Classical Stability of Sudden and Big Rip Singularities

TL;DR

This paper analyzes the classical stability of sudden and Big Rip cosmological singularities under small perturbations, providing conditions under which these singularities remain stable or become unstable.

Contribution

It offers a comprehensive gauge-invariant perturbation analysis of sudden and Big Rip singularities, identifying stability conditions across all curvature types.

Findings

Sudden singularities with finite scale factor and density are generally stable.

Big Rip singularities can be stable or unstable depending on specific parameters.

Stability conditions are derived for scalar, vector, and tensor perturbations.

Abstract

We introduce a general characterization of sudden cosmological singularities and investigate the classical stability of homogeneous and isotropic cosmological solutions of all curvatures containing these singularities to small scalar, vector, and tensor perturbations using gauge invariant perturbation theory. We establish that sudden singularities at which the scale factor, expansion rate, and density are finite are stable except for a set of special parameter values. We also apply our analysis to the stability of Big Rip singularities and find the conditions for their stability against small scalar, vector, and tensor perturbations.