  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.
