“Bouncing” of simple cosmological models with torsion

The known cosmological solutions of the Einstein-Cartan-Sciama-Kibble (ECSK) field equations are reviewed. The prevention of singularities is explained by means of the extension of the Hawking-Penrose singularity theorems to the ECSK theory. Singularity prevention in semiclassical “spinning dust” models derives from the postulated form of the canonical energy-momentum and spin angular momentum tensors for the matter distribution. The effects of shear, vorticity, and pressure are examined. The singularity behavior of cosmological models incorporating the Dirac field as the source of the metric and torsion is discussed. In these models one finds an enhancement, rather than a prevention of singularity formation. Finally, the consequences of spin and torsion for observational cosmology and for particle creation in the early universe are noted.