Cosmological inflation in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>F</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>R</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="script">G</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math>gravity

Cosmological inflation is discussed in the framework of $F(R,\mathcal{G})$ gravity where $F$ is a generic function of the curvature scalar $R$ and the Gauss--Bonnet topological invariant $\mathcal{G}$. 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 $R$, ${R}_{\ensuremath{\mu}\ensuremath{\nu}}$, ${R}_{\ensuremath{\sigma}\ensuremath{\mu}\ensuremath{\nu}}^{\ensuremath{\lambda}}$, etc., in the action. Cosmological dynamics results driven by two effective masses (lengths) are related to the $R$ scalaron and the $\mathcal{G}$ scalaron working respectively at early and very early epochs of cosmic evolution. In this sense, a double inflationary scenario naturally emerges.

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