Topological invariant quintessence

Abstract

The issues of quintessence and cosmic acceleration can be discussed in the framework of $F(R, {\cal G})$ theories of gravity where $R$ is the Ricci curvature scalar and ${\cal G}$ is the Gauss-Bonnet topological invariant. It is possible to show that such an approach exhausts all the curvature content related to the Riemann tensor giving rise to a fully geometric approach to dark energy.