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Recently the first example of a unitary theory of Lorentz-invariant massive gravity allowing for stable self-accelerating de Sitter solutions was found, extending the quasidilaton theory. In this paper we further generalize this new action for the quasidilaton field by introducing general Lagrangian terms which are consistent with the quasidilaton symmetry while leading to second order equations of motion. We find that the structure of the theory, compared to the simplest stable example, does not change on introducing these new terms., Comment: 11 pages

We present the first example of a unitary theory of Lorentz-invariant massive gravity, with all degrees of freedom propagating on a strictly homogeneous and isotropic, self-accelerating de Sitter background. The theory is a simple extension of the quasidilaton theory, respecting the symmetry of the original theory but allowing for a new type of coupling between the massive graviton and the quasidilaton scalar., Comment: 4 pages

We place observational constraints on slow-variation single-field inflationary models by carrying out the cosmological Monte Carlo simulation with the recent data of Planck combined with the WMAP large-angle polarization, baryon acoustic oscillations, and ACT/SPT temperature data. Our analysis covers a wide variety of models with second-order equations of motion-- including potential-driven slow-roll inflation, non-minimally coupled models, running kinetic couplings, Brans-Dicke theories, potential-driven Galileon inflation, field-derivative couplings to the Einstein tensor, and k-inflation. In the presence of running kinetic exponential couplings, covariant Galileon terms, and field-derivative couplings, the tensor-to-scalar ratio of the self-coupling potential gets smaller relative to that in standard slow-roll inflation, but the models lie outside the 68 % CL observational contour. We also show that k-inflation models can be tightly constrained by adding the bounds from the scalar non-Gaussianities. The small-field inflationary models with asymptotic flat Einstein-frame potentials in the regime phi >> M_{pl} generally fit the data very well. These include the models such as Kahler-moduli inflation, non-minimally coupled Higgs inflation, and inflation in Brans-Dicke theories in the presence of the potential V(phi)=3M^2 (phi-M_{pl})^2/4 with the Brans-Dicke parameter omega_{BD}

We present a review of cosmological solutions in non-linear massive gravity, focusing on the stability of perturbations. Although homogeneous and isotropic solutions have been found, these are now known to suffer from either Higuchi ghost or a new non-linear ghost instability. We discuss two approaches to alleviate this issue. By relaxing the symmetry of the background by e.g. breaking isotropy in the hidden sector, it is possible to accommodate a stable cosmological solution. Alternatively, extending the theory to allow for new dynamical degrees of freedom can also remove the conditions which lead to the instability. As examples for this case, we study the stability of self-accelerating solutions in the quasi-dilatonic extension and generic cosmological solutions in the varying mass extension. While the quasi-dilaton case turns out to be unstable, the varying mass case allows stable regimes of parameters. Viable self-accelerating solutions in the varying mass theory yet remain to be found., Comment: 20 pages, prepared for CQG focus issue ; v2: Published version

We investigate nonlinear stability of two classes of cosmological solutions in massive gravity: isotropic Friedmann-Lemaitre-Robertson-Walker (FLRW) solutions and anisotropic FLRW solutions. For this purpose we construct the linear cosmological perturbation theory around axisymmetric Bianchi type--I backgrounds. We then expand the background around the two classes of solutions, which are fixed points of the background evolution equation, and analyze linear perturbations on top of it. This provides a consistent truncation of nonlinear perturbations around these fixed point solutions and allows us to analyze nonlinear stability in a simple way. In particular, it is shown that isotropic FLRW solutions exhibit nonlinear ghost instability. On the other hand, anisotropic FLRW solutions are shown to be ghost-free for a range of parameters and initial conditions., Comment: 28 pages ; v2. Minor changes to match the published version

