  Cosmic history can be traced considering further curvature contributions
inside the gravitational action. Assuming that standard General Relativity can
be extended by other curvature invariants, we discuss the possibility that an
action containing higher-order curvature terms can fit, in principle, the whole
universe evolution. In particular, a theory like $F(R,{\cal G})$, with $R$ the
Ricci scalar and $\cal G$ the Gauss-Bonnet topological term, contains all the
curvature invariants that, depending on the energy regime, can address
inflation, matter dominated and dark energy regimes. In this paper, we
investigate this possibility considering how $F(R,{\cal G})$ models can lead
gravity from ultraviolet to infrared scales. Specifically, we will take into
account a cosmographic approach for this purpose.
