Little Rip, $\Lambda$CDM and singular dark energy cosmology from Born-Infeld-$f(R)$ gravity

Understand

We study late-time cosmic accelerating dynamics from Born-Infeld-$f(R)$ gravity in a simplified conformal approach.

• We find that a variety of cosmic efects such as Little Rip, $\Lambda$CDM universe and dark energy cosmology with finite-time future singularities may occur.
• Unlike the convenient Born-Infeld gravity where in the absence of matter only de Sitter expansion may emerge, apparentlly any FRW cosmology maybe reconstructed from this conformal version of the Born-Infeld-$f(R)$ theory.
• Despite the fact that the explicit form of $f(R)$ is fixed by the conformal ansatz, the relation between the two metrics in this approach may be changed so as to bring out any desired FRW cosmology.