Dynamic compactification with stabilized extra dimensions in cubic Lovelock gravity

TL;DR

This paper investigates dynamic compactification in cubic Lovelock gravity, revealing the existence of realistic regimes where both the observable universe and extra dimensions stabilize, differing from Einstein-Gauss-Bonnet gravity.

Contribution

It demonstrates that cubic Lovelock gravity admits stable compactification regimes with maximally symmetric solutions, unlike Einstein-Gauss-Bonnet gravity, and shows coexistence with isotropizing solutions.

Findings

Existence of phenomenologically realistic compactification regimes.

Presence of at least one maximally symmetric solution in cubic Lovelock gravity.

Coexistence of compactification and isotropizing solutions for certain parameters.

Abstract

In this paper the dynamic compactification in Lovelock gravity with a cubic term is studied. The ansatz will be of space-time where the three dimensional space and the extra dimensions are constant curvature manifolds with independent scale factors. The numerical analysis shows that there exist a phenomenologically realistic compactification regime where the three dimensional hubble parameter and the extra dimensional scale factor tend to a constant. This result comes as surprise as in Einstein-Gauss-Bonnet gravity this regime exists only when the couplings of the theory are such that the theory does not admit a maximally symmetric solution (i.e. "geometric frustration"). In cubic Lovelock gravity however there always exists at least one maximally symmetric solution which makes it fundamentally different from the Einstein-Gauss-Bonnet case. Moreover, in opposition to Einstein-Gauss-Bonnet Gravity, it is also found that for some values of the couplings and initial conditions these compactification regimes can coexist with isotropizing solutions.