# Stability of the Einstein static Universe in Einstein-Cartan-Brans-Dicke gravity

## TL;DR

This paper investigates the stability of the Einstein static universe within Einstein-Cartan-Brans-Dicke gravity, demonstrating that stable, non-singular, oscillating cosmological solutions exist under certain parameter conditions.

## Contribution

It introduces the analysis of Einstein static universe stability in Einstein-Cartan-Brans-Dicke gravity with torsion and spin effects, revealing conditions for stable, oscillating universe models.

## Key findings

- Existence of stable Einstein static solutions under specific parameters.
- Stable solutions allow for non-singular, oscillating cosmological scenarios.
- Parameter space analysis shows large regions of stability for the model.

## Abstract

In the present work we consider the existence and stability of Einstein static {\sf ES} Universe in Brans-Dicke ({\sf BD}) theory with non-vanishing spacetime torsion. In this theory, torsion field can be generated by the {\sf BD} scalar field as well as the intrinsic angular momentum (spin) of matter. Assuming the matter content of the Universe to be a Weyssenhoff fluid, which is a generalization of perfect fluid in general relativity ({\sf GR}) in order to include the spin effects, we find that there exists a stable {\sf ES} state for a suitable choice of the model parameters. We analyze the stability of the solution by considering linear homogeneous perturbations and discuss the conditions under which the solution can be stable against these type of perturbations. Moreover, using dynamical system techniques and numerical analysis, the stability regions of the {\sf ES} Universe are parametrized by the {\sf BD} coupling parameter and first and second derivatives of the {\sf BD} scalar field potential, and it is explicitly shown that a large class of stable solutions exists within the respective parameter space. This allows for non-singular emergent cosmological scenarios where the Universe oscillates indefinitely about an initial {\sf ES} solution and is thus past eternal.