Isotropic and Anisotropic Bouncing Cosmologies in Palatini Gravity

TL;DR

This paper investigates bouncing cosmologies within Palatini gravity theories, showing that certain quadratic models can produce non-singular, regular bounces in both isotropic and anisotropic universes, addressing big bang and anisotropy issues.

Contribution

It demonstrates that a specific quadratic Palatini gravity model yields regular bouncing solutions in both isotropic and anisotropic scenarios, solving key cosmological singularity problems without exotic matter.

Findings

All $f(R)$ models with isotropic bounces have shear singularities in anisotropic cases.

The quadratic model with $R+a R^2/R_P+R_{ ext{μν}}R^{ ext{μν}}/R_P$ provides regular bounces for a wide range of equations of state.

The model offers a purely gravitational resolution to big bang and anisotropy problems.

Abstract

We study isotropic and anisotropic (Bianchi I) cosmologies in Palatini $f(R)$ and $f(R,R_{\mu\nu}R^{\mu\nu})$ 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 $R+a R^2/R_P+R_{\mu\nu}R^{\mu\nu}/R_P$ 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.