Introduction to Palatini theories of gravity and nonsingular cosmologies

TL;DR

This paper provides an overview of Palatini theories of gravity, focusing on their mathematical foundations and applications to non-singular cosmologies that avoid the big bang singularity, including multiple perfect fluids.

Contribution

It offers a detailed derivation of field equations for general Lagrangian Palatini theories and extends previous non-singular cosmology analyses to more complex fluid models.

Findings

Palatini theories can produce non-singular cosmological models.

Extended analysis includes multiple perfect fluids in non-singular scenarios.

Mathematical framework for Palatini gravity is systematically developed.

Abstract

These notes are a summary of lectures given at the Instituto de Astronomia of the Universidad Nacional Autonoma de Mexico (UNAM), the Dipartimento di Fisica of the Universita degli studi di Salerno (Italy), and the Instituto de Fisica Corpuscular of the Universitat de Valencia (Spain) during the year 2012. Basic mathematical aspects of Palatini theories of gravity, which are constructed assuming that metric and connection are independent geometrical entities, are briefly introduced and discussed, and followed by a detailed derivation of the field equations of some rather general Lagrangian theories. Applications to the early universe are considered paying special attention to the avoidance of the big bang singularity. The analysis of non-singular cosmologies carried out in arXiv:1005.4136 [gr-qc] is extended to include several perfect fluids.