Friedmann Dynamics Recovered from Compactified Einstein–Gauss–Bonnet Cosmology

Abstract

In this paper cosmological dynamics in Einstein-Gauss-Bonnet gravity with a perfect fluid source in arbitrary dimension is studied. A systematic analysis is performed for the case that the theory does not admit maximally symmetric solutions. Considering two independent scale factors, namely one for the three dimensional space and one for the extra dimensional space, is found that a regime exists where the two scale factors tend to a constant value via damped oscillations for not too negative pressure of the fluid, so that asymptotically the evolution of the $(3+1)$-dimensional Friedmann model with perfect fluid is recovered. At last, it is worth emphasizing that the present numerical results strongly support a 't Hooft-like interpretation of the parameter $1/D$ (where $D$ is the number of extra dimensions) as a small expansion parameter in very much the same way as it happens in the large $N$ expansion of gauge theories with $1/N$. Indeed, the dependence on $D$ of many of the relevant physical quantities computed here manifests a clear WKB-like pattern, as expected on the basis of large $N$ arguments.