Singularities in cosmologies with interacting fluids

TL;DR

This paper analyzes the behavior of flat isotropic universes with two interacting perfect fluids near finite-time singularities, revealing diverse asymptotic solutions including attractors, big rip, and cyclic-like singularities.

Contribution

It provides a comprehensive classification of singularities and asymptotic behaviors in cosmological models with interacting fluids, including new solutions and series representations.

Findings

Identified attractors for standard decay and phantom matter at early times.

Discovered solutions describing collapsing universes and big rip singularities.

Found a complex logarithmic branch point singularity resembling cyclic universes.

Abstract

We study the dynamics near finite-time singularities of flat isotropic universes filled with two interacting but otherwise arbitrary perfect fluids. The overall dynamical picture reveals a variety of asymptotic solutions valid locally around the spacetime singularity. We find the attractor of all solutions with standard decay, and for `phantom' matter asymptotically at early times. We give a number of special asymptotic solutions describing universes collapsing to zero size and others ending at a big rip singularity. We also find a very complicated singularity corresponding with a logarithmic branch point that resembles of cyclic universe, and give an asymptotic local series representation of the general solution in the neighborhood of infinity.