Regularized big bang singularity: Geodesic congruences

TL;DR

This paper explores a regularization of the big bang singularity within 4D general relativity using degenerate metrics, analyzing geodesic behavior and implications for cosmological singularity theorems.

Contribution

It introduces a novel regularization approach allowing degenerate metrics in 4D GR and studies geodesic congruences in this modified cosmological model.

Findings

Calculation of geodesic expansion in the regularized model

Insights into the behavior of timelike and null geodesics

Discussion on implications for singularity theorems

Abstract

We investigate a particular regularization of big bang singularity, which remains within the domain of 4-dimensional general relativity but allowing for degenerate metrics. We study the geodesics and geodesic congruences in the modified Friedmann-Lema\^itre-Robertson-Walker universe. In particular, we calculate the expansion of timelike and null geodesic congruences. Based on these results, we also briefly discuss the cosmological singularity theorems.