Stochastic Einstein equations

TL;DR

This paper explores stochastic Einstein equations where the 3D space metric is stochastic, linking probability densities to Perelman's entropy, and examines their implications using the Friedman Universe as an example.

Contribution

It introduces stochastic Einstein equations with metrics linked to Perelman's entropy, analyzing their effects on cosmological models like the Friedman Universe.

Findings

Dynamical evolution of the Friedman Universe remains unchanged

Connection established between general relativity and Ricci flows

Stochastic metrics linked to entropy functional

Abstract

Stochastic Einstein equations are considered when 3D space metric $\gamma_{ij}$ are stochastic functions. The probability density for the stochastic quantities is connected with the Perelman's entropy functional. As an example, the Friedman Universe is considered. It is shown that for the Friedman Universe the dynamical evolution is not changed. The connection between general relativity and Ricci flows is discussed.