Initial data on big bang singularities in symmetric settings

TL;DR

This paper introduces a geometric framework for initial data at big bang singularities, unifying various results in symmetric cosmological models and providing new insights into their structure.

Contribution

It proposes a general geometric notion of initial data on big bang singularities and reinterprets existing solutions within this framework.

Findings

Rephrases Bianchi class A orthogonal stiff solutions in geometric terms

Rephrases $ ext{T}^3$-Gowdy symmetric vacuum solutions in geometric terms

Provides a unified perspective on initial data at big bang singularities

Abstract

In a recent article, we propose a general geometric notion of initial data on big bang singularities. This notion is of interest in its own right. However, it also serves the purpose of giving a unified perspective on many of the results in the literature. In the present article, we give a partial justification of this statement by rephrasing the results concerning Bianchi class A orthogonal stiff solutions and solutions in the $\mathbb{T}^{3}$-Gowdy symmetric vacuum setting in terms of our general geometric notion of initial data on the big bang singularity.