Conserved Quantities in Expanding G\"odel Cosmology

TL;DR

This paper investigates perturbations in an expanding G"odel universe, identifying gauge-invariant conserved quantities, including a spatial metric trace perturbation, for different matter contents, enhancing understanding of such cosmological models.

Contribution

It introduces gauge-invariant conserved quantities in expanding G"odel cosmology, extending previous work to include matter content beyond dust.

Findings

Identified a conserved spatial metric trace perturbation in EG cosmology.

Extended conservation results to perfect fluid matter content.

Demonstrated gauge invariance of key perturbation quantities.

Abstract

At linear order we study perturbations to a G\"odel background spacetime which includes expansion in addition to rotation. We investigate the transformation behaviour of these perturbations under gauge transformations and construct gauge invariant quantities. Using the perturbed energy conservation equation we find that there are conserved quantities in Expanding G\"odel (EG) Cosmology, in particular a spatial metric trace perturbation, {\zeta} SMTP , which is conserved on large scales for pressureless dust. We finally extend our discussion to a perfect fluid matter content to also obtain conserved quantities in this context.