# Analysis of big bounce in Einstein--Cartan cosmology

## TL;DR

This paper investigates how Einstein--Cartan gravity modifies early universe dynamics, showing that fermion spin-induced torsion replaces the big bang with a bounce, with specific conditions for closed universes.

## Contribution

It demonstrates the conditions under which a nonsingular big bounce occurs in Einstein--Cartan cosmology, highlighting differences between closed, open, and flat universes.

## Key findings

- A closed universe requires a threshold function of scale factor and temperature.
- Open and flat universes do not have the bounce restriction.
- The scale factor exhibits a double bounce behavior during temperature variation.

## Abstract

We analyze the dynamics of a homogeneous and isotropic universe in the Einstein--Cartan theory of gravity. The spin of fermions produces spacetime torsion that prevents gravitational singularities and replaces the big bang with a nonsingular big bounce. We show that a closed universe exists only when a particular function of its scale factor and temperature is higher than some threshold value, whereas an open and a flat universes do not have such a restriction. We also show that a bounce of the scale factor is double: as the temperature increases and then decreases, the scale factor decreases, increases, decreases, and then increases.