Bouncing cosmologies from Born-Infeld-type gravity

Abstract

We construct a Born-Infeld-type $f(R,\mathcal{G})$ modification of gravity, where $\mathcal{G}$ is the Gauss-Bonnet term, by embedding Born-Infeld electrodynamics in a five-dimensional pure modified gravity. This method leads to the correspondence between curvature scalars and electromagnetic field strength scalars -- $R\leftrightarrow F_{\hat{I}¼\hat{I}½}{F}^{\hat{I}¼\hat{I}½}$ and $\mathcal{G}\leftrightarrow (\hat{I}{\mu }_{\hat{I}¼\hat{I}½\ddot{I}\ddot{I}ƒ}{F}^{\hat{I}¼\hat{I}½}{F}^{\ddot{I}\ddot{I}ƒ}{)}^2$ -- allowing us to replicate the structure of Born-Infeld electrodynamics in the gravitational sector. The resulting Born-Infeld-type gravity is a ghost-free $f(R,\mathcal{G})$ theory which reduces to Einstein gravity in the low energy limit. In this work we focus on bouncing cosmological solutions of such a theory, which require positive spatial curvature. By using both the Jordan and Einstein frame analyses, we find a vast space of bouncing solutions with different asymptotic behaviors, including solutions with multiple bounces grouped together. Observational consequences of such solutions will be investigated in the future.

46 pages, 24 figures