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

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).