Emerging Universe from Scale Invariance

TL;DR

This paper presents a scale invariant gravity model with an $R^{2}$ term that enables a stable emerging universe scenario through spontaneous symmetry breaking and nonlinear scalar dynamics.

Contribution

It introduces a novel scale invariant model with an $R^{2}$ term and a non metric measure, demonstrating stable emerging universe solutions via spontaneous symmetry breaking.

Findings

Stable emerging universe solutions exist within the model.

Spontaneous symmetry breaking generates a non-trivial dilaton potential.

Nonlinear scalar dynamics are crucial for solution stability.

Abstract

We consider a scale invariant model which includes a $R^{2}$ term in action and show that a stable "emerging universe" scenario is possible. The model belongs to the general class of theories, where an integration measure independent of the metric is introduced. To implement scale invariance (S.I.), a dilaton field is introduced. The integration of the equations of motion associated with the new measure gives rise to the spontaneous symmetry breaking (S.S.B) of S.I. After S.S.B. of S.I. in the model with the $R^{2}$ term (and first order formalism applied), it is found that a non trivial potential for the dilaton is generated. The dynamics of the scalar field becomes non linear and these non linearities are instrumental in the stability of some of the emerging universe solutions, which exists for a parameter range of the theory.