Bulk viscous matter with decaying vacuum energy density: A model for late-time evolution of the Universe

Abstract

In this study, we combine viscous dark matter and running vacuum energy density in a single cosmological setting and investigate their cosmological implications. Specifically, we consider a well-studied form of running vacuum energy density model inspired by $f\left(R\right)$-gravity or, equivalently from the Brans–Dicke scalar-tensor theory that arises from a covariant action, i.e., ${\rho }_{\Lambda }=l\frac{\ddot{a}}{a}+\lambda {\left(\frac{\dot{a}}{a}\right)}^2+\frac{1}{2}\eta {\rho }_m$ and a recently proposed general parameterization for bulk viscosity $\zeta ={\zeta }_0+{\zeta }_1\frac{\dot{a}}{a}+{\zeta }_2\frac{\ddot{a}}{\dot{a}}$, where $l,\lambda ,\eta ,{\zeta }_0,{\zeta }_1$ and ${\zeta }_2$ are constants. In this setup, we derived analytical solutions for the Hubble parameter and the scale factor of the universe within the framework of Eckart’s theory of bulk viscosity. The viability of the proposed model equation is tested by constraining its free model parameters using the Hubble parameter $H\left(z\right)$ and type Ia supernovae (SNe Ia) observations at different redshifts, and the goodness-of-fit of the model to the data was also checked by a ${\chi }^2$ function minimization. Various significant cosmological parameters were estimated and analytically explained in the evolution dynamics of the universe, and a comparison of our proposed model with the $\Lambda$CDM model was studied. The application of dynamical systems analysis reveals the physical aspects of the new phase space that emerge from the model and derives stability conditions that ensure complete cosmological dynamics. The model is consistent with the local and generalized second laws of thermodynamics at the apparent horizon throughout the evolution of the universe.