A Note on the Viability of Gauss-Bonnet Cosmology

TL;DR

This paper investigates the dynamics of vacuum Gauss-Bonnet cosmology in 4+1 dimensions, revealing that most trajectories from the standard singularity lead to re-collapse, with only a negligible measure evolving smoothly to Einstein phase.

Contribution

The study provides a detailed analysis of the background dynamics in Gauss-Bonnet cosmology, highlighting the limited conditions under which smooth evolution to Einstein phase occurs.

Findings

Most trajectories from the standard singularity lead to re-collapse.

Trajectories from non-standard singularity evolve into the Kasner regime.

The measure of trajectories leading to smooth evolution is negligibly small.

Abstract

In this paper, we analyze the viability of a vacuum Gauss-Bonnet cosmology by examining the dynamics of the homogeneous and anisotropic background in 4+1 dimensions. The trajectories of the system either originate from the standard singularity or from non-standard type, the later is characterized by the divergence of time derivative of the Hubble parameters for its finite value. At the onset, the system should relax to Einstein phase at late times as the effect of Gauss-Bonnet term becomes negligible in the low energy regime. However, we find that most of the trajectories emerging from the standard big-bang singularity lead to future re-collapse whereas the system beginning its evolution from the non-standard singularity enters the Kasner regime at late times. This leads to the conclusion that the measure of trajectories giving rise to a smooth evolution from a standard singularity to the Einstein phase is negligibly small for generic initial conditions.