Viscous Unified Dark Matter Models Under Scrutiny: Uncovering Inconsistencies from Dynamical System Analysis

TL;DR

This study critically evaluates viscous unified dark matter models, revealing that many fail to produce a radiation-dominated era unless specific parameter constraints are met, impacting their viability in cosmological modeling.

Contribution

It provides a rigorous dynamical system analysis of viscous dark matter models, identifying key parameter constraints necessary for realistic cosmological evolution.

Findings

Models with certain viscosity parameterizations cannot produce radiation domination.

The exponent s must be between 0 and 0.5 for correct cosmological evolution.

Current observational fits often fall outside the viable parameter range.

Abstract

Viscous unified dark matter models aim to describe the dark sector of the Universe, as the dark matter fluid itself gives rise to an accelerated expansion due to a negative bulk viscous pressure. However, in most studies, radiation is often disregarded as a minor factor in dynamical system analyses, overlooking whether radiation domination is achievable. In this paper, we rigorously examine this critical aspect for common parameterizations of bulk viscosity, denoted as $\xi$, within two general classes of viscous unified models. Our findings reveal significant inconsistencies in models where $\xi \propto H^{1-2s} \rho_{m}^{s}$ with $s\leq 0$, and surprisingly, in models where $\xi \propto \rho_{m}^{s}$ with exponents $s<0$, as they both fail to produce a radiation-dominated era. Moreover, the exponent $s$ must lye within the interval $0 \leq s < 1/2$ for the latter model to correctly describes the cosmological evolution. These results underscore the need of including these constraints as a prior in statistical analyses of observational data, with implications for current statistical inferences for the second model, where both prior and best-fit values of $s$ often fall outside the acceptable range.