Big Rip and Big Crunch Cosmological Models in a Gravitational Field with Torsion

Abstract

The gravitational field with torsion is being constructed by using the parametrized absolute parallelism geometry. A generalized law of variation of Hubble’s parameter in evolutionary cosmological models is used. The cosmological models under the influence of the gravitational field with torsion are obtained and discussed. A new model of the Universe is presented using a special class of Riemann–Cartan geometry. This model is oscillating with expansion and contraction at different stages. It behaves normally as the conventional Big Bang model in the first half-age until it reaches the moment of a Big Rip, then reverses its behavior as a result of a changes in the pressure and torsion until it reaches a Big Crunch at the end of the second half-age. We suppose that the Big Rip singularity is replaced by a regular maximum of the scale factor at the Big Rip due to a possible physical mechanism of quantum nature. The positivity condition for the energy density of matter leads to exclusion of open and closed universes.