Toward a Universal Formulation of the Halo Mass Function

We compute the dark matter halo mass function using the excursion set formalism for a diffusive barrier with linearly drifting average which captures the main features of the ellipsoidal collapse model. We evaluate the non-Markovian corrections due to the sharp filtering of the linear density field in real space with a path-integral method. We find an unprecedented agreement with N-body simulation data with deviations ≲5% over the range of masses probed by the simulations. This indicates that the excursion set in combination with a realistic modeling of the collapse threshold can provide a robust estimation of the halo mass function.