Cosmological Singularities and Bel-Robinson Energy

TL;DR

This paper introduces a classification scheme for cosmological singularities in FRW universes using Bel-Robinson energy, encompassing known and novel singularity types, and applies it to both flat and curved models.

Contribution

It develops a comprehensive classification of cosmological singularities based on Bel-Robinson energy, extending to curved universes and predicting new singularity types.

Findings

Classifies all known cosmological singularities using Bel-Robinson energy.

Predicts new types of singularities beyond existing models.

Shows that asymptotic behaviors in flat universes also apply to curved universes.

Abstract

We consider the problem of describing the asymptotic behaviour of \textsc{FRW} universes near their spacetime singularities in general relativity. We find that the Bel-Robinson energy of these universes in conjunction with the Hubble expansion rate and the scale factor proves to be an appropriate measure leading to a complete classification of the possible singularities. We show how our scheme covers all known cases of cosmological asymptotics possible in these universes and also predicts new and distinct types of singularities. We further prove that various asymptotic forms met in flat cosmologies continue to hold true in their curved counterparts. These include phantom universes with their recently discovered big rips, sudden singularities as well as others belonging to graduated inflationary models.