A Study of Finite-time Singularities of Loop Quantum Cosmology Interacting Multifluids

TL;DR

This paper analyzes finite-time singularities in a loop quantum cosmology model with three interacting fluids, demonstrating the absence of certain singularities using an analytical approach and exploring the system's fixed points and dark energy behavior.

Contribution

It introduces an analytical dominant balances method to study singularities in a multifluid LQC system, avoiding numerical simulations and providing new insights into singularity absence.

Findings

No Big Rip or Type III singularities occur in the model.

Existence of non-singular solutions for a wide range of initial conditions.

Fixed point analysis reveals stable cosmological behaviors.

Abstract

In this work we study the occurrence of finite-time cosmological singularities in a cosmological system comprising from three fluids. Particularly, the system contains two dark fluids, namely that of dark energy and dark matter, which are interacting, and of a non-interacting baryonic fluid. For the study we adopt the phase space approach by constructing the cosmological dynamical system in such a way so that it rendered to be an autonomous polynomial dynamical system, and in order to achieve this, we appropriately choose the variables of the dynamical system. By employing a rigid mathematical framework, that of dominant balances analysis, we demonstrate that there exist non-singular solutions of the dynamical system, which correspond to a general set of initial conditions, which proves that no Big Rip or Type III finite-time singularities occur in this LQC multifluid dynamical system. Thus the new feature of this work is that we are able to do this using an analytic technique instead of adopting a numerical approach. In addition, we perform a fixed point analysis of the cosmological dynamical system, and we examine the behavior of the total effective equation of state parameter, at the fixed points, as a function of the free parameters of the system. Finally, we investigate the phenomenological implications of the dark energy equation of state which we assumed that it governs the dark energy fluid.