Dark energy in modified Gauss-Bonnet gravity: Late-time acceleration and the hierarchy problem

Abstract

Dark energy cosmology is considered in a modified Gauss-Bonnet (GB) model of gravity where an arbitrary function of the GB invariant, $f(G)$, is added to the general relativity action. We show that a theory of this kind is endowed with a quite rich cosmological structure: it may naturally lead to an effective cosmological constant, quintessence, or phantom cosmic acceleration, with a possibility for the transition from deceleration to acceleration. It is demonstrated in the paper that this theory is perfectly viable, since it is compliant with the solar system constraints. Specific properties of $f(G)$ gravity in a de Sitter (dS) universe, such as dS and SdS solutions, their entropy, and its explicit one-loop quantization are studied. The issue of a possible solution of the hierarchy problem in modified gravities is also addressed.