction equations are reduced to a feasible level. In the low energy limit, we confirm that the standard result of four-dimensional Einstein gravity is reproduced on large scales, whereas on small scales we find that the perturbation dynamics is described by the four-dimensional Brans-Dicke theory. In the high energy limit, all the non-local contributions drop off from the junction equations, leaving a closed system of equations on the brane. We show that, for inflation models driven by a scalar field on the brane, the Sasaki-Mukhanov equation holds on the high energy brane in its original four-dimensional form.

DOI： 10.1088/1475-7516/2006/12/008

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMERICAN PHYSICAL SOC  

We present effective gravitational equations at low energies in a $Z_2$-symmetric braneworld with the Gauss-Bonnet term. Our derivation is based on the geometrical projection approach, and we solve iteratively the bulk geometry using the gradient expansion scheme. Although the original field equations are quite complicated due to the presence of the Gauss-Bonnet term, our final result clearly has the form of the Einstein equations plus correction terms, which is simple enough to handle. As an application, we consider homogeneous and isotropic cosmology on the brane. We also comment on the holographic interpretation of bulk gravity in the Gauss-Bonnet braneworld.

DOI： 10.1103/PhysRevD.74.104031

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：IOP PUBLISHING LTD  

The braneworld model of Dvali-Gabadadze-Porrati (DGP) provides an interesting alternative to a positive cosmological constant by modifying gravity at large distances. We investigate the asymptotic behavior of homogeneous and anisotropic cosmologies on the DGP brane. It is shown that all Bianchi models except type IX isotropize, as in general relativity, if the so called $E_{\mu\nu}$ term satisfies some energy condition. Isotropization can proceed slower in DGP gravity than in general relativity.

DOI： 10.1088/0264-9381/23/15/005

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

We study the holographic representation of the entanglement entropy, recently proposed by Ryu and Takayanagi, in a braneworld context. The holographic entanglement entropy of a de Sitter brane embedded in an anti-de Sitter (AdS) spacetime is evaluated using geometric quantities, and it is compared with two kinds of de Sitter entropy: a quarter of the area of the cosmological horizon on the brane and entropy calculated from the Euclidean path integral. We show that the three entropies coincide with each other in a certain limit. Remarkably, the entropy obtained from the Euclidean path integral is in precise agreement with the holographic entanglement entropy in all dimensions. We also comment on the case of a five-dimensional braneworld model with the Gauss-Bonnet term in the bulk.

DOI： 10.1103/PhysRevD.74.064027

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMERICAN PHYSICAL SOC  

We study the spectrum of gravitational waves generated from inflation in the Randall-Sundrum braneworld. Since the inflationary gravitational waves are of quantum-mechanical origin, the initial configuration of perturbations in the bulk includes Kaluza-Klein quantum fluctuations as well as fluctuations in the zero mode. We show, however, that the initial fluctuations in Kaluza-Klein modes have no significant effect on the late time spectrum, irrespective of the energy scale of inflation and the equation of state parameter in the post-inflationary stage. This is done numerically, using the Wronskian formulation.

DOI： 10.1103/PhysRevD.73.124031

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Language：English   Publishing type：Research paper (scientific journal)  

We study the generation and evolution of gravitational waves (tensor perturbations) in the context of Randall-Sundrum braneworld cosmology. We assume that the initial and final stages of the background cosmological model are given by de Sitter and Minkowski phases, respectively, and they are connected smoothly by a radiation-dominated phase. This setup allows us to discuss the quantum-mechanical generation of the perturbations and to see the final amplitude of the well-defined zero mode. Using the Wronskian formulation, we numerically compute the power spectrum of gravitational waves, and find that the effect of initial vacuum fluctuations in the Kaluza-Klein modes is subdominant, contributing not more than 10% of the total power spectrum. Thus it is confirmed that the damping due to the Kaluza-Klein mode generation and the enhancement due to the modification of the background Friedmann equation are the two dominant effects, but they cancel each other, leading to the same spectral tilt as the standard four-dimensional result. Kaluza-Klein gravitons that escape from the brane contribute to the energy density of the dark radiation at late times. We show that a tiny amount of the dark radiation is generated due to this process. © 2006 The American Physical Society.

DOI： 10.1103/PhysRevD.73.044005

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

We study the generation and evolution of gravitational waves (tensor perturbations) in the context of Randall-Sundrum braneworld cosmology. We assume that the initial and final stages of the background cosmological model are given by de Sitter and Minkowski phases, respectively, and they are connected smoothly by a radiation-dominated phase. This setup allows us to discuss the quantum-mechanical generation of the perturbations and to see the final amplitude of the well-defined zero mode. Using the Wronskian formulation, we numerically compute the power spectrum of gravitational waves, and find that the effect of initial vacuum fluctuations in the Kaluza-Klein modes is subdominant, contributing not more than 10% of the total power spectrum. Thus it is confirmed that the damping due to the Kaluza-Klein mode generation and the enhancement due to the modification of the background Friedmann equation are the two dominant effects, but they cancel each other, leading to the same spectral tilt as the standard four-dimensional result. Kaluza-Klein gravitons that escape from the brane contribute to the energy density of the dark radiation at late times. We show that a tiny amount of the dark radiation is generated due to this process.

