Grand rip and grand bang/crunch cosmological singularities

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 nonsingular 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.

Figure 1

Singularities at $t=0$ for ${\eta }_0=1$.