Viscous unified dark matter models under scrutiny: Uncovering inconsistencies from dynamical system analysis

TL;DR: This study scrutinizes viscous unified dark matter models, revealing inconsistencies in models with specific bulk viscosity parameterizations, particularly those with negative exponents, which fail to produce a radiation-dominated era, necessitating revised statistical analyses.

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.