The Osgood Criterion and Finite-Time Cosmological Singularities

TL;DR

This paper uses Osgood's criterion to identify and analyze finite-time singularities in various cosmological models, showing how initial conditions influence singularity formation and suggesting ways to avoid them.

Contribution

It applies Osgood's criterion to cosmology, providing a novel method to detect and potentially eliminate finite-time singularities in universe models.

Findings

Certain initial conditions lead to finite-time singularities.

Choice of initial conditions depends on matter parameters and cosmological constant.

Osgood's criterion can help in designing singularity-free cosmological models.

Abstract

In this paper, we apply Osgood's criterion from the theory of ordinary differential equations to detect finite-time singularities in a spatially flat FLRW universe in the context of a perfect fluid, a perfect fluid with bulk viscosity, and a Chaplygin and anti-Chaplygin gas. In particular, we applied Osgood's criterion to demonstrate singularity behaviour for Type 0/big crunch singularities as well as Type II/sudden singularities. We show that in each case the choice of initial conditions is important as a certain number of initial conditions leads to finite-time, Type 0 singularities, while other precise choices of initial conditions which depend on the cosmological matter parameters and the cosmological constant can avoid such a finite-time singularity. Osgood's criterion provides a powerful and yet simple way of deducing the existence of these singularities, and also interestingly enough, provides clues of how to eliminate singularities from certain cosmological models.