Conserved Quantities in Expanding G\"odel Cosmology

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.