Through the Big Bang

TL;DR

This paper develops a relational description of Bianchi IX cosmology, revealing that the big bang/crunch can be a regular point in the evolution and predicting chaotic behavior in vacuum-dominated cases.

Contribution

It introduces a relational framework for classical Bianchi IX cosmology, decoupling scale from other degrees of freedom and analyzing singularities in a novel way.

Findings

Relational description predicts infinite chaos in vacuum-dominated Bianchi IX.

Big bang/crunch can be a regular point, not an end, in relational evolution.

Identifies two connected singular solutions with continuous relational DOFs.

Abstract

All measurements are comparisons. The only physically accessible degrees of freedom (DOFs) are dimensionless ratios. The objective description of the universe as a whole thus predicts only how these ratios change collectively as one of them is changed. Here we develop a description for classical Bianchi IX cosmology implementing these relational principles. The objective evolution decouples from the volume and its expansion degree of freedom. We use the relational description to investigate both vacuum dominated and quiescent Bianchi IX cosmologies. In the vacuum dominated case the relational dynamical system predicts an infinite amount of change of the relational DOFs, in accordance with the well known chaotic behaviour of Bianchi IX. In the quiescent case the relational dynamical system evolves uniquely though the point where the decoupled scale DOFs predict the big bang/crunch. This is a non-trivial prediction of the relational description; the big bang/crunch is not the end of physics - it is instead a regular point of the relational evolution. Describing our solutions as spacetimes that satisfy Einstein's equations, we find that the relational dynamical system predicts two singular solutions of GR that are connected at the hypersurface of the singularity such that relational DOFs are continuous and the orientation of the spatial frame is inverted.