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arXiv · 1801.05690

Regularization of the big bang singularity with random perturbations

Edward Belbruno·BingKan Xue
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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.

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Edward Belbruno, BingKan Xue. 2018-01-13. Regularization of the big bang singularity with random perturbations. https://doi.org/10.1088/1361-6382%2Faaab3d

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