Left: Dark matter HMF for the different simulations considered in this paper. The shaded regions show the measurements based on the MS (1σ Poissonian scatter); the dashed lines correspond to the MSII simulation; and the squares with errorbars are for the PMS simulation (1σ Poissonian scatter). Right: Impact of different cosmological parameters on the evolution of the HMF. The left-most panels show the HMFs expected for the MS and PMS cosmological models (dashed black and solid red lines, respectively). In the central and right-most panels, the HMFs for the MS are compared with runs with theoretical expectations obtained modifying the following parameters: σ₈ (assumed to be the same as in the PMS; blue solid line); σ₈ and the spectral index (as in the PMS; cyan dotted line); Ω_m (as in the PMS; green solid line).