Physical constraints on the halo mass function

We analyse the effect of two relevant physical constraints on the mass multiplicity function of dark matter haloes in a Press-Schechter type algorithm. Considering the random walk of linear Gaussian density fluctuations as a function of the smoothing scale, we simultaneously (i) account for mass semi-positivity and (ii) avoid the `cloud-in-cloud' problem. It is shown that the former constraint implies a severe cut-off of low-mass objects, balanced by an increase on larger mass scales. The analysis is performed both for scale-free power spectra and for the standard cold dark matter (CDM) model. Our approach shows that the well-known `infrared' divergence of the standard Press-Schechter mass function is caused by unphysical, negative mass events which inevitably occur in a Gaussian distribution of density fluctuations.