For two types of quintessence models having thawing and tracking properties, there exist analytic solutions for the dark energy equation of state w expressed in terms of several free parameters. We put observational bounds on the parameters in such scenarios by using the recent data of Supernovae type Ia, Cosmic Microwave Background, and Baryon Acoustic Oscillations. The observational constraints are quite different depending on whether or not the recent BAO data from BOSS are taken into account. With the BOSS data the upper bounds of today's values of w (=w_0) in thawing models is very close to -1, whereas without this data the values of w_0 away from -1 can be still allowed. The tracker equation of state w_{(0)} during the matter era is constrained to be w_{(0)}<-0.949 at 95 % confidence level even without the BOSS data, so that the tracker models with w away from -1 are severely disfavored. We also study observational constraints on scaling models in which w starts to evolve from 0 in the deep matter era and show that the transition to the equation of state close to w=-1 needs to occur at an early cosmological epoch. In the three classes of quintessence models studied in this paper, the past evolution of the Hubble parameters in the best-fit models shows only less than the 2.5 % difference compared to the LCDM., Comment: 12 pages, 10 figures

We consider the 3-form field, which has been considered as a candidate for realizing inflation, coupled to a scalar field which models the relativistic matter particles produced during the reheating epoch. We have investigated the stability conditions for this theory and found that introducing such a coupling does not lead to any ghosts or Laplacian instabilities. We have also investigated the reheating temperature and the production of particles due to parametric resonances. We have found that this process is more efficient in this theory compared to the result of the standard-scalar-field inflationary scenario., Comment: 10 pages, no figure

We investigate circumstances under which one can generalize Horndeski's most general scalar-tensor theory of gravity. Specifically we demonstrate that a nonlinear combination of purely kinetic gravity terms can give rise to an accelerating universe without the addition of extra propagating degrees of freedom on cosmological backgrounds, and exhibit self tuning to bring a large cosmological constant under control. This nonlinear approach leads to new properties that may be instructive for exploring the behaviors of gravity., Comment: 16 pages, 7 figures

We argue that all homogeneous and isotropic solutions in nonlinear massive gravity are unstable. For this purpose, we study the propagating modes on a Bianchi type--I manifold. We analyze their kinetic terms and dispersion relations as the background manifold approaches the homogeneous and isotropic limit. We show that in this limit, at least one ghost always exists and that its frequency tends to vanish for large scales, meaning that it cannot be integrated out from the low energy effective theory. This ghost mode is interpreted as a leading nonlinear perturbation around a homogeneous and isotropic background., Comment: 4 pages, uses REVTeX4.1; v2: minor update to match the published version

We consider the Eddington-Born-Infeld (EBI) model here without assuming any cosmological constant. The EBI scalar field is supposed to play a role of both dark matter and dark energy. Different eras in cosmology are reconstructed for the model. A comparison is drawn with $\Lambda$CDM model using Supernova Ia, WMAP7 and BAO data. It seems that the EBI field in this form does not give good fit to observational data in comparison to the $\Lambda$CDM model., Comment: 8 pages, 4 figures

We consider the minimally coupled 3-form field which has been considered as a candidate to realize inflation. We have studied the conditions to avoid ghosts and Laplacian instabilities and found that some classes of potentials, e.g. the Mexican-hat one, will in general be unstable. We then propose other classes of potentials which are instead free from any instability, drive a long-enough slow-roll regime followed by an oscillatory epoch, and as a consequence, can provide successful inflation. Finally, we also provide stable potentials which lead to a small enough propagation speed for the scalar perturbations, giving a possibility for these models to produce non-Gaussianities., Comment: 18 pages, 12 figures, add new informations in V2, correct some typos in V3

