Isotropic and anisotropic bouncing cosmologies in Palatini gravity

Abstract

We study isotropic and anisotropic (Bianchi I) cosmologies in Palatini f (R) and f (R, R µν R µν ) theories of gravity and consider the existence of non-singular bouncing solutions in the early universe. We find that all f (R) models with isotropic bouncing solutions develop shear singularities in the anisotropic case. On the contrary, the simple quadratic model R + aR 2 /R P + R µν R µν /R P exhibits regular bouncing solutions in both isotropic and anisotropic cases for a wide range of equations of state, including dust (for a < 0) and radiation (for arbitrary a). It thus represents a purely gravitational solution to the big bang singularity and anisotropy problems of general relativity without the need for exotic (w > 1) sources of matter/energy.

Introduction to Palatini Theories of Gravity and Nonsingular Cosmologies

“…This value of the density implies that f R = 1 − 2aρ d /ρ P = 0. This condition, f R = 0, characterizes the location of the bounce in Palatini f (R) theories with a single fluid with constant equation of state [5]. For our quadratic model, in particular, bouncing solutions exist if the dynamics allows to reach the density…”

“…(20) and (22) can be used to write the field equations for the metric and the connection for specific choices of the Lagrangian f (g µν , R α βµν ). To make contact with the literature [26], [5] , [23], we now focus on the case f (R,…”

“…The classification of the bouncing solutions of the model (82) with a fluid with constant w was carried out in [5]. It was found that for every value of the parameter a there exist an infinite number of bouncing solutions, which depend on the particular equation of state w. The bouncing solutions can be divided into two large classes:…”

“…This observation has been possible thanks to the formulas presented in section 5, where we have extended the analysis carried out in [5] for a single perfect fluid with constant equation of state to include several perfect fluids with arbitrary equation of state w(ρ). This allows to explore the dynamics of realistic cosmological models with several fluids and is a necessary step prior to the consideration of the growth and evolution of inhomogeneities in these nonsingular backgrounds.…”

“…This allows to explore the dynamics of realistic cosmological models with several fluids and is a necessary step prior to the consideration of the growth and evolution of inhomogeneities in these nonsingular backgrounds. Though the model (82) has been proposed on grounds of mathematical simplicity and motivated by the form of the effective action provided by perturbative quantization schemes in curved backgrounds, its ability to successfully deal with cosmological [5] and black hole singularities [27] as well as other aspects of quantum gravity phenomenology [26] demands further theoretical work to provide a more solid ground to it. In this sense, we note that the effective dynamics of loop quantum cosmology [4] in a Friedmann-Robertson-Walker background filled with a massless scalar can be exactly reproduced by a Palatini f (R) theory [22].…”