String-inspired Gauss-Bonnet gravity reconstructed from the universe expansion history and yielding the transition from matter dominance to dark energy

TL;DR

This paper reconstructs scalar-Gauss-Bonnet and modified Gauss-Bonnet gravities from the universe's expansion history, demonstrating models that transition from matter dominance to dark energy-driven acceleration, consistent with observations.

Contribution

It introduces new reconstructed gravity models that naturally produce the matter to dark energy transition without requiring exotic matter components.

Findings

Matter dominance and acceleration transition can occur with matter only.

Late-time acceleration can be de Sitter or ΛCDM-like with w close to -1.

Stability criteria for de Sitter solutions are derived from one-loop effective action.

Abstract

We consider scalar-Gauss-Bonnet and modified Gauss-Bonnet gravities and reconstruct these theories from the universe expansion history. In particular, we are able to construct versions of those theories (with and without ordinary matter), in which the matter dominated era makes a transition to the cosmic acceleration epoch. It is remarkable that, in several of the cases under consideration, matter dominance and the deceleration-acceleration transition occur in the presence of matter only. The late-time acceleration epoch is described asymptotically by de Sitter space but may also correspond to an exact $\Lambda$CDM cosmology, having in both cases an effective equation of state parameter $w$ close to -1. The one-loop effective action of modified Gauss-Bonnet gravity on the de Sitter background is evaluated and it is used to derive stability criteria for the ensuing de Sitter universe.