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arXiv · 1507.02241

The Osgood Criterion and Finite-Time Cosmological Singularities

Ikjyot Singh Kohli
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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.

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BibTeXRIS

Ikjyot Singh Kohli. 2016-04-27. The Osgood Criterion and Finite-Time Cosmological Singularities. https://doi.org/10.1002/andp.201500360

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