We consider spatially homogeneous and isotropic cosmologies with non-zero
torsion. Given the high symmetry of these universes, we adopt a specific form
for the torsion tensor that preserves the homogeneity and isotropy of the
spatial surfaces. Employing both covariant and metric-based techniques, we
derive the torsional versions of the continuity, the Friedmann and the
Raychaudhuri equations. These formulae demonstrate how, by playing the role of
the spatial curvature, or that of the cosmological constant, torsion can
drastically change the evolution of the classic homogeneous and isotropic
Friedmann universes. In particular, torsion alone can lead to exponential
expansion. For instance, in the presence of torsion, the Milne and the
Einstein-de Sitter universes evolve like the de Sitter model. We also show
that, by changing the expansion rate of the early universe, torsion can affect
the primordial nucleosynthesis of helium-4. We use this sensitivity to impose
strong cosmological bounds on the relative strength of the associated torsion
field, requiring that its ratio to the Hubble expansion rate lies in the narrow
interval (−0.005813,+0.019370) around zero. Interestingly, the introduction
of torsion can \textit{reduce} the production of primordial helium-4, unlike
other changes to the standard thermal history of an isotropic universe.
Finally, turning to static spacetimes, we find that there exist torsional
analogues of the classic 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.Comment: Revised article. Section on BBN limits on torsion added. References
added and update
