Evolution of the turnaround density with redshift. Upper panel: data points: Ω_ta vs. redshift for the three Virgo cosmologies [ΛSCDM (black points), OCDM (red points), and SCDM (magenta points)] and for the MDPL2 ΛSCDM run. Each point corresponds to the mean value of Ω_ta in the halo sample at that z, and the error bars (in most cases smaller than the symbol size) correspond to the standard error on the mean. Solid lines: spherical-collapse prediction for Ω_ta vs. z for the corresponding cosmology. Lower panel: ratio of Ω_ta in simulations over the spherical-collapse prediction as a function of z for the Virgo and MDPL2 simulations. There is a small, evolving offset between the kinematically measured turnaround density in simulated halos and the spherical-collapse prediction.