On the stability of static ghost cosmologies

TL;DR

This paper demonstrates that a static universe with a ghost scalar field is linearly stable against various perturbations, contrasting with traditional models, and explores implications for initial states in cosmology.

Contribution

It introduces a stable static ghost cosmology and analyzes its response to different perturbations, revealing unique stability properties not present in conventional models.

Findings

Homogeneous and isotropic perturbations are stable with oscillatory solutions.

Density perturbations remain unchanged over time.

Vortical distortions vanish and gravitational waves oscillate with constant amplitude.

Abstract

We consider the classical linear stability of a static universe filled with a non-interacting mixture of isotropic radiation and a ghost scalar field. Unlike the conventional Einstein static model, this cosmology is stable against homogeneous and isotropic perturbations. This is shown by means of exact oscillatory solutions about the original static state. We also examine the linear response of the static ghost universe to all types of inhomogeneous fluctuations, namely density, vorticity and gravitational-wave perturbations. The results show that the static background constrains the linear evolution of these distortions, to the extent that density perturbations remain time invariant, vortical distortions vanish and gravitational waves oscillate with constant amplitude. We discuss the potential implications of these results for past-eternal initial states in classical general relativistic cosmology.