Bounce Conditions in f(R) Cosmologies

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 bounces solutions. It is found that unlike the case of General Relativity, a bounce appears to be possible in open and flat cosmologies.Comment: 11 pages LaTe

The evolution of density perturbations in f(R) gravity

We give a rigorous and mathematically well defined presentation of the Covariant and Gauge Invariant theory of scalar perturbations of a Friedmann-Lemaitre-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 simple background solution of R^n gravity. We obtain exact solutions of the perturbations equations for scales much bigger than the Hubble radius. These solutions have a number of interesting features. In particular, we find that for all values of n there is always a growing mode for the density contrast, even if the universe undergoes an accelerated expansion. Such a behaviour does not occur in standard General Relativity, where as soon as Dark Energy dominates, the density contrast experiences an unrelenting decay. This peculiarity is sufficiently novel to warrant further investigation on fourth order gravity models.Comment: 21 pages, 2 figures, typos corrected, submitted to PR

One-loop corrections to the Drell--Yan process in SANC (II). The neutral current case

Radiative corrections to the neutral current Drell--Yan-like processes are considered. Complete one-loop electroweak corrections are calculated within the SANC system. Theoretical uncertainties are discussed. Numerical results are presented for typical conditions of LHC experiments.Comment: 17 pages, 9 figures, 3 table

The evolution of tensor perturbations in scalar-tensor theories of gravity

The evolution equations for tensor perturbations in a generic scalar tensor theory of gravity are presented. Exact solution are given for a specific class of theories and Friedmann-Lema\^{i}tre-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, no amplification is possible if the gravitational interaction is attractive.Comment: 11 pages, 2 figures, submitted to Physical Review

The evolution of cosmological gravitational waves in 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-Lemaitre-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 perturbations in Fourth Order Gravity, we apply the formalism to a simple background solution of R^n gravity. We obtain the exact solutions of the perturbation equations for scales much bigger than and smaller than the Hubble radius. It is shown that the evolution of tensor modes is highly sensitive to the choice of n and an interesting new feature arises. During the radiation dominated era, their exist a growing tensor perturbation for nearly all choices of n. This occurs even when the background model is undergoing accelerated expansion as opposed to the case of General Relativity. Consequently, cosmological gravitational wave modes can in principle provide a strong constraint on the theory of gravity independent of other cosmological data sets.Comment: 19 pages, 4 figures; v2: corrected to match version accepted for publication in PR

The phase portrait of a matter bounce in Horava-Lifshitz cosmology

The occurrence of a bounce in FRW cosmology requires modifications of general relativity. An example of such a modification is the recently proposed Horava-Lifshitz theory of gravity, which includes a ``dark radiation'' term with a negative coefficient in the analog of the Friedmann equation. This paper describes a phase space analysis of models of this sort with the aim of determining to what extent bouncing solutions can occur. A simplification, valid in the relevant region, allows a reduction of the dimension of phase space so that visualization in three dimensions is possible. It is found that a bounce is possible, but not generic in models under consideration. Apart from previously known bouncing solutions some new ones are also described. Other interesting solutions found include ones which describe a novel sort of oscillating universes.Comment: 14 pages, 8 figure

Cosmological dynamics in six-order gravity

We consider cosmological dynamics in generalized modified gravity theory with the $R\Box R$ term added to the action of the form $R+R^N$. Influence of $R \Box R$ term to the known solutions of modified gravity is described. We show that in particular case of $N=3$ these two non-Einstein terms are equally important on power-law solutions. These solutions and their stability have been studied using dynamical system approach. Some results for the case of $N \ne 3$ (including stability of de Sitter solution in the theory under investigation) have been found using other methods

A Geometrical Approach to Strong Gravitational Lensing in f(R) Gravity

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 R^n gravity. We find that for this case more bending is expected for R^n gravity theories in comparison to GR and is dependent on the value of n and the value of distance of closest approach of the incident null geodesic.Comment: 9 page

Compactifying the state space for alternative theories of gravity

In this paper we address important issues surrounding the choice of variables when performing a dynamical systems analysis of alternative theories of gravity. We discuss the advantages and disadvantages of compactifying the state space, and illustrate this using two examples. We first show how to define a compact state space for the class of LRS Bianchi type I models in $R^n$-gravity and compare to a non--compact expansion--normalised approach. In the second example we consider the flat Friedmann matter subspace of the previous example, and compare the compact analysis to studies where non-compact non--expansion--normalised variables were used. In both examples we comment on the existence of bouncing or recollapsing orbits as well as the existence of static models.Comment: 18 pages, revised to match published versio

Dynamics of f(R)-cosmologies containing Einstein static models

We study the dynamics of homogeneous isotropic FRW cosmologies with positive spatial curvature in $f(R)$-gravity, paying special attention to the existence of Einstein static models and only study forms of $f(R)=R^n$ for which these static models have been shown to exist. We construct a compact state space and identify past and future attractors of the system and recover a previously discovered future attractor corresponding to an expanding accelerating model. We also discuss the existence of universes which have both a past and future bounce, a phenomenon which is absent in General Relativity.Comment: 14 pages, 6 figure