# Friedmann-like universes with weak torsion: a dynamical system approach

## TL;DR

This paper analyzes the stability of Friedmann-like universes with weak torsion using dynamical systems, finding that such models are generally stable and can transition from torsional to torsion-free states.

## Contribution

It applies dynamical-system techniques to study the stability of Friedmann-like universes with weak torsion, identifying equilibrium points and their stability properties.

## Key findings

- Weak torsion universes are generally stable attractors.
- Equilibrium states can act as intermediate saddle points.
- Models can transition from torsional to torsion-free universes.

## Abstract

We consider Friedmann-like universes with torsion and take a step towards studying their stability. In so doing, we apply dynamical-system techniques to an autonomous system of differential equations, which monitors the evolution of these models via the associated density parameters. Assuming relatively weak torsion, we identify the system's equilibrium points. These are found to represent homogeneous and isotropic spacetimes with nonzero torsion that undergo accelerated expansion. We then examine the linear stability of the aforementioned fixed points. Our results indicate that Friedmann-like cosmologies with weak torsion are generally stable attractors, either asymptotically or in the Lyapunov sense. In addition, depending on the equation of state of the matter, the equilibrium states can also act as intermediate saddle points, marking a transition from a torsional to a torsion-free universe.