Future Singularities of Isotropic Cosmologies

TL;DR

This paper investigates the types of future singularities in isotropic cosmological models, showing that most incomplete universes can only have singularities characterized by a non-integrable Hubble parameter, and discusses new inhomogeneous singularities.

Contribution

It demonstrates that in isotropic universes, only singularities with non-integrable Hubble parameters are possible, and introduces new lapse singularities in inhomogeneous models.

Findings

Most hyperbolic, future-incomplete isotropic universes have singularities with non-integrable Hubble parameter.

Examples from literature illustrate the occurrence of such singularities.

New types of lapse singularities are identified in inhomogeneous models.

Abstract

We show that globally and regularly hyperbolic future geodesically incomplete isotropic universes, except for the standard all-encompassing `big crunch', can accommodate singularities of only one kind, namely, those having a non-integrable Hubble parameter, $H$. We analyze several examples from recent literature which illustrate this result and show that such behaviour may arise in a number of different ways. We also discuss the existence of new types of lapse singularities in inhomogeneous models, impossible to meet in the isotropic ones.