Grand Rip and Grand Bang/Crunch cosmological singularities

TL;DR

This paper introduces a unifying framework for analyzing various cosmological singularities, including new types called grand rip and grand bang/crunch, characterized by diverging energy density and pressure faster than traditional models.

Contribution

It proposes a generalized approach using power and asymptotic expansions of the barotropic index to classify and understand diverse future cosmological singularities.

Findings

Identifies new singularities called grand rip and grand bang/crunch.

Shows these singularities involve diverging energy density and pressure faster than $t^{-2}$.

Demonstrates the scale factor lacks a convergent power series near these singularities.

Abstract

The present accelerated expansion of the universe has enriched the list of possible scenarios for its fate, singular or not. In this paper a unifying framework for analyzing such behaviors is proposed, based on generalized power and asymptotic expansions of the barotropic index $w$, or equivalently of the deceleration parameter $q$, in terms of the time coordinate. Besides well known singular and non-singular future behaviors, other types of strong singularities appear around the phantom divide in flat models, with features similar to those of big rip or big bang/crunch, which we have dubbed grand rip and grand bang/crunch respectively, since energy density and pressure diverge faster than $t^{-2}$ in coordinate time. In addition to this, the scale factor does not admit convergent generalized power series around these singularities with a finite number of terms with negative powers.