Primordial brusque bounce in Born-Infeld determinantal gravity

Abstract

We study a particular exact solution to the Born-Infeld determinantal gravity consisting of a cosmological model which undergoes a brusque bounce. The latter consists of an event characterized by a non-null (but finite) value of the squared Hubble rate occurring at a minimum (non-null) scale factor. The energy density and pressure of the fluid covering the whole manifold are perfectly well behaved in such an event, but the curvature invariants turn out to be undefined there because of the undefined character of the time derivative of H. It is shown that the spacetime results geodesically complete and singularity free, and that it corresponds to a picture of an eternal Universe in which a (somewhat unconventional) bounce replaces the standard Big Bang singularity. This example tends to emphasize that, beyond Einstein's theory of General Relativity, and in the context of extended theories of gravity formulated by purely torsional means, the criterion of a singularity based on pathologies of scalars constructed upon the Riemann curvature tensor, becomes objectionable.