Turnaround density as a probe of the cosmological constant

Spherical collapse predicts that a single value of the turnaround density (average matter density within the scale on which a structure detaches from the Hubble flow) characterizes all cosmic structures at the same redshift. It has been recently shown by Korkidis et al. that this feature persists in complex non-spherical galaxy clusters identified in N-body simulations. Here we show that the low-redshift evolution of the turnaround density constrains the cosmological parameters, and that it can be used to derive a local constraint on $\Omega_\Lambda$ alone, independent of $\Omega_m$. The turnaround density thus provides a promising new way to exploit upcoming large cosmological datasets.