Imprints of dark energy on cosmic structure formation - III. Sparsity of dark matter halo profiles

We study the imprint of dark energy on the density profile of dark matter haloes using a set of high-resolution large volume cosmological N-body simulations from the Dark Energy Universe Simulation Series. We first focus on the analysis of the goodness of fit of the Navarro-Frenk-White (NFW) profile which we find to vary with halo mass and redshift. We also find that the fraction of haloes ill-fitted by NFW varies with cosmology, thus indicating that the mass assembly of haloes with perturbed density profiles carries a characteristic signature of dark energy. To access this information independently of any parametric profile, we introduce a new observable quantity: the halo sparsity s(Delta). This is defined as the mass ratio M-200/M-Delta, i.e. the ratio of mass inside a sphere of radius r(200) to that contained within a radius r(Delta), enclosing 200 and delta times the mean matter density, respectively. We find the average sparsity to be nearly independent of the total halo mass, while its value can be inferred to better than a few per cent from the ratio of the integrated halo mass functions at overdensities delta and 200, respectively. This provides a consistency relation that can validate observational measurements of the halo sparsity. Most importantly, the sparsity significantly varies with the underlying dark energy model, thus providing an alternative cosmological probe.