The extended Galileon models possess tracker solutions with de Sitter attractors along which the dark energy equation of state is constant during the matter-dominated epoch, i.e. w_DE = -1-s, where s is a positive constant. Even with this phantom equation of state there are viable parameter spaces in which the ghosts and Laplacian instabilities are absent. Using the observational data of the supernovae type Ia, the cosmic microwave background (CMB), and baryon acoustic oscillations, we place constraints on the tracker solutions at the background level and find that the parameter s is constrained to be s=0.034 (-0.034,+0.327) (95% CL) in the flat Universe. In order to break the degeneracy between the models we also study the evolution of cosmological density perturbations relevant to the large-scale structure (LSS) and the Integrated-Sachs-Wolfe (ISW) effect in CMB. We show that, depending on the model parameters, the LSS and the ISW effect is either positively or negatively correlated. It is then possible to constrain viable parameter spaces further from the observational data of the ISW-LSS cross-correlation as well as from the matter power spectrum., Comment: 17 pages, 9 figures, uses RevTeX4-1

For very general scalar-field theories in which the equations of motion are at second-order, we evaluate the three-point correlation function of primordial scalar perturbations generated during inflation. We show that the shape of non-Gaussianities is well approximated by the equilateral type. The equilateral non-linear parameter f_NL^equil is derived on the quasi de Sitter background where the slow-variation parameters are much smaller than unity. We apply our formula for f_NL^equil to a number of single-field models of inflation--such as k-inflation, k-inflation with Galileon terms, potential-driven Galileon inflation, nonminimal coupling models (including field-derivative coupling models), and Gauss-Bonnet gravity., Comment: 17 pages, 1 figure, uses RevTeX. The version to appear in Physical Review D

We compute the three-point correlation function of primordial scalar density perturbations in a general single-field inflationary scenario, where a scalar field phi has a direct coupling with the Ricci scalar R and the Gauss-Bonnet term GB. Our analysis also covers the models in which the Lagrangian includes a function non-linear in the field kinetic energy X=-(nabla phi)^2/2, and a Galileon-type field self-interaction G(phi, X)*(Box phi), where G is a function of phi and X. We provide a general analytic formula for the equilateral non-Gaussianity parameter f_{NL}^{equil} associated with the bispectrum of curvature perturbations. A quasi de Sitter approximation in terms of slow-variation parameters allows us to derive a simplified form of f_{NL}^{equil} convenient to constrain various inflation models observationally. If the propagation speed of the scalar perturbations is much smaller than the speed of light, the Gauss-Bonnet term as well as the Galileon-type field self-interaction can give rise to large non-Gaussianities testable in future observations. We also show that, in Brans-Dicke theory with a field potential (including f(R) gravity), f_{NL}^{equil} is of the order of slow-roll parameters as in standard inflation driven by a minimally coupled scalar field., Comment: 25 pages, added subsection, uses RevTeX4-1

We study linear metric perturbations around a spherically symmetric static spacetime for general f(R,G) theories, where R is the Ricci scalar and G is the Gauss-Bonnet term. We find that unless the determinant of the Hessian of f(R,G) is zero, even-type perturbations have a ghost for any multi-pole mode. In order for these theories to be plausible alternatives to General Relativity, the theory should satisfy the condition that the ghost is massive enough to effectively decouple from the other fields. We study the requirement on the form of f(R,G) which satisfies this condition. We also classify the number of propagating modes both for the odd-type and the even-type perturbations and derive the propagation speeds for each mode., Comment: 15 pages, uses RevTeX4-1

We study the evolution of matter density perturbations in Galileon cosmology where the late-time cosmic acceleration can be realized by a field kinetic energy. We obtain full perturbation equations at linear order in the presence of five covariant Lagrangians ${cal L}_i$ ($i=1,...,5$) satisfying a Galilean symmetry in the flat space-time. The equations for a matter perturbation as well as an effective gravitational potential are derived under a quasi-static approximation on sub-horizon scales. This approximation can reproduce full numerical solutions with high accuracy for the wavelengths relevant to large-scale structures. For the model parameters constrained by the background expansion history of the Universe the growth rate of matter perturbations is larger than that in the LCDM model, with the growth index $gamma$ today typically smaller than 0.4. We also find that, even on very large scales associated with the Integrated-Sachs-Wolfe (ISW) effect in Cosmic Microwave Background (CMB) temperature anisotropies, the effective gravitational potential exhibits a temporal growth during the transition from the matter era to the epoch of cosmic acceleration. These properties are useful to distinguish the Galileon model from the LCDM in future high-precision observations., Comment: 17 pages, 5 figures

