Non-comoving Cold Dark Matter in a $\Lambda$CDM background

We examine the evolution of peculiar velocities of cold dark matter (CDM) in localized arrays of inhomogeneous cosmic structures in a $\Lambda$CDM background that can be identified as a frame comoving with the Cosmic Microwave (CMB). These arrays are constructed by smoothly matching to this cosmological background regions of Szekeres-II models whose source is an imperfect fluid reinterpreted as non-comoving dust, keeping only first order terms in $v/c$. Considering a single Szekeres-II region matched along two comoving interfaces to a $\Lambda$CDM background, the magnitudes of peculiar velocities within this region are compatible with values reported in the literature, while the present day Hubble expansion scalar differs from that of the $\Lambda$CDM background value by a 10\% factor, a result that might provide useful information to the ongoing debate on the $H_0$ tension. While the models cannot describe the virialization process, we show through a representative example that structures of galactic cluster mass reach the onset of this process at redshifts around $z\sim 3$.