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: σ₈, Ω_M, Ω_b, n_s, h, M_ν, w₀, 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.