Isotropization in the approach to big rip singularities for Cardassian models

TL;DR

This paper extends Cardassian models to general homogeneous geometries and demonstrates that big rip singularities are common, with the universe tending to isotropize as it approaches these singularities, similar to late-time accelerated expansion.

Contribution

It generalizes Cardassian models beyond homogeneous and isotropic cases and analyzes the isotropization process near big rip singularities.

Findings

Big rip singularities occur in more general homogeneous models.

Isotropization happens as the universe approaches a big rip.

The isotropization resembles late-time acceleration in cosmology.

Abstract

Cardassian models are an alternative to general relativity which have been proposed as an approach to explaining accelerated cosmic expansion while avoiding directly introducing dark energy. They are generally formulated only in the homogeneous and isotropic case. In this paper an extension of the usual formulation to general spatially homogeneous geometries is given. A characteristic feature of many classes of Cardassian models is the occurrence of big rip singularities where the scale factor tends to infinity after a finite time. It is shown that big rip singularities are also widespread in more general homogeneous cases. It is also shown that there is isotropization in the approach to a big rip singularity which bears a strong resemblance to the late-time isotropization observed in cosmological spacetimes which accelerate forever in the future.