Stability of the Einstein Static Universe in open cosmological models

TL;DR

This paper investigates the stability of Einstein Static universes within open cosmological models under quantum gravity modifications, revealing conditions for neutral stability or instability in different frameworks.

Contribution

It extends stability analysis of Einstein Static solutions to open models in Loop Quantum Cosmology and Horava-Lifshitz gravity, highlighting new stability conditions.

Findings

Found neutrally stable solutions in open models within Loop Quantum Cosmology.

Identified parameter-dependent stability in Horava-Lifshitz gravity.

Demonstrated modifications alter classical stability properties.

Abstract

The stability properties of the Einstein Static solution of General Relativity are altered when corrective terms arising from modification of the underlying gravitational theory appear in the cosmological equations. In this paper the existence and stability of static solutions are considered in the framework of two recently proposed quantum gravity models. The previously known analysis of the Einstein Static solutions in the semiclassical regime of Loop Quantum Cosmology with modifications to the gravitational sector is extended to open cosmological models where a static neutrally stable solution is found. A similar analysis is also performed in the framework of Horava-Lifshitz gravity under detailed balance and projectability conditions. In the case of open cosmological models the two solutions found can be either unstable or neutrally stable according with the admitted values of the parameters.