Globally hyperbolic geodesically complete cosmological model

TL;DR

This paper presents a new cosmological model with cylindrical symmetry, featuring a stiff fluid, that is globally hyperbolic, geodesically complete, and asymptotically flat, with a universe evolving from contraction to expansion.

Contribution

It introduces a novel perfect fluid cosmological model with specific symmetry and completeness properties, expanding understanding of possible universe evolutions.

Findings

The model is globally hyperbolic and geodesically complete.

Curvature invariants are regular everywhere.

The universe transitions from contraction to expansion.

Abstract

In this talk we shall show a perfect fluid cosmological model and its properties. The model possesses an orthogonally transitive abelian two-dimensional group of isometries that corresponds to cylindrical symmetry. The matter content is a stiff fluid that satisfies the energy and generic conditions. The metric is not separable in comoving coordinates for the fluid. The curvature invariants are shown to be regular everywhere in the coordinate chart and also indicate that the spacetime is asymptotically flat. Furthermore the causal geodesics are studied in order to determine that they are complete and that the model is globally hyperbolic. The model goes through an initial contracting epoch that is followed by an expanding era.