Cosmological implications of Born-Infeld-f(R) gravity

In this paper, a modified Born-Infeld gravitation theory with an f(R) function being added to the determinant action is analyzed from a cosmological viewpoint. The corresponding accelerating dynamics are studied in a simplified conformal approach without matter. Three different structures for the auxiliary metric function are analyzed, with the aim to establish a deeper understanding of the role of this function in cosmology. After performing the analysis, it is seen that by modifying the auxiliary metric function, a Big Rip singularity or either a Little Rip dark energy model may arise.