Gauss-Bonnet Cosmology Unifying Late and Early-time Acceleration Eras with Intermediate Eras

TL;DR

This paper explores vacuum $F(G)$ gravity to unify early and late-time cosmic acceleration with intermediate eras, revealing limitations in producing scale-invariant primordial spectra compared to $F(R)$ gravity.

Contribution

It demonstrates the potential of vacuum $F(G)$ gravity to model a unified cosmic evolution with singularities, but highlights its inability to generate scale-invariant primordial spectra.

Findings

Unified cosmological evolution with Type IV singularities in $F(G)$ gravity.

Inability of $F(G)$ models to produce scale-invariant primordial spectra.

Contrast with $F(R)$ gravity which can produce compatible spectra.

Abstract

In this paper we demonstrate that with vacuum $F(G)$ gravity it is possible to describe the unification of late and early-time acceleration eras with the radiation and matter domination era. The Hubble rate of the unified evolution contains two mild singularities, so called Type IV singularities, and the evolution itself has some appealing features, such as the existence of a deceleration-acceleration transition at late times. We also address quantitatively a fundamental question related to modified gravity models description of cosmological evolution: Is it possible for all modified gravity descriptions of our Universe evolution, to produce a nearly scale invariant spectrum of primordial curvature perturbations? As we demonstrate, the answer for the $F(G)$ description is no, since the resulting power spectrum is not scale invariant, in contrast to the $F(R)$ description studied in the literature. Therefore, although the cosmological evolution can be realized in the context of vacuum $F(G)$ gravity, the evolution is not compatible with the observational data, in contrast to the $F(R)$ gravity description of the same cosmological evolution.