Analytic Derivation of the Halo Mass Function from the Non-Linear Cosmic Density Field

Abstract

We estimate the halo mass function (HMF) by applying the excursion set approach to the non-linear cosmic density field. Thereby, we account for the non-Gaussianity of today's density distribution and constrain the HMF independent of the linear collapse threshold $\delta_{\textrm{crit}}$. We consider a spherical region as a halo, if its density today exceeds the virial overdensity threshold $\Delta$. We model the probability distribution of the non-linear density field by a superposition of a Gaussian and a lognormal distribution, which we constrain with the bispectrum of density fluctuations, predicted by the kinetic field theory description of cosmic structure formation. Two different excursion set approaches are compared. The first treats the density $\delta$ as an uncorrelated random walk of the smoothing scale $R$. The second assumes $\delta(R)$ to be correlated. We find that the resulting HMFs correspond well to the HMF found in numerical simulations if the correlation of $\delta(R)$ is taken into account. Furthermore, the HMF depends only weakly on the choice of the density threshold $\Delta$.