Description
We construct a Born--Infeld-type $f(R,{\cal G})$ modification of gravity, where ${\cal G}$ 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 ${\cal G}\leftrightarrow (\epsilon_{\mu\nu\rho\sigma}F^{\mu\nu}F^{\rho\sigma})^2$ -- allowing us to replicate the structure of Born--Infeld electrodynamics in the gravitational sector. The resulting Born--Infeld-type gravity is a ghost-free $f(R,{\cal G})$ 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.
