Gauss-Bonnet as effective cosmological constant

TL;DR

This paper explores how Gauss-Bonnet terms in higher-dimensional gravity can generate effective cosmological constants, presenting explicit accelerating vacuum solutions in 5 and 6 dimensions with distinct behaviors in different solution branches.

Contribution

The paper provides explicit examples of accelerating vacuum solutions in Einstein-Gauss-Bonnet gravity, highlighting two solution branches with different limits and dependencies on the Gauss-Bonnet parameter.

Findings

Both solution branches have constant curvature and independent effective cosmological constants.

The '-' branch reduces to the bare cosmological constant as the Gauss-Bonnet parameter approaches zero.

The '+' branch is singular at zero Gauss-Bonnet parameter and inversely proportional to it when the bare value vanishes.

Abstract

It is known that Gauss-Bonnet terms in higher dimensional gravity can produce an effective cosmological constant. We add extra examples to this picture by presenting explicitly two branches of accelerating vacuum solutions to the Einstein-Gauss-Bonnet gravities with a bare cosmological constant in 5 and 6 dimensions. Both branches of solutions are of constant curvature and the effective cosmological constants are independent of the acceleration parameter. One branch (the "-" branch) of the solutions is well defined in the limit when the Gauss-Bonnet parameter approaches zero, in which case the effective cosmological constant becomes identical with the bare value, while the other (i.e. the "+") branch is singular in the same limit, and beyond this singular limit, the effective cosmological constant is inversely proportional to the Gauss-Bonnet parameter with a negative constant of proportionality when the bare value vanishes.