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The abundance of galaxy clusters can constrain both the geometry and growthof structure in our Universe. However, this probe could be significantlycomplicated by recent claims of nonuniversality -- non-trivial dependences withrespect to the cosmological model and redshift. In this work we analyse thedependance of the mass function on the way haloes are identified and establishif this can cause departures from universality. In order to explore thisdependance, we use a set of different N-body cosmological simulations (LeSBARBINE simulations), with the latest cosmological parameters from the Planckcollaboration; this first suite of simulations is followed by a lowerresolution set, carried out with different cosmological parameters. We identifydark matter haloes using a Spherical Overdensity algorithm with varyingoverdensity thresholds (virial, 2000rho_c, 1000rho_c, 500rho_c, 200rho_c and200rho_b) at all redshifts. We notice that, when expressed in term of therescaled variable nu, the mass functionfor virial haloes is a nearly universalas a function of redshift and cosmology, while this is clearly not the case forthe other overdensities we considered. We provide fitting functions for thehalo mass function parameters as a function of overdensity, that allow topredict, to within a few percent accuracy, the halo mass function for a widerange of halo definitions, redshifts and cosmological models. We then show howthe departures from universality associated with other halo definitions can bederived by combining the universality of the virial definition with theexpected shape of the density profile of halos.

The universality of the virial halo mass function and models for non-universality of other halo definitions