On the Stability of Einstein Static Universe in Doubly General Relativity Scenario

TL;DR

This paper investigates the stability of the Einstein Static Universe within the gravity's rainbow framework, showing conditions under which a stable, non-singular emergent universe can exist without violating energy conditions.

Contribution

It introduces a rainbow FRW model and analyzes the stability of Einstein static solutions considering quantum gravity modifications, extending the emergent universe scenario.

Findings

Positive energy condition implies positive spatial curvature.

Stable Einstein static solutions exist with energy-dependent cosmological constant.

Stability persists against scalar, vector, and tensor perturbations.

Abstract

By presenting a relation between average energy of the ensemble of probe photons and energy density of the Universe, in the context of {\it gravity's rainbow} or {\it doubly general relativity} scenario, we introduce a rainbow FRW Universe model. By analyzing the fixed points in flat FRW model modified by two well known rainbow functions, we find that the finite time singularity avoidance (i.e. Big-Bang) may still remain as a problem. Then, we follow the "Emergent Universe" scenario in which there is no beginning of time and consequently there is no Big-Bang singularity. Moreover, we study the impact of a high energy quantum gravity modifications related to the gravity's rainbow on the stability conditions of an "Einstein static Universe" (ESU). We find that independent of a particular rainbow function, the positive energy condition dictates a positive spatial curvature for the Universe. In fact, without raising a nonphysical energy condition in the quantum gravity regimes, we can address an agreement between gravity's rainbow scenario and basic assumption of modern version of "Emergent Universe". We show that in the absence and presence of an energy-dependent cosmological constant $\Lambda(\epsilon)$, a stable Einstein static solution is available versus the homogeneous and linear scalar perturbations under the variety of obtained conditions. Also, we explore the stability of ESU against the vector and tensor perturbations.