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 gr...

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 ...

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...

Class. Quant. Grav. 36 (2019) no.9, 095003 Dec 2018

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 Horndesk...

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...

Aya Iyonaga, Kazufumi Takahashi, Tsutomu Kobayashi

JCAP 12 (2018) 002 Sep 2018

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 fr...

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 ...

Hiroaki W. H. Tahara, Sakine Nishi, Tsutomu Kobayashi, Jun'ichi Yokoyama

JCAP07(2018)058 May 2018

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 scala...

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 t...

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 ...

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 i...

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 la...

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 pertur...

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...

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 ...

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, descri...

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 ...

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...

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 p...

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...

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 know...

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 o...

Tsutomu Kobayashi, Masaru Siino, Masahide Yamaguchi, Daisuke Yoshida

Sep 2015

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 w...

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 correc...

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 ...

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 term...

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...

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 construc...

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 f...

Xian Gao, Tsutomu Kobayashi, Masahide Yamaguchi, Daisuke Yoshida

Phys. Rev. D 90, 124073 (2014) Sep 2014

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...

We derive a variety of exact black hole solutions in a subclass of Horndeski's scalar-tensor theory possessing shift symmetry, , and reflection symmetry, . The theory admits two arbitrary functions of $X:=-(\partial\ph...

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...

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 ...

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 insta...

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 ...

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...

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 with $X=-\partial^{\mu}\phi\partial_{\mu}\...

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 fo...

Tsutomu Kobayashi, Masaru Siino, Masahide Yamaguchi, Daisuke Yoshida

May 2012

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 Stückelberg fields are given explicitly, showing nontrivial conf...

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...

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...

A generic second-order scalar-tensor theory contains a nonlinear derivative self-interaction of the scalar degree of freedom à la Galileon models, which allows for the Vainshtein screening mechanism. We investigate this effect on subhor...

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 kineti...

Antonio De Felice, Tsutomu Kobayashi, Shinji Tsujikawa

Phys.Lett.B706:123-133, 2011 Aug 2011

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 o...

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 ac...

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...

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 fi...

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 superhorizo...

We present a comprehensive study of primordial fluctuations generated from G-inflation, in which the inflaton Lagrangian is of the form with . The Lagrangian still gives rise to second-order g...

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...

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 ...

We propose a new class of inflation model, G-inflation, which has a Galileon-like nonlinear derivative interaction of the form in the Lagrangian with the resultant equations of motion being of second order. It is ...

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 s...

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 ...

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....

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 ad...

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 ...

Kazuhiro Yamamoto, Tsutomu Kobayashi, Gen Nakamura

Phys.Rev.D80:063514,2009 Jul 2009

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 numeri...

We explore the possibility that the dark matter and dark energy are mimicked by a single fluid or by a single -essence-like scalar field. The so called Chaplygin gas unified dark matter models can reproduce the observed matter power spectrum by...

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 parame...

Recently it was shown that an inflationary background can be realized by any -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 id...

Although 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 discus...

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 ...

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 replac...

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...

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 Mye...

Tsutomu Kobayashi, Tetsuya Shiromizu, Claudia de Rham

Phys.Rev.D77:124012,2008 Feb 2008

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...

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 e...

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 ...

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 cons...

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 assum...

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 i...

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 oth...

Tsutomu Kobayashi, Roy Maartens, Tetsuya Shiromizu, Keitaro Takahashi

Phys.Rev.D75:103501,2007 Jan 2007

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 ap...

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 ...

We present effective gravitational equations at low energies in a -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 ...

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 cosmologie...

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 evalu...

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 K...

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...

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 give...

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 solut...

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 ...

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 ...

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 thr...

We introduce a -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 powe...

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 ...