Speed of light in the extended gravity theories

We shall investigate the possibility of formulation of varying speed of light (VSL) in the framework of Palatini non-linear Ricci scalar and Ricci squared theories. Different speeds of light including the causal structure constant, electromagnetic, and gravitational wave speeds are discussed. We shall see that two local frames are distinguishable and discuss about the velocity of light in these two frames. We shall investigate which one of these local frames is inertial.Comment: 19 pages. to appear in Classical Quantum Gravit

Breakdown of the initial value formulation of scalar-tensor gravity and its physical meaning

We revisit singularities of two distinct kinds in the Cauchy problem of general scalar-tensor theories of gravity (previously discussed in the literature), and of metric and Palatini f(R) gravity, in both their Jordan and Einstein frame representations. Examples and toy models are used to shed light onto the problem and it is shown that, contrary to common lore, the two conformal frames are equivalent with respect to the initial value problem.Comment: 14 pages, LaTex, to appear in Phys. Rev.

Modified gravity with R-matter couplings and (non-)geodesic motion

We consider alternative theories of gravity with a direct coupling between matter and the Ricci scalar We study the relation between these theories and ordinary scalar-tensor gravity, or scalar-tensor theories which include non-standard couplings between the scalar and matter. We then analyze the motion of matter in such theories, its implications for the Equivalence Principle, and the recent claim that they can alleviate the dark matter problem in galaxies.Comment: typos corrected, minor changes, version published in CQ

f(R) Gravity with Torsion: The Metric-Affine Approach

The role of torsion in f(R) gravity is considered in the framework of metric-affine formalism. We discuss the field equations in empty space and in presence of perfect fluid matter taking into account the analogy with the Palatini formalism. As a result, the extra curvature and torsion degrees of freedom can be dealt as an effective scalar field of fully geometric origin. From a cosmological point of view, such a geometric description could account for the whole Dark Side of the Universe.Comment: 12 page

f(R,L_m) gravity

We generalize the $f(R)$ type gravity models by assuming that the gravitational Lagrangian is given by an arbitrary function of the Ricci scalar $R$ and of the matter Lagrangian $L_m$. We obtain the gravitational field equations in the metric formalism, as well as the equations of motion for test particles, which follow from the covariant divergence of the energy-momentum tensor. The equations of motion for test particles can also be derived from a variational principle in the particular case in which the Lagrangian density of the matter is an arbitrary function of the energy-density of the matter only. Generally, the motion is non-geodesic, and takes place in the presence of an extra force orthogonal to the four-velocity. The Newtonian limit of the equation of motion is also considered, and a procedure for obtaining the energy-momentum tensor of the matter is presented. The gravitational field equations and the equations of motion for a particular model in which the action of the gravitational field has an exponential dependence on the standard general relativistic Hilbert--Einstein Lagrange density are also derived.Comment: 6 pages, no figures; minor modifications, references added; accepted for publication in EPJ

On the non-minimal gravitational coupling to matter

The connection between $f(R)$ theories of gravity and scalar-tensor models with a "physical" metric coupled to the scalar field is well known. In this work, we pursue the equivalence between a suitable scalar theory and a model that generalises the $f(R)$ scenario, encompassing both a non-trivial scalar curvature term and a non-minimum coupling of the scalar curvature and matter. This equivalence allows for the calculation of the PPN parameters $\beta$ and $\gamma$ and, eventually, a solution to the debate concerning the weak-field limit of $f(R)$ theories.Comment: 11 page

On The Existence Of Anisotropic Cosmological Models In Higher-Order Theories Of Gravity

We investigate the behaviour on approach to the initial singularity in higher-order extensions of general relativity by finding exact cosmological solutions for a wide class of models in which the Lagrangian is allowed to depend nonlinearly upon the three possible linear and quadratic scalars built from the Riemann tensor; $R$, $R_{ab}R^{ab}$ and $R_{abcd}R^{abcd}$. We present new anisotropic vacuum solutions analagous to the Kasner solutions of general relativity and extend previous results to a much wider range of fourth order theories of gravity. We discuss the implications of these results for the behaviour of the more general anisotropic Bianchi type VIII and IX cosmologies as the initial singularity is approached. Furthermore, we also consider the existence conditions for some other simple anisotropic Bianchi I vacuum solutions in which the expansion in each direction is of exponential, rather than power-law behaviour and their relevance for cosmic ``no-hair'' theorems.Comment: 24 pages, submitted to CQ

f(R) Gravity and scalar-tensor theory

In the present paper we will investigate the relation between scalar-tensor theory and $f(R)$ theories of gravity. Such studies have been performed in the past for the metric formalism of $f(R)$ gravity; here we will consider mainly the Palatini formalism, where the metric and the connections are treated as independent quantities. We will try to investigate under which circumstances $f(R)$ theories of gravity are equivalent to scalar-tensor theory and examine the implications of this equivalence, when it exists.Comment: minor changes to match published version, references adde

A tomographic description for classical and quantum cosmological perturbations

Classical and quantum perturbations can be described in terms of marginal distribution functions in the framework of tomographic cosmology. In particular, the so called Radon transformation and the mode-parametric quantum oscillator description can give rise to links between quantum and classical regimes. The approach results a natural scheme to discuss the transition from the quantum to the classical perturbations and then it could be a workable scheme to connect primordial fluctuations with the today observed large scale structure.Comment: 12 page

Scalar potential in F(R) supergravity

We derive a scalar potential in the recently proposed N=1 supersymmetric generalization of f(R) gravity in four space-time dimensions. Any such higher-derivative supergravity is classically equivalent to the standard N=1 supergravity coupled to a chiral (matter) superfield, via a Legendre-Weyl transform in superspace. The Kaehler potential, the superpotential and the scalar potential of that theory are all governed by a single holomorphic function. We also find the conditions for the vanishing cosmological constant and spontaneous supersymmetry breaking, without fine-tuning, which define a no-scale F(R) supergravity. The F(R) supergravities are suitable for physical applications in the inflationary cosmology based on supergravity and superstrings.Comment: 10 pages, LateX, no figures; section 4 extende