Deformed Horava-Lifshitz Cosmology and Stability of Einstein Static Universe

TL;DR

This paper investigates the stability of the Einstein static universe within deformed Hořava-Lifshitz cosmology, deriving conditions for stability against various perturbations and highlighting the influence of matter fields and cosmological parameters.

Contribution

It provides new stability criteria for the Einstein static universe in deformed Hořava-Lifshitz cosmology, including conditions for scalar, vector, and tensor perturbations, and explores effects of matter fields and cosmological parameters.

Findings

No stable Einstein static universe for flat case ($k=0$).

Stability against tensor perturbations for large $mbda$ values.

Conditions on matter fields for stability in curved universes.

Abstract

Stability of the Einstein static universe versus the linear scalar, vector and tensor perturbations is investigated in the context of deformed Ho\v{r}ava-Lifshitz cosmology inspired by entropic force scenario. A general stability condition against the linear scalar perturbations is obtained. Using this general condition, it is shown that there is no stable Einstein static universe for the case of flat universe, $k=0$. For the the special case of large values of running parameter of HL gravity $\omega$, in a positively curved universe $k>0$, the domination of the quintessence and phantom matter fields with barotropic equation of state parameter $\beta<-\frac{1}{3}$ is necessary while for a negatively curved universe $k<0$, the matter fields with $\beta> -\frac{1}{3}$ are needed to be the dominant fields of the universe. Also, a neutral stability against the vector perturbations is obtained. Finally, an inequality including the cosmological parameters of the Einstein static universe is obtained for the stability against the tensor perturbations. It turns out that for large $\omega$ values, there is a stability against the tensor perturbations.