Friedmann-like universes with torsion

Abstract

We consider spatially homogeneous and isotropic cosmologies with non-vanishing torsion, which assumes a specific form due to the high symmetry of these universes. Using covariant and metric-based techniques, we derive the torsional versions of the continuity, the Friedmann and the Raychaudhuri equations. These show how torsion can drastically change the standard evolution of the Friedmann models, by playing the role of the spatial curvature or that of the cosmological constant. We find, for example, that torsion alone can lead to exponential expansion and thus make the Einstein–de Sitter universe look like the de Sitter cosmos. Also, by modifying the expansion rate of the early universe, torsion could have affected the primordial abundance of helium-4. We show, in particular, that torsion can reduce the production of primordial helium-4, unlike other changes to the standard thermal history of the universe. These theoretical results allow us to impose strong observational bounds on the relative strength of the associated torsion field, confining its ratio to the Hubble rate within the narrow interval (-0.005813,+0.019370) around zero. Finally, turning to static spacetimes, we demonstrate that there exist torsional analogues of the Einstein static universe with all three types of spatial geometry. These models can be stable when the torsion field and the universe’s spatial curvature have the appropriate profiles.