Big bounce and closed universe from spin and torsion

TL;DR

This paper explores how spin and torsion in Einstein-Cartan gravity can eliminate singularities, leading to a big bounce in a closed universe, and discusses conditions for inflation and dark energy acceleration.

Contribution

It demonstrates that spin-torsion coupling prevents singularities and allows a closed universe only above certain scale factor-temperature thresholds.

Findings

Big bounce replaces the Big Bang singularity.

Closed universe exists only above a specific scale factor-temperature product.

Conditions for inflation and dark energy acceleration are derived.

Abstract

We analyze the dynamics of a homogeneous and isotropic universe in the Einstein$--$Cartan theory of gravity. The coupling between the spin and torsion prevents gravitational singularities and replaces the Big Bang with a nonsingular big bounce, at which the universe transitions from contraction to expansion. We show that a closed universe exists only when the product of the scale factor and temperature is higher than a particular threshold, contrary to a flat universe and an open universe, which are not restricted. During inflation, this product must increase to another threshold, so that the universe can reach dark-energy acceleration.