The Dominant Balance at Cosmological Singularities

TL;DR

This paper introduces a method for analyzing finite-time singularities in vector fields, with applications to cosmology, specifically examining singularities in isotropic universes filled with perfect fluids in general relativity.

Contribution

It proposes a new technique for asymptotic analysis of vector fields near finite-time singularities, tailored for cosmological applications.

Findings

Defined finite-time singularities of vector fields

Developed an asymptotic analysis method for such singularities

Applied the method to isotropic universes with perfect fluids

Abstract

We define the notion of a finite-time singularity of a vector field and then discuss a technique suitable for the asymptotic analysis of vector fields and their integral curves in the neighborhood of such a singularity. Having in mind the application of this method to cosmology, we also provide an analysis of the time singularities of an isotropic universe filled with a perfect fluid in general relativity.