We use the 1+ 1+ 2 covariant approach to clarify a number of aspects of spherically symmetric solutions of non-minimally coupled scalar tensor theories. Particular attention is focused on the extension of Birkhoff's theorem and the nature of quasi-local horizons in this context.
The dynamical system approach has recently acquired great importance in the investigation on higher order theories of gravity. In this talk I review some of the main results obtained with this method and I consider briefly a number of further developments. © 2007 IOP Publishing Ltd.
The evolution equations for tensor perturbations in a generic scalar-tensor theory of gravity are presented. Exact solutions are given for a specific class of theories and Friedmann-Lemaître-Robertson-Walker backgrounds. In these cases it is shown that, although the evolution of tensor models depends on the choice of parameters of the theory,...
We present for the first time the complete matter power spectrum for Rn gravity which has been derived from the fourth order scalar perturbation equations. This leads to the discovery of a characteristic signature of fourth order gravity in the matter power spectrum, the details of which have not seen before in other studies in this area and...
We investigate the connection between dark energy and fourth-order gravity by analyzing the behavior of scalar perturbations around a Friedmann-Robertson- Walker background. The evolution equations for scalar perturbations are derived using the covariant and gauge invariant approach and applied to two simple, yet widely studied f(R) gravity...
We give a rigorous and mathematically clear presentation of the covariant and gauge-invariant theory of gravitational waves in a perturbed Friedmann-Lemaître-Robertson-Walker universe for fourth order gravity, where the matter is described by a perfect fluid with a barotropic equation of state. As an example of a consistent analysis of tensor...
We present a detailed investigation of the cosmological dynamics based on exp(-R/Λ) gravity. We apply the dynamical system approach to both the vacuum and matter cases and obtain exact solutions and their stability in the finite and asymptotic regimes. The results show that cosmic histories exist which admit a double de Sitter phase which could...
The covariant gauge-invariant perturbation theory of scalar cosmological perturbations is developed for a general scalar-tensor Friedmann-Lemaitre- Robertson-Walker cosmology in a vacuum. The perturbation equations are then solved exactly in the long wavelength limit for a specific coupling, potential, and background. Differences with the...
Building on earlier work, we discuss a general framework for exploring the cosmological dynamics of Higher Order Theories of Gravity. We show that once the theory of gravity has been specified, the cosmological equations can be written as a first-order autonomous system and we give several examples which illustrate the utility of our method. We...
We give a rigorous and mathematically well defined presentation of the covariant and gauge invariant theory of scalar perturbations of a Friedmann-Lemaître-Robertson-Walker universe for fourth order gravity, where the matter is described by a perfect fluid with a barotropic equation of state. The general perturbations equations are applied to a...
We present a new approach of the reconstruction method based on the use of the cosmic parameters instead of a time law for the scale factor. This solution generating technique allows the derivation and analysis of a set of new non-trivial exact cosmological solutions for f(R)-gravity. Specifically, we find two new cyclic solutions and we...
We investigate the conditions for a bounce to occur in Friedmann-Robertson-Walker cosmologies for the class of fourth-order gravity theories. The general bounce criterion is determined and constraints on the parameters of three specific models are given in order to obtain bounce solutions. Furthermore, unlike the case of general relativity, a...
A detailed analysis of dynamics of cosmological models based on R n gravity is presented. We show that the cosmological equations can be written as a first-order autonomous system and analysed using the standard techniques of dynamical system theory. In the absence of perfect fluid matter, we find exact solutions whose behaviour and stability...
We give the equations governing the shear evolution in Bianchi spacetimes for general f(R) theories of gravity. We consider the case of R n-gravity and perform a detailed analysis of the dynamics in Bianchi I cosmologies which exhibit local rotational symmetry. We find exact solutions and study their behaviour and stability in terms of the...
We pursue a (l+3)-covariant analysis of cosmological peculiar velocity of pressure-free matter induced by the matter density perturbations in modified f(R) gravity theories. Instead of working in a quasi-Newtonian Eulerian frame, we select a curvature comoving Lagrangian frame, which means the shear and heat energy flux are non-zero. This is...
We consider the case of Rn-gravity and perform a detailed analysis of the dynamics in Bianchi I cosmologies which exhibit local rotational symmetry (LRS). We find exact solutions and study their behaviour and stability in terms of the values of the parameter n. In particular, we found a set of cosmic histories in which the universe is initially...
We study the phase space of Friedmann-Lemaître-Robertson-Walker (FLRW) models derived from scalar-tensor gravity where the non-minimal coupling is F() = ξ2 and the effective potential is V() = λn. Our analysis allows one to unfold many features of the cosmology of this class of theories. For example, the evolution mechanism towards states...
We develop a new covariant formalism to treat spherically symmetric spacetimes in metric f(R) theories of gravity. Using this formalism we derive the general equations for a static and spherically symmetric metric in a general f(R) gravity. These equations are used to determine the conditions for which the Schwarzschild metric is the only...
We present a framework for the study of lensing in spherically symmetric spacetimes within the context of f(R) gravity. Equations for the propagation of null geodesics, together with an expression for the bending angle, are derived for any f(R) theory and then applied to an exact spherically symmetric solution of Rn gravity. We find that for...
We present a new framework for the study of lensing in spherically symmetric spacetimes within the context of f(R) gravity. © 2012 American Institute of Physics.