Cosmological constraints on the interacting viscous dark matter and decaying vacuum energy models
We investigate an interacting dark sector scenario in which a deviation from the standard dilution law of cold dark matter is parametrized by a perturbative correction $\epsilon$, thereby inducing a dynamical vacuum component. We extend this framework by allowing dark matter to behave as an imperfect fluid with bulk viscosity. Within the Eckart formalism, we consider a power-law dependence of the bulk viscous coefficient on the dark matter energy density which yields an effective density scaling for the viscous pressure. We obtain the parameter constraints using multi-nested sampling with \texttt{Dynesty}, employing DES 5YR Type Ia Supernovae, DESI Baryon Acoustic Oscillations, Cosmic Chronometers, the local $H_0$ measurement from H0DN, and Cosmic Microwave Background distance priors. Redshift Space Distortion measurements from SDSS-IV and the DES weak-lensing constraint on $S_8$ are included to probe structure formation. We also examine the thermodynamic consistency of the cosmological scenarios and find that they satisfy the Generalized Second Law of thermodynamics. We find that bulk viscous effects can modify the late-time interaction dynamics, while their contribution is suppressed once early-Universe information is included. These results provide observational and thermodynamic constraints on departures from the standard cold dark matter evolution and a constant vacuum energy.