Continuation of Bianchi Spacetimes Through The Big Bang

TL;DR

This paper introduces a relational framework in General Relativity that allows for a smooth continuation of cosmological models through the Big Bang singularity without quantum gravity, by removing scale as a dynamical variable.

Contribution

It develops a scale-invariant, relational description of cosmological spacetimes enabling solutions to pass through the Big Bang singularity in various Bianchi models.

Findings

Solutions pass smoothly through the Big Bang in flat FLRW, Bianchi I, and Bianchi IX models.

Relational variables decouple from scale, enabling a continuous extension through the singularity.

The framework avoids quantum gravity effects by using a scale-invariant approach.

Abstract

In this paper we present a framework in which the relational description of General Relativity can be used to smoothly continue cosmological dynamical systems through the Big Bang without invoking quantum gravity effects. Cosmological spacetimes contain as a key dynamical variable a notion of scale through the volume factor $\nu$. However no cosmological observer is ever able to separate their measuring apparatus from the system they are measuring, in that sense every measurement is a relative one and measurable dynamical variables are in fact dimensionless ratios. This is manifest in the identification of a scaling symmetry or ``Dynamical Similarity" in the Einstein-Hilbert action associated with the volume factor. By quotienting out this scaling symmetry, we form a relational system defined on a contact manifold whose dynamical variables are decoupled from scale. When the phase space is reduced to shape space, we show that there exist unique solutions to the equations of motion that pass smoothly through the initial cosmological singularity in flat FLRW, Bianchi I and Quiescent Bianchi IX cosmologies.