Tracing the cosmic history by Gauss-Bonnet gravity

TL;DR

This paper explores how extending General Relativity with higher-order curvature invariants like $F(R,{ m extbf{G}})$ can model the entire cosmic evolution, from inflation to dark energy, using a cosmographic approach.

Contribution

It introduces a framework for using $F(R,{ m extbf{G}})$ gravity models to describe the full history of the universe's expansion.

Findings

$F(R,{ m extbf{G}})$ models can unify different cosmic epochs.

Cosmographic analysis constrains the form of $F(R,{ m extbf{G}})$ functions.

Higher-order curvature terms are viable for describing ultraviolet to infrared gravitational regimes.

Abstract

Cosmic history can be traced considering further curvature contributions inside the gravitational action. Assuming that standard General Relativity can be extended by other curvature invariants, we discuss the possibility that an action containing higher-order curvature terms can fit, in principle, the whole universe evolution. In particular, a theory like $F(R,{\cal G})$, with $R$ the Ricci scalar and $\cal G$ the Gauss-Bonnet topological term, contains all the curvature invariants that, depending on the energy regime, can address inflation, matter dominated and dark energy regimes. In this paper, we investigate this possibility considering how $F(R,{\cal G})$ models can lead gravity from ultraviolet to infrared scales. Specifically, we will take into account a cosmographic approach for this purpose.