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 -- $R\leftrightarrow F_{\mu \nu }{F}^{\mu \nu }$ and $\mathcal{G}\leftrightarrow ({\epsilon }_{\mu \nu \rho \sigma }{F}^{\mu \nu }{F}^{\rho \sigma }{)}^2$ -- 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.

v2: 47 pages, 24 figures; Accepted version