Barotropic index w-singularities in cosmology

TL;DR

This paper introduces a new type of cosmological singularity called a w-singularity, characterized by finite scale factor and vanishing energy density and pressure, with unique properties and duality relations to big-bang singularities.

Contribution

It presents an explicit cosmological model with a novel w-singularity, expanding understanding of singularities beyond traditional classifications.

Findings

w-singularities occur with finite scale factor and vanishing energy density and pressure.

w-singularities differ from type IV and big-brake singularities in key aspects.

Examples of w-singularities are found in f(R), scalar field, and brane cosmologies.

Abstract

We find an explicit cosmological model which allows a special type of cosmological singularity which we call a $w$-singularity. This singularity has the scale factor finite, the energy density and pressure vanishing, and the only singular behaviour appears in a time-dependent barotropic index $w(t)$. It is different from the type IV cosmological singularity in that it does not exhibit the divergence of the higher derivatives of the Hubble parameter and from the big-brake since it does not fulfill the anti-Chaplygin gas equation of state. We also find an interesting duality between the $w$-singularities and the big-bang singularities. Physical examples of $w$-singularities appear in $f(R)$, scalar field and brane cosmologies.