Dynamic compactification with stabilized extra dimensions in cubic Lovelock gravity

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.

Field-theoretical construction of currents and superpotentials in Lovelock gravity

“…Indeed, Λ 0 is related to the coupling constant α 0 only that is considered in (6.4) together with other α p only, there is no other sense for Λ 0 . This treatment is close to the one in [35,36].…”

Anisotropic cosmological dynamics in Einstein–Gauss–Bonnet gravity: an example of dynamical compactification in $$7+1$$ dimensions

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