The cosmology dependence of the concentration-mass-redshift relation

The concentrations of dark matter haloes provide crucial information about their internal structure and how it depends on mass and redshift - the so-called concentration-mass-redshift relation, denoted c(M, z). We present here an extensive study of the cosmology-dependence of c(M, z) that is based on a suite of 72 gravity-only, full N-body simulations in which the following cosmological parameters were varied: sigma(8), omega(M), omega(b), n(s), h, M-nu, w(0), and w(a). We characterize the impact of these parameters on concentrations for different halo masses and redshifts. In agreement with previous works, and for all cosmologies studied, we find that there exists a tight correlation between the characteristic densities of dark matter haloes within their scale radii, r(-2), and the critical density of the universe at a suitably defined formation time. This finding, when combined with excursion set modelling of halo formation histories, allows us to accurately predict the concentrations of dark matter haloes as a function of mass, redshift, and cosmology. We use our simulations to test the reliability of a number of published models for predicting halo concentration and highlight when they succeed or fail to reproduce the cosmological c(M, z) relation.