Cosmology in Palatini theories of gravity

TL;DR

This paper reviews recent developments in Palatini gravity theories, focusing on their cosmological applications such as explaining cosmic acceleration and avoiding the big bang singularity, with explicit derivations of field equations.

Contribution

It provides a comprehensive analysis of extended Palatini gravity theories, including f(R) models and those with torsion, highlighting their potential in cosmological modeling.

Findings

f(R) theories can explain cosmic acceleration

Certain models avoid the big bang singularity

Explicit field equations for extended Palatini theories are derived

Abstract

We discuss recent results on the cosmology of extended theories of gravity formulated in the Palatini approach, i.e., assuming that metric and connection are independent fields. In particular, we focus on the attempts to explain the cosmic speedup with f(R) theories and on models that avoid the big bang singularity. The field equations for gravity Lagrangians of the form f(g_{\mu\nu},{R^\alpha}_{\beta\mu\nu}) (including torsion) are explicitly derived and discussed.