Multifractality in the general cosmological solution of Einstein's equations

TL;DR

This paper explores the potential for multifractal turbulence in the early universe's inhomogeneous regions, based on scale invariance in Einstein's equations and the behavior of Bianchi type IX models.

Contribution

It demonstrates the scale invariance of vacuum Bianchi type IX equations and discusses the possibility of multifractal turbulence near cosmological singularities.

Findings

Scale invariance of Bianchi type IX equations established

Potential for multifractal turbulence in early universe suggested

Differences between gravitational and hydrodynamical turbulence outlined

Abstract

We demonstrate the scale invariance of the vacuum Bianchi type IX equations and use this to argue for the possibility of multifractal turbulence as a realisation of the suggestion by Belinski that there will be a fragmentation of local regions of inhomogeneous Mixmaster chaos on approach to an initial inhomogeneous cosmological singularity. Differences between the gravitational and hydrodynamical situations are outlined. Various potential obstacles to this picture of gravitational turbulence are discussed.