Turning Around along the Cosmic Web

A bound-violation designates a case that the turn-around radius of a bound object exceeds the upper limit put by the spherical collapse model based on the standard $\Lambda$CDM paradigm. Given that the turn-around radius of a bound object is a stochastic quantity and that the spherical model overly simplifies the true gravitational collapse which actually proceeds anisotropically along the cosmic web, the rarity of the occurrence of a bound violation may depend on the web environment. Assuming a Planck cosmology, we numerically construct the bound-zone peculiar velocity profiles along the cosmic web (filaments and sheets) around the isolated groups with virial mass $M_{\rm v}\ge 3\times 10^{13}\,h^{-1}M_{\odot}$ identified in the Small MultiDark Planck simulations and determine the radial distances at which their peculiar velocities equal the Hubble expansion speed as the turn-around radii of the groups. It is found that although the average turn-around radii of the isolated groups are well below the spherical bound-limit on all mass scales, the bound violations are not forbidden for individual groups and that the cosmic web has an effect of reducing the rarity of the occurrence of a bound violation. Explaining that the spherical bound limit on the turn-around radius in fact represents the threshold distance up to which the intervention of the external gravitational field in the bound-zone peculiar velocity profiles around the non-isolated groups stays negligible, we discuss the possibility of using the threshold distance scale to constrain locally the equation of state of dark energy .