Early-time cosmic dynamics in $f(R)$ and $f(|\hat\Omega|)$ extensions of Born-Infeld gravity

TL;DR

This paper investigates early-universe dynamics in modified Born-Infeld gravity theories, demonstrating the persistence of nonsingular bouncing solutions and inflationary phases in these extensions.

Contribution

It introduces two extensions of Born-Infeld gravity in the Palatini formulation and analyzes their early-universe solutions, highlighting the robustness of nonsingular and inflationary behaviors.

Findings

Nonsingular bouncing solutions are stable in the extended theories.

Inflationary solutions occur even with radiation dominance.

Extensions preserve key features of original Born-Infeld gravity.

Abstract

We consider two types of modifications of Born-Infeld gravity in the Palatini formulation and explore their dynamics in the early universe. One of these families considers $f(R)$ corrections to the Born-Infeld Lagrangian, which can be seen as modifications of the dynamics produced by the quantum effects of matter, while the other consists on different powers of the elementary building block of the Born-Infeld Lagrangian, which we denote by $|\hat\Omega|$. We find that the two types of nonsingular solutions that arise in the original Born-Infeld theory are also present in these extensions, being bouncing solutions a stable and robust branch. Singular solutions with a period of approximate de Sitter inflation are found even in universes dominated by radiation.