Interacting model of bulk viscous and decaying vacuum energy

We discuss the dynamics of interacting viscous model with time-varying cosmological constant, Λ(t), which is a natural generalization of the standard Lambda-Cold-Dark matter (ΛCDM) model in Friedmann-Lemaître-Robertson-Walker (FLRW) spacetime. The Λ(t) is motivated by different cosmological approaches. Recent investigations involving the renormalization of quantum field theory (QFT) in curved spacetime yield a time-varying Λ, so-called running vacuum model (RVM) in which it acquires a dynamical component through quantum effects. We discuss both the background and perturbation equations for viscous RVM using a more generalized parametrization form of vacuum density. We employ the cosmic data, namely distant Type Ia Supernovae (Pantheon+), Baryonic Acoustic Oscillations DESI, Cosmic Chronometers and growth data. We anchor ΛCDM and viscous RVM on two Hubble constant priors of Planck2018 and SH0ES R22 that reflect the Hubble tension. Using these data samples we assess the viability and compare viscous RVM with the standard ΛCDM model. The Gelman-Rubin statistic (or R-hat statistic) is used to assess the convergence of Markov Chain Monte Carlo (MCMC) simulations. We also discuss the stability of viscous RVM using information criterion such as AIC, BIC and DIC. The constraints on parameters show that the viscous RVM is consistent with the standard ΛCDM model and alleviates the Hubble tension up to 0.569σ.