Viscous fluid dynamics with decaying vacuum energy density

In this work, we investigate the dynamics of bulk viscous models withdecaying vacuum energy density (VED) in a spatially homogeneous and isotropicflat Friedmann-Lema\^{i}tre- Robertson-walker (FLRW) spacetime. We particularlyare interested to study the viscous model which considers first order deviationfrom equilibrium, i.e., the Eckart theory. In the first part, using thedifferent forms of the bulk viscous coefficient, we find the main cosmologicalparameters, like Hubble parameter, scale factor, deceleration parameter andequation of state parameter analytically. We discuss some cosmologicalconsequences of the evolutions and dynamics of the different viscous modelswith decaying VED. We examine the linear perturbation growth in the context ofthe bulk viscous model with decaying VED to see if it survives this furtherlevel of scrutiny. The second part of the work is devoted to constrain theviscous model of the form $\zeta \propto H$, where $\zeta$ is the bulk viscouscoefficient and $H$ is the Hubble parameter, using three different combinationsof data from type Ia supernovae (Pantheon), $H(z)$ (cosmic chronometers),Baryon Acoustic Oscillation and $f(z)\sigma_8(z)$ measurements with MarkovChain Monte Carlo (MCMC) method. We show that the considered model iscompatible with the cosmological probes, and the $\Lambda$CDM recovered inlate-time of the evolution of the Universe. Finally, we obtain selectioninformation criteria (AIC and BIC) to study the stability of the models.