Regularization of the big bang singularity with random perturbations

TL;DR

This paper demonstrates how to regularize the big bang singularity in a contracting universe with scalar fields by incorporating stochastic perturbations, revealing a discrete set of conditions for a smooth transition to expansion.

Contribution

It extends previous deterministic models by including random perturbations, showing that the universe's transition through the big bang can be uniquely extended under specific co-prime number conditions.

Findings

Regularization of the big bang with stochastic methods.

Discrete set of equation of state values for smooth transition.

Robustness of the transition under random perturbations.

Abstract

We show how to regularize the big bang singularity in the presence of random perturbations modeled by Brownian motion using stochastic methods. We prove that the physical variables in a contracting universe dominated by a scalar field can be continuously and uniquely extended through the big bang as a function of time to an expanding universe only for a discrete set of values of the equation of state satisfying special co-prime number conditions. This result significantly generalizes a previous result \cite{Xue:2014} that did not model random perturbations. This result implies that the extension from a contracting to an expanding universe for the discrete set of co-prime equation of state is robust, which is a surprising result. Implications for a purely expanding universe are discussed, such as a non-smooth, randomly varying scale factor near the big bang.