The excursion set approach, and an improved model for the multiplicity function

Abstract

I compare numerical multiplicity function with the theoretical multiplicity function obtained by means of the excursion set model and an improved version of the barrier shape which implicitly takes account of total angular momentum acquired by the proto-structure during evolution and of a non-zero cosmological constant. I describe the better agreement of the multiplicity function obtained in this paper with simulations of other previous models. While the theoretical multiplicity function of the present paper is in agreement with high resolution N -body simulations, the comparison of the theoretical multiplicity function of the present paper with the theoretical multiplicity function of several authors shows some discrepancies: e.g., the maximum value of the multiplicity function from simulations at $\nu \sim 1$ is smaller, and its low mass tail is shallower when compared with the ST multiplicity function. The multiplicity function of the present paper gives a good fit to simulations results and was obtained from a sound theoretical background.