  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.

High Energy Physics - Theory;Astrophysics;General Relativity and Quantum Cosmology;High Energy Physics - Phenomenology