Exploring interacting bulk viscous model with decaying vacuum density

In the present work, we study a cosmological model composed of a viscous dark matter interacting with decaying vacuum energy in a spatially flat Universe. In the first part, we find the analytical solution of different cosmological parameters by assuming the physically viable forms of bulk viscosity and decaying vacuum density with the interaction term. The second part is dedicated to constrain the free parameters of the interacting viscous model with decaying vacuum energy by employing latest observational data of $Pantheon+$, Cosmic Chronometer and f(z)σ₈(z). We find that the interacting model just deviate very slightly from well-known concordance ΛCDM model and can alleviate effectively the current H₀ tension between local measurement by R21 and global measurement by Planck 2018, and the excess in the mass fluctuation amplitude σ₈ essentially vanish in this context. We report the Hubble constants as H₀=72.150+0.989-0.779, and 72.202+0.796-0.937 \;km s⁻¹ Mpc⁻¹, deceleration parameters as q₀=-0.533 ± 0.024, and -0.531 ± 0.024, and equation of state parameters as w₀=-0.689 ± 0.016, and -0.687 ± 0.016 for ΛCDM and interacting models, respectively. It is found that the interacting model is in good agreement with ΛCDM. Further, we discuss the amplitude of matter power spectrum σ₈ and its associated parameter S₈ using f(z)σ₈(z) data. Finally, the information selection criterion and Bayesian inference are discussed to distinguish the interacting model with ΛCDM model.