On the average comoving number density of halos

I compare the numerical multiplicity function recently given by Yahagi et al. with the theoretical multiplicity function obtained bymeans of the excursion set model and an improved version of the barrier shape obtained by Del Popolo & Gambera, which implicitly takes into account the total angular momentum acquired by the protostructure during evolution and a nonzero cosmological constant. I show that the multiplicity function obtained here is in better agreement with the recent simulations of Yahagi et al. than other previous models (Sheth & Tormen; Sheth et al.; Jenkins et al.) and that, unlike some previous multiplicity function models (Jenkins et al.; Yahagi et al.), it was obtained from a sound theoretical background.