Cosmological singularities in Born-Infeld determinantal gravity

The Born-Infeld determinantal gravity has been recently proposed as a way to smooth the big bang singularity. This theory is formulated on the Weitzenbock space-time and the teleparallel representation is used instead of the standard Riemannian representation. We find that although this theory is shown to be singularity free for a certain region of the parameter space in which the divergence of the Hubble rate in the high-energy regime is substituted by a de Sitter stage or a bounce in a Friedmann-Lemaitre-Robertson-Walker universe, cosmological singularities-such as a big rip, big bang, big freeze, and sudden singularities-can emerge in other regions of the configuration space of the theory. We also show that all these singular events exist even though the universe is filled with a perfect fluid with a constant equation of state.