We derive the equation of matter density perturbations on sub-horizon scales around a flat Friedmann-Lema\^\i tre-Robertson-Walker background for the general Lagrangian density $f(R,\GB)$ that is a function of a Ricci scalar $R$ and a Gauss-Bonnet term $\GB$. We find that the effective gravitational constant generically scales as distance squared at small distances. The effect of this diminishing of the gravitational constant might be important in the gravitational dynamics of cosmic objects such as galaxies, which can be in principle tested by observations. We also provide the general expressions for the effective anisotropic stress, which is useful to constrain modified gravity models from observations of large-scale structure and weak lensing. We also find that there is a special class of theories which evade this unusual behaviour and that the condition to belong to this special class is exactly the same as the one for not having super-luminal modes with propagation speed proportional to their wavenumber., Comment: Accepted for publication in Progress of Theoretical Physics, references added and typos corrected, 13 pages

We study the cosmology of a covariant Galileon field with five covariant Lagrangians and confront this theory with the most recent cosmological probes: the type Ia supernovae data (Constitution and Union2 sets), cosmic microwave background (WMAP7) and the baryon acoustic oscillations (SDSS7). In the Galileon cosmology with a late-time de Sitter attractor, there is a tracker that attracts solutions with different initial conditions to a common trajectory. Including the cosmic curvature K, we place observational constraints on two distinct cases: (i) the tracker, and (ii) the generic solutions to the equations of motion. We find that the tracker solution can be consistent with the individual observational data, but it is disfavored by the combined data analysis. The generic solutions fare quite well when a non-zero curvature parameter is taken into account, but the Akaike and Bayesian information criteria show that they are not particularly favored over the LCDM model., Comment: 14 pages, 4 figures

The study of linear perturbation theory for general functions of the Ricci and Gauss-Bonnet scalars is done over an empty anisotropic universe, i.e. the Kasner-type background, in order to show that an anisotropic background in general has ghost degrees of freedom, which are absent on Friedmann-Lemaitre-Robertson-Walker (FLRW) backgrounds. The study of the scalar perturbation reveals that on this background the number of independent propagating degrees of freedom is four and reduces to three on FLRW backgrounds, as one mode becomes highly massive to decouple from the physical spectrum. When this mode remains physical, there is inevitably a ghost mode., Comment: 9 pages, uses RevTeX4.1

We derive the equations of linear cosmological perturbations for the general Lagrangian density $f (R,\phi, X)/2+L_c$, where $R$ is a Ricci scalar, $\phi$ is a scalar field, and $X=-(\nabla \phi)^2/2$ is a field kinetic energy. We take into account a nonlinear self-interaction term $L_c$ recently studied in the context of "Galileon" cosmology, which keeps the field equations at second order. Taking into account a scalar-field mass explicitly, the equations of matter density perturbations and gravitational potentials are obtained under a quasi-static approximation on sub-horizon scales. We also derive conditions for the avoidance of ghosts and Laplacian instabilities associated with propagation speeds. Our analysis includes most of modified gravity models of dark energy proposed in literature and thus it is convenient to test the viability of such models from both theoretical and observational points of view., Comment: 17 pages, no figures

In Brans-Dicke theory a non-linear self interaction of a scalar field allows a possibility of realizing the late-time cosmic acceleration, while recovering the General Relativistic behavior at early cosmological epochs. We extend this to more general modified gravitational theories in which a de Sitter solution for dark energy exists without using a field potential. We derive a condition for the stability of the de Sitter point and study the background cosmological dynamics of such theories. We also restrict the allowed region of model parameters from the demand for the avoidance of ghosts and instabilities. A peculiar evolution of the field propagation speed allows us to distinguish those theories from the LCDM model., Comment: 14 pages, 4 figures, version to appear in JCAP

