An exhaustive list of isotropic apocalyptic scenarios

Abstract

We study the possible types of future singularities in the isotropic homogeneous cosmological models for the arbitrary equation of state of the contents of the Universe. We obtain all known types of these singularities as well as two new types using a simple approach. No additional singularity types are possible. We name the new singularities type "Big Squeeze" and "Little Freeze". The "Big Squeeze" is possible only in the flat Universe after a finite time interval. The density of the matter and dark energy tends to zero and its pressure to minus infinity. This requires the dark energy with a specific equation of state that has the same asymptotical behaviour at low densities as the generalised Chaplygin gas. The "Little Freeze" involves an eternal expansion of the Universe. Some solutions can mimic the $\Lambda$CDM model.