We present a complete analysis of the imprint of tensor anisotropies on the Cosmic Microwave Background for a class of f(R) gravity theories within the PPF-CAMB framework. We derive the equations, both for the cosmological background and gravitationa
l wave perturbations, required to obtain the standard temperature and polarization power spectra, taking care to include all effects which arise from f(R) modifications of both the background and the perturbation equations. For R^n gravity, we show that for n different from 2, the initial conditions in the radiation dominated era are the same as those found in General Relativity. We also find that by doing simulations which involve either modifying the background evolution while keeping the perturbation equations fixed or fixing the background to be the Lambda-CDM model and modifying the perturbation equations, the dominant contribution to deviations from General Relativity in the temperature and polarization spectra can be attributed to modifications in the background. This demonstrates the importance of using the correct background in perturbative studies of f(R) gravity. Finally an enhancement in the B-modes power spectra is observed which may allow for lower inflationary energy scales.
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-ord
er autonomous system and we give several examples which illustrate the utility of our method. We also discuss a number of results which have appeared recently in the literature.
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 perfe
ct 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.
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.