Over the past decade, f(R) theories have been extensively studied as one of the simplest modifications to General Relativity. In this article we review various applications of f(R) theories to cosmology and gravity - such as inflation, dark energy, local gravity constraints, cosmological perturbations, and spherically symmetric solutions in weak and strong gravitational backgrounds. We present a number of ways to distinguish those theories from General Relativity observationally and experimentally. We also discuss the extension to other modified gravity theories such as Brans-Dicke theory and Gauss-Bonnet gravity, and address models that can satisfy both cosmological and local gravity constraints., Comment: 156 pages, 14 figures, Invited review article in Living Reviews in Relativity, Published version, Comments are welcome

We describe the linear cosmological perturbations of a perfect fluid at the level of an action, providing thus an alternative to the standard approach based only on the equations of motion. This action is suited not only to perfect fluids with a barotropic equation of state, but also to those for which the pressure depends on two thermodynamical variables. By quantizing the system we find that (1) some perturbation fields exhibit a noncommutativity quite analogous to the one observed for a charged particle moving in a strong magnetic field, (2) local curvature and pressure perturbations cannot be measured simultaneously, (3) ghosts appear if the null energy condition is violated., Comment: 4 pages, uses RevTeX. Title modified, references and comments added.

We study the propagation of the scalar modes around a Friedmann-Lemaitre-Robertson-Walker universe for general modifications of gravity in the presence of a real scalar field. In general, there will be two propagating scalar perturbation fields, which will have in total four degrees of freedom. Two of these degrees will have a superluminal propagation--with k-dependent speed of propagation--whereas the other two will travel with the speed of light. Therefore, the scalar degrees of freedom do not modify the general feature of modified gravity models: the appearance of modes whose frequency depends on the second power of the modulus of the wave vector. Constraints are given and special cases are discussed., Comment: 13 pages, 1 figure, uses RevTeX

We discuss solar system constraints on f(G) gravity models, where f is a function of the Gauss-Bonnet term G. We focus on cosmologically viable f(G) models that can be responsible for late-time cosmic acceleration. These models generally give rise to corrections of the form epsilon*(r/rs)^p to the vacuum Schwarzschild solution, where epsilon = H^2 rs^2 << 1, rs is the Schwarzschild radius of Sun, and H is the Hubble parameter today. We generally estimate the strength of modifications to General Relativity in order to confront models with a number of experiments such as the deflection of light and the perihelion shift. We show that cosmologically viable f(G) models can be consistent with solar system constraints for a wide range of model parameters., Comment: 19 pages, uses ReVTeX

We have found for the general class of Modified Gravity Models f(R,G) a new instability which can arise in vacuum for the scalar modes of the cosmological perturbations if the background is not de Sitter. In particular, the short-wavelength modes, if stable, in general have a group velocity which depends linearly in k, the wave number. Therefore these modes will be in general superluminal. We have also discussed the condition for which in general these scalar modes will be ghost-like. There is a subclass of these models, defined out of properties of the function f(R,G) and to which the f(R) and f(G) models belong, which however does not have this feature., Comment: 17 pages, 1 figure, uses RevTeX, references added

We derive exact solutions of the seven-dimensional Einstein-Maxwell equations for a spacetime exhibiting Poincare invariance along four-dimensions and spherical symmetry in the extra-dimensions. Such topology generically arises in the context of braneworld models. Our solutions generalise previous results on Ricci-flat spacetimes admitting the two-sphere and are shown to include wormhole configurations. A regular coordinate system suitable to describe the whole spacetime is singled-out and we discuss the physical relevance of the derived solutions., Comment: 14 pages, 8 figures, uses RevTeX. Physical discussion clarified, wormhole solutions added. References added