DOI： 10.1103/PhysRevD.73.044005

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：American Physical Society  

We study the quantum-mechanical generation of gravitational waves during inflation on a brane embedded in a five-dimensional anti de Sitter bulk. To make the problem well posed, we consider the setup in which both initial and final phases are given by a de Sitter brane with different values of the Hubble expansion rate. Assuming that the quantum state is in a de Sitter invariant vacuum in the initial de Sitter phase, we numerically evaluate the amplitude of quantum fluctuations of the growing solution of the zero mode in the final de Sitter phase. We find that the vacuum fluctuations of the initial Kaluza-Klein gravitons as well as of the zero mode gravitons contribute to the final amplitude of the zero mode on small scales, and the power spectrum is quite well approximated by what we call the rescaled spectrum, which is obtained by rescaling the standard four-dimensional calculation following a simple mapping rule. Our results confirm the speculation raised in Ref. [T. Kobayashi, H. Kudoh, and T. Tanaka, Phys. Rev. D 68, 044025 (2003).PRVDAQ0556-282110.1103/ PhysRevD.68.044025] before. © 2005 The American Physical Society.

DOI： 10.1103/PhysRevD.71.124028

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

We study the quantum-mechanical generation of gravitational waves during inflation on a brane embedded in a five-dimensional anti-de Sitter bulk. To make the problem well-posed, we consider the setup in which both initial and final phases are given by a de Sitter brane with different values of the Hubble expansion rate. Assuming that the quantum state is in a de Sitter invariant vacuum in the initial de Sitter phase, we numerically evaluate the amplitude of quantum fluctuations of the growing solution of the zero mode in the final de Sitter phase. We find that the vacuum fluctuations of the initial Kaluza-Klein gravitons as well as of the zero mode gravitons contribute to the final amplitude of the zero mode on small scales, and the power spectrum is quite well approximated by what we call the rescaled spectrum, which is obtained by rescaling the standard four-dimensional calculation following a simple mapping rule. Our results confirm the speculation raised in Ref. \cite{Kobayashi:2003cn} before.

DOI： 10.1103/PhysRevD.71.124028

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：SPRINGER/PLENUM PUBLISHERS  

We consider a Vaidya-type radiating spacetime in Einstein gravity with the Gauss-Bonnet combination of quadratic curvature terms. Simply generalizing the known static black hole solutions in Einstein-Gauss-Bonnet gravity, we present an exact solution in arbitrary dimensions with the energy-momentum tensor given by a null fluid form. As an application, we derive an evolution equation for the ``dark radiation'' in the Gauss-Bonnet braneworld.

DOI： 10.1007/s10714-005-0192-y

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Publishing type：Research paper (scientific journal)  

Tensor perturbations in an expanding braneworld of the Randall Sundrum type are investigated. We consider a model composed of a slow-roll inflation phase and the succeeding radiation phase. The effect of the presence of an extra dimension through the transition to the radiation phase is studied, giving an analytic formula for leading order corrections.

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Publishing type：Research paper (scientific journal)  

We consider black-string-type solutions in five-dimensional Einstein-Gauss-Bonnet gravity. Numerically constructed solutions under static, axially symmetric and translationally invariant metric ansatz are presented. The solutions are specified by two asymptotic charges: mass of a black string and a scalar charge associated with the radion part of the metric. Regular black string solutions are found if and only if the two charges satisfy a fine-tuned relation, and otherwise the spacetime develops a singular event horizon or a naked singularity. We can also generate bubble solutions from the black strings by using a double Wick rotation.

DOI： 10.1103/PhysRevD.71.084005

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：IOP PUBLISHING LTD  

Tensor type perturbations in the expanding brane world of the Randall Sundrum type are investigated. We consider a model composed of slow-roll inflation phase and the succeeding radiation phase. The effect of the presence of an extra dimension through the transition to the radiation phase is studied, giving an analytic formula for leading order corrections.

DOI： 10.1088/1475-7516/2004/10/015

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMERICAN PHYSICAL SOC  

We introduce a $(5+m)$-dimensional vacuum description of five-dimensional bulk inflaton models with exponential potentials that makes analysis of cosmological perturbations simple and transparent. We show that various solutions, including the power-law inflation model recently discovered by Koyama and Takahashi, are generated from known $(5+m)$-dimensional vacuum solutions of pure gravity. We derive master equations for all types of perturbations, and each of them becomes a second order differential equation for one master variable supplemented by simple boundary conditions on the brane. One exception is the case for massive modes of scalar perturbations. In this case, there are two independent degrees of freedom, and in general it is difficult to disentangle them into two separate sectors.

DOI： 10.1103/PhysRevD.69.064037

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

We study primordial gravitational waves from inflation in Randall-Sundrum braneworld model. The effect of small change of the Hubble parameter during inflation is investigated using a toy model given by connecting two de Sitter branes. We analyze the power spectrum of final zero-mode gravitons, which is generated from the vacuum fluctuations of both initial Kaluza-Klein modes and zero-mode. The amplitude of fluctuations is confirmed to agree with the four-dimensional one at low energies, whereas it is enhanced due to the normalization factor of zero-mode at high energies. We show that the five-dimensional spectrum can be well approximated by applying a simple mapping to the four-dimensional fluctuation amplitude.

DOI： 10.1103/PhysRevD.68.044025

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Language：English   Publishing type：Research paper (scientific journal)  

We study primordial gravitational waves from inflation in the Randall-Sundrum braneworld model. The effect of a small change of the Hubble parameter during inflation is investigated using a toy model given by connecting two de Sitter branes. We analyze the power spectrum of the final zero-mode gravitons, which is generated from the vacuum fluctuations of both the initial Kaluza-Klein modes and the zero mode. The amplitude of fluctuations is confirmed to agree with the four-dimensional one at low energies, whereas it is enhanced due to the normalization factor of the zero mode at high energies. We show that the five-dimensional spectrum can be well approximated by applying a simple mapping to the four-dimensional fluctuation amplitude. © 2003 The American Physical Society.

DOI： 10.1103/PhysRevD.68.044025

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