Emergent Universe in f(Q) gravity theories

TL;DR

This paper explores how $f(Q)$ gravity theories can model a stable Einstein Static universe, potentially resolving the Big Bang singularity by providing a non-singular emergent universe scenario.

Contribution

It investigates stable solutions in $f(Q)$ gravity for curved FRW universes and proposes a method for transitioning from static to inflationary phases.

Findings

Stable Einstein Static solutions exist in $f(Q)$ gravity.

The model can describe a non-singular emergent universe.

A mechanism for exit from static to inflationary phase is proposed.

Abstract

One resolution of the ancient cosmic singularity, i.e., the Big Bang Singularity (BBS), is to assume an inflationary stage preceded by a long enough static state in which the universe and its physical properties would oscillate around certain equilibrium points. The early period is referred to as the Einstein Static (ES) Universe phase, which characterizes a static phase with positive spatial curvature. A stable Einstein static state can serve as a substitute for BBS, followed by an inflationary period known as the Emergent Scenario. The initial need has not been fulfilled within the context of General Relativity, prompting the investigation of modified theories of gravity. The current research aims to find such a solution within the framework of symmetric teleparallel gravity, specifically in the trendy $f(Q)$ theories. An analysis has been conducted to investigate stable solutions for both positively and negatively curved spatial FRW universes, in the presence of a perfect fluid, by utilizing various torsion-free and curvature-free affine connections. Additionally, we propose a method to facilitate an exit from a stable ES to a subsequent inflationary phase. We demonstrate that $f(Q)$ gravity theories have the ability to accurately depict the emergence of the universe.