Stochastic Einstein equations with fluctuating volume

TL;DR

This paper introduces a stochastic model of Einstein's equations with fluctuating spacetime volume, demonstrating that quantum-inspired fluctuations can lead to cosmological solutions avoiding the initial big bang singularity.

Contribution

It formulates stochastic Einstein equations with a perfect-fluid source and applies them to a fluctuating FLRW cosmology, showing potential to resolve classical singularities.

Findings

Solutions avoid the initial big bang singularity

Fluctuations modeled as quantum spacetime effects

Classical singularities can be circumvented in stochastic models

Abstract

We develop a simple model to study classical fields on the background of a fluctuating spacetime volume. It is applied to formulate the stochastic Einstein equations with a perfect-fluid source. We investigate the particular case of a stochastic Friedmann-Lema\^itre-Robertson-Walker cosmology, and show that the resulting field equations can lead to solutions which avoid the initial big bang singularity. By interpreting the fluctuations as the result of the presence of a quantum spacetime, we conclude that classical singularities can be avoided even within a stochastic model that include quantum effects in a very simple manner.