Turnaround density evolution encodes cosmology in simulations

The mean matter density within the turnaround radius, which is the boundary that separates a nonexpanding structure from the Hubble flow, was recently proposed as a novel cosmological probe. According to the spherical collapse model, the evolution with cosmic time of this turnaround density, $\rm \rho_{ta}(z)$, can be used to determine both $\rm \Omega_m$ and $\Omega_\Lambda$, independently of any other currently used probe. The properties of $\rm \rho_{ta}$ predicted by the spherical collapse model were also shown to persist in the presence of full three-dimensional effects in $\rm \Lambda$CDM N-body cosmological simulations when considering galaxy clusters at the present time, $z=0$. However, a small offset was discovered between the spherical-collapse prediction of the value of $\rho_{ta}$ at $z=0$ and its value measured in simulations. In this letter, we explore whether this offset evolves with cosmic time; whether it differs in different cosmologies; whether its origin can be confidently identified; and whether it can be corrected. We found that the offset does evolve slightly with redshift, and that it correlates strongly with the deviation from spherical symmetry of the dark matter halo distribution inside and outside of the turnaround radius. We used an appropriate metric to quantify deviations in the environment of a structure from spherical symmetry. We found that using this metric, we can construct a sphericity-selected sample of halos for which the offset of $\rho_{ta}$ from the spherical collapse prediction is zero, independently of redshift and cosmology. We found that a sphericity-selected halo sample allows us to recover the simulated cosmology, and we conclude that the turnaround density evolution indeed encodes the cosmology in N-body simulations.