Beyond the Friedmann-Lemaitre-Robertson-Walker Big Bang singularity

TL;DR

This paper introduces a modified Einstein equation that remains smooth at the Big Bang singularity, extending the applicability of Einstein's theory in cosmological models.

Contribution

A new tensor equation derived from Einstein's equation that is valid at the Big Bang singularity, avoiding the breakdown of standard formulations.

Findings

Equation remains smooth at the Big Bang singularity

Equivalent to Einstein's equation where defined

Applicable in wider cosmological situations

Abstract

Einstein's equation, in its standard form, breaks down at the Big Bang singularity. A new version, equivalent to Einstein's whenever the latter is defined, but applicable in wider situations, is proposed. The new equation remains smooth at the Big Bang singularity of the Friedmann-Lemaitre-Robertson-Walker model. It is a tensor equation defined in terms of the Ricci part of the Riemann curvature. It is obtained by taking the Kulkarni-Nomizu product between Einstein's equation and the metric tensor.