Constraining viscous dark energy models with the latest cosmological data

Based on the assumption that the dark energy possessing bulk viscosity is homogenously and isotropically permeated in the universe, we propose three new viscous dark energy (VDE) models to characterize the accelerating universe. By constraining these three models with the latest cosmological observations, we find that they just deviate very slightly from the standard cosmological model and can alleviate effectively the current $H_0$ tension between the local observation by the Hubble Space Telescope and the global measurement by the Planck Satellite. Interestingly, we conclude that a spatially flat universe in our VDE model with cosmic curvature is still supported by current data, and the scale invariant primordial power spectrum is strongly excluded at least at the $5.5σ$ confidence level in three VDE models as the Planck result. We also give the $95\%$ upper limits of the typical bulk viscosity parameter $η$ in three VDE scenarios.