Topological invariant quintessence

TL;DR

This paper explores a geometric approach to dark energy by analyzing $F(R, { m extbf{G}})$ theories of gravity, which incorporate Ricci scalar and Gauss-Bonnet invariants, to explain cosmic acceleration.

Contribution

It demonstrates that $F(R, { m f G})$ theories encompass all curvature-related aspects of the Riemann tensor, providing a comprehensive geometric framework for dark energy.

Findings

$F(R, { m f G})$ theories fully describe curvature contributions to dark energy.

The approach offers a unified geometric perspective on cosmic acceleration.

It extends the understanding of modified gravity models in cosmology.

Abstract

The issues of quintessence and cosmic acceleration can be discussed in the framework of $F(R, {\cal G})$ theories of gravity where $R$ is the Ricci curvature scalar and ${\cal G}$ is the Gauss-Bonnet topological invariant. It is possible to show that such an approach exhausts all the curvature content related to the Riemann tensor giving rise to a fully geometric approach to dark energy.