Classical big-bounce cosmology: dynamical analysis of a homogeneous and irrotational Weyssenhoff fluid

TL;DR

This paper analyzes a homogeneous, irrotational Weyssenhoff fluid in general relativity, showing it can produce a bounce avoiding initial singularity and exhibit oscillatory or inflationary behaviors depending on conditions.

Contribution

It provides a dynamical analysis of Weyssenhoff fluids without assuming specific spacetime metrics, revealing conditions for bounces and oscillations in cosmological models.

Findings

Weyssenhoff spin contributions can cause a cosmological bounce.

Some models exhibit eternal oscillatory behavior without singularities.

Inflationary periods require fine-tuning of parameters.

Abstract

A dynamical analysis of an effective homogeneous and irrotational Weyssenhoff fluid in general relativity is performed using the 1+3 covariant approach that enables the dynamics of the fluid to be determined without assuming any particular form for the space-time metric. The spin contributions to the field equations produce a bounce that averts an initial singularity, provided that the spin density exceeds the rate of shear. At later times, when the spin contribution can be neglected, a Weyssenhoff fluid reduces to a standard cosmological fluid in general relativity. Numerical solutions for the time evolution of the generalised scale factor in spatially-curved models are presented, some of which exhibit eternal oscillatory behaviour without any singularities. In spatially-flat models, analytical solutions for particular values of the equation-of-state parameter are derived. Although the scale factor of a Weyssenhoff fluid generically has a positive temporal curvature near a bounce, it requires unreasonable fine tuning of the equation-of-state parameter to produce a sufficiently extended period of inflation to fit the current observational data.