Wormholes in a viscous universe

We study the static and spherically symmetric wormhole spacetime configurations at present time in a viscous universe. Considering three classes of viscous models, i.e., bulk viscosity as a function of Hubble constant $H_0$, present cosmic temperature $T_0$ and dark energy density $\rho_0$, respectively, we obtain several wormhole solutions. Through the analysis for the anisotropic solutions, we conclude that, to some extent, these three classes of viscous models have very high degeneracy with each other, and deviate slightly from the ideal fluid consequence. Subsequently, without the loss of generality, to investigate the traversabilities, energy conditions and stability for the wormhole solution, we study the wormhole solution of the constant redshift function of the viscous $\omega$CDM model with a constant bulk viscosity coefficient. We obtain the following conclusions: the value of traversal velocity decreases for decreasing bulk viscosity, and the traversal velocity for a traveler depends on not only the wormhole geometry but also the effects of cosmological background evolution; the null energy condition will be violated more clearly when the bulk viscosity or the cosmic expansion velocity decreases; for the case of a positive surface energy density, the range of the junction radius decreases and the values of the parameter $\lambda$ are further restricted when the throat radius of the wormhole $r_0/M$ increases, bulk viscosity coefficient $\zeta_0$ decreases and present-day Hubble parameter $H_0$ decreases, respectively; for the case of a negative surface energy density, by increasing $r_0/M$, decreasing $\zeta_0$ and increasing $H_0$, the values of the parameter $\lambda$ are less restricted, one may conclude that the total stability region increases, and the range of the junction radius increases, increases and decreases, respectively. \end{abstract}