Friedmann-like universes with torsion

TL;DR

This paper explores how torsion in homogeneous and isotropic universes influences cosmic evolution, deriving modified equations, analyzing effects on expansion and nucleosynthesis, and identifying stable static models with torsion.

Contribution

It introduces a specific torsion form compatible with symmetry, derives torsional cosmological equations, and demonstrates torsion's significant impact on universe dynamics and stability.

Findings

Torsion can induce exponential expansion similar to dark energy.

Strong bounds on torsion strength are derived from primordial helium-4 production.

Torsion allows for stable static universe models with various spatial geometries.

Abstract

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.