The impact of constrained interacting dark energy on the bound-zone velocity profile

We numerically study the effects of constrained interacting dark energy (CIDER) on the bound-zone velocity profiles around massive dark matter halos. Analyzing the CIDER simulations performed by Baldi (2023) for three different cases of dark sector coupling ($\beta=0.03$, $0.05$ and $0.08$) as well as for the standard $\Lambda$CDM cosmology ($\beta=0$), we determine the mean peculiar velocity profiles in the bound zones around the friends-of-friends halos with masses larger than $M_{\rm cut}=3\times 10^{13}\,h^{-1}M_{\odot}$ at three redshifts, $z=0$, $0.5$ and $1$. It is found that the universal power-law formula proposed by Falco et al. (2024) originally for the $\Lambda$CDM case still describes well the bound-zone velocity profiles, $V(r)$, even in the CIDER models. The slope of $V(r)$, turns out to be significantly affected by the CIDER, progressively decreasing as $\beta$ increases. Meanwhile, the amplitude of $V(r)$ exhibits little dependence on $\beta$, which is ascribed to the identical Hubble parameters shared by the $\Lambda$CDM and CIDER models in the entire redshift range. Our results imply that the bound-zone velocity slope can break a degeneracy even between the $\Lambda$CDM and CIDER models with $\beta\le 0.03$, which the standard cosmological diagnostics fail to distinguish. We devise a simple analytic formula for the bound-zone slope as a function of $\beta$, and prove its validity at all of the three redshifts. It is concluded that the slope of the mean bound-zone peculiar velocity profile should be in principle a powerful probe of dark sector interaction.