Cosmological inflation in $F(R,\mathcal{G})$ gravity

TL;DR

This paper explores cosmological inflation within $F(R,\mathcal{G})$ gravity, demonstrating that the theory can account for all curvature invariants and naturally leads to a double inflationary scenario driven by two effective masses.

Contribution

It introduces a framework where $F(R,\mathcal{G})$ gravity can exhaust all curvature invariants without derivatives, leading to a natural double inflation scenario.

Findings

The theory can account for all curvature invariants without derivatives.

A double inflationary scenario naturally emerges from the dynamics.

Two effective masses drive inflation at different cosmic epochs.

Abstract

Cosmological inflation is discussed in the framework of $F(R,{\cal G})$ gravity where $F$ is a generic function of the curvature scalar $R$ and the Gauss-Bonnet topological invariant $\cal G$. The main feature that emerges in this analysis is the fact that this kind of theory can exhaust all the curvature budget related to curvature invariants without considering derivatives of $R,$ $R_{\mu\nu}$, $R^{\lambda}_{\sigma\mu\nu}$ etc. in the action. Cosmological dynamics results driven by two effective masses (lenghts) related to the $R$ scalaron and the $\cal G$ scalaron working respectively at early and very early epochs of cosmic evolution. In this sense, a double inflationary scenario naturally emerges.