The Classical and Loop Quantum Cosmology Phase Space of Interacting Dark Energy and Superfluid Dark Matter

TL;DR

This paper analyzes the phase space of a cosmological model with interacting dark energy and superfluid dark matter, comparing classical and loop quantum cosmology, revealing differences in fixed points and singular solutions.

Contribution

It introduces a detailed phase space analysis of coupled dark energy and superfluid dark matter in both classical and loop quantum cosmology contexts, highlighting novel fixed point behaviors.

Findings

Classical cosmology shows unstable matter and radiation fixed points with no de Sitter points.

Loop quantum cosmology admits stable de Sitter fixed points for certain parameters.

Non-singular solutions in loop quantum cosmology occur with negative pressure superfluid dark matter.

Abstract

In this paper we study in detail the phase space of a cosmological system consisting of two coupled fluids, namely a dark energy fluid coupled with a superfluid dark matter fluid. The dark matter fluid is assumed to have a superfluid equation of state, hence it is not pressureless and our aim is to find the impact of this non-trivial equation of state on the phase space of the coupled system. We shall use two theoretical contexts, namely that of classical cosmology and that of loop quantum cosmology. In the classical case, we investigated the existence and stability of fixed points, and as we will show, no de Sitter fixed points occur, however matter and radiation domination fixed points occur, which are hyperbolic and unstable. We also show that there exist limited sets of initial conditions for which singular solutions occur in the phase space. With regard to the loop quantum cosmology case, we demonstrate that stable de Sitter fixed points exist, for some values of the free parameters of the theory, and interestingly enough, for the same values, singular solutions corresponding to general sets of initial conditions occur. To our knowledge this feature does not occur so frequently in loop quantum cosmological frameworks. We also demonstrate that non-singular solutions corresponding to a general set of initial conditions occur, however these occur when the dark matter superfluid has negative pressure, so it is a rather physically unappealing situation.