Cosmological inflation in $F(R,\mathcal{G})$ gravity
  Cosmological inflation is discussed in the framework of $F(R,{\cal G})$
gravity where $F$ is a generic function of the curvature scalar $R$ and the
Gauss-Bonnet topological invariant $\cal G$. The main feature that emerges in
this analysis is the fact that this kind of theory can exhaust all the
curvature budget related to curvature invariants without considering
derivatives of $R,$ $R_{\mu\nu}$, $R^{\lambda}_{\sigma\mu\nu}$ etc. in the
action. Cosmological dynamics results driven by two effective masses (lenghts)
related to the $R$ scalaron and the $\cal G$ scalaron working respectively at
early and very early epochs of cosmic evolution. In this sense, a double
inflationary scenario naturally emerges.
