Bouncing Cosmologies From Born–Infeld-Type Gravity

Abstract

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