Cosmology of a covariant Galileon field

We study the cosmology of a covariant scalar field respecting a Galilean symmetry in flat space-time. We show the existence of a tracker solution that finally approaches a de Sitter fixed point responsible for cosmic acceleration today. The viable region of model parameters is clarified by deriving conditions under which ghosts and Laplacian instabilities of scalar and tensor perturbations are absent. The field equation of state exhibits a peculiar phantom-like behavior along the tracker, which allows a possibility to observationally distinguish the Galileon gravity from the Lambda-CDM model.Comment: 4 pages, uses RevTe

Generalized Galileon cosmology

We study the cosmology of a generalized Galileon field $\phi$ with five covariant Lagrangians in which $\phi$ is replaced by general scalar functions $f_{i}(\phi)$ (i=1,...,5). For these theories, the equations of motion remain at second-order in time derivatives. We restrict the functional forms of $f_{i}(\phi)$ from the demand to obtain de Sitter solutions responsible for dark energy. There are two possible choices for power-law functions $f_{i}(\phi)$, depending on whether the coupling $F(\phi)$ with the Ricci scalar $R$ is independent of $\phi$ or depends on $\phi$. The former corresponds to the covariant Galileon theory that respects the Galilean symmetry in the Minkowski space-time. For generalized Galileon theories we derive the conditions for the avoidance of ghosts and Laplacian instabilities associated with scalar and tensor perturbations as well as the condition for the stability of de Sitter solutions. We also carry out detailed analytic and numerical study for the cosmological dynamics in those theories.Comment: 24 pages, 10 figures, version to appear in Physical Review

Cosmological perturbation in f(R,G) theories with a perfect fluid

In order to classify modified gravity models according to their physical properties, we analyze the cosmological linear perturbations for f(R,G) theories (R being the Ricci scalar and G, the Gauss-Bonnet term) with a minimally coupled perfect fluid. For the scalar type perturbations, we identify in general six degrees of freedom. We find that two of these physical modes obey the same dispersion relation as the one for a non-relativistic de Broglie wave. This means that spacetime is either highly unstable or its fluctuations undergo a scale-dependent super-luminal propagation. Two other modes correspond to the degrees of freedom of the perfect fluid, and propagate with the sound speed of such a fluid. The remaining two modes correspond to the entropy and temperature perturbations of the perfect fluid, and completely decouple from the other modes for a barotropic equation of state. We then provide a concise condition on f(R,G) theories, that both f(R) and R+f(G) do fulfill, to avoid the de Broglie type dispersion relation. For the vector type perturbation, we find that the perturbations decay in time. For the tensor type perturbation, the perturbations can be either super-luminal or sub-luminal, depending on the model. No-ghost conditions are also obtained for each type of perturbation.Comment: 12 pages, uses RevTe

Linear growth of matter density perturbations in f(R,G) theories

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 page

Solar system constraints on f(G) gravity models

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 ReVTe

Construction of cosmologically viable f(G) gravity models

We derive conditions under which f(G) gravity models, whose Lagrangian densities f are written in terms of a Gauss-Bonnet term G, are cosmologically viable. The most crucial condition to be satisfied is that f_GG, the second derivative of f with respect to G, must be positive, which is required to ensure the stability of a late-time de-Sitter solution as well as the existence of standard radiation/matter dominated epochs. We present a number of explicit f(G) models in which a cosmic acceleration is followed by the matter era. We find that the equation of state of dark energy can cross the phantom divide before reaching the present Universe. The viable models have asymptotic behavior f_GG goes to +0 when |G| goes to infinity, in which case a rapid oscillation of perturbations occurs unless such an oscillating degree of freedom is suppressed relative to a homogeneous mode in the early universe. We also introduce an iterative method to avoid numerical instabilities associated with a large mass of the oscillating mode.Comment: 12 pages, 5 figures, uses ReVTeX. Added references, minor correction

Inflationary gravitational waves in the effective field theory of modified gravity

In the approach of the effective field theory of modified gravity, we derive the second-order action and the equation of motion for tensor perturbations on the flat isotropic cosmological background. This analysis accommodates a wide range of gravitational theories including Horndeski theories, its generalization, and the theories with spatial derivatives higher than second order (e.g., Horava-Lifshitz gravity). We obtain the inflationary power spectrum of tensor modes by taking into account corrections induced by higher-order spatial derivatives and slow-roll corrections to the de Sitter background. We also show that the leading-order spectrum in concrete modified gravitational theories can be mapped on to that in General Relativity under a disformal transformation. Our general formula will be useful to constrain inflationary models from the future precise measurement of the B-mode polarization in the cosmic microwave background.Comment: 11 pages, no figure