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

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 such theory is endowed with a quite rich cosmological structure: it may naturally lead to an effective cosmological constant, quintessence or phantom cosmic acceleration, with a possible transition from deceleration to acceleration. It is demonstrated in the paper that this theory is perfectly viable, since it is compliant with Solar System constraints. Specific properties of $f(G)$ gravity in a de Sitter 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 addressed too.