The Big Bang in $T^3$ Gowdy Cosmological Models

TL;DR

This paper explores the connection between stationary axisymmetric spacetimes and $T^3$ Gowdy cosmological models, proposing a method to generate solutions with specific initial conditions near the Big Bang.

Contribution

It establishes a formal relationship enabling the generation of Gowdy models from initial singularity data, advancing solution construction in cosmology.

Findings

Demonstrates a method to derive Gowdy models from singularity data

Shows potential to construct solutions with arbitrary spatial behavior at the Big Bang

Provides preliminary insights into the behavior of cosmological solutions near the initial singularity

Abstract

We establish a formal relationship between stationary axisymmetric spacetimes and $T^3$ Gowdy cosmological models which allows us to derive several preliminary results about the generation of exact cosmological solutions and their possible behavior near the initial singularity. In particular, we argue that it is possible to generate a Gowdy model from its values at the singularity and that this could be used to construct cosmological solutions with any desired spatial behavior at the Big Bang.