Dissipative $\Lambda$CDM model with causal sign-switching bulk viscous pressure

TL;DR

This paper introduces a novel analytical solution for a dissipative $DM$ model with causal viscous effects, demonstrating sign-switching bulk viscous pressure that explains both early deceleration and late acceleration of the universe, consistent with thermodynamics.

Contribution

It provides the first complete analytical solution for the Hubble parameter in a dissipative $DM$ model with a novel bulk viscous coefficient form and explores a unified dark matter framework.

Findings

Model predicts sign-switching bulk viscous pressure.

The viscous pressure sign change correlates with relaxation time.

Model satisfies thermodynamic laws and entropy conditions.

Abstract

Extending the standard $\Lambda$CDM model by considering dissipative effects within a causal viscous framework, and obtaining an analytical solution for the Hubble parameter remains a challenge in the literature. In this work, we resolve this dilemma by deriving a complete and original solution for the Hubble parameter by introducing a novel form for the bulk viscous coefficient associated with bulk viscous dark matter (vDM). A thorough analysis of the model is conducted by deriving theoretical constraints on the parameters and comparing the model with the latest observational data sets. Intriguingly, we find that the model predicts a sign-switching bulk viscous pressure, which facilitates both the early decelerated expansion and the late accelerated expansion of the universe. Also, the redshift at which the viscous pressure switches sign is found to be strongly correlated with the relaxation time parameter of the viscous fluid. Thermodynamic analysis revealed that, the model satisfies both the covariant and generalized second law of thermodynamics as well as the convexity condition for entropy. Additionally, we reconstructed the model by unifying viscous dark matter and dark energy into a single unified dark matter (UDM) component, and found that this unified model predicts identical dynamical evolution for the Universe, while satisfying the necessary near-equilibrium condition throughout that evolution (both in early and late phases).