Excursion set theory for generic moving barriers and non-Gaussian initial conditions
De Simone, Andrea ; Maggiore, Michele ; Riotto, Antonio
In: Monthly Notices of the Royal Astronomical Society, 2011, vol. 412, no. 4, p. 2587-2602
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- Excursion set theory, where density perturbations evolve stochastically with the smoothing scale, provides a method for computing the mass function of cosmological structures like dark matter haloes, sheets and filaments. The computation of these mass functions is mapped into the so-called first-passage time problem in the presence of a moving barrier. In this paper we use the path-integral formulation of the excursion set theory developed recently to analytically solve the first-passage time problem in the presence of a generic moving barrier, in particular the barrier corresponding to ellipsoidal collapse. We perform the computation for both Gaussian and non-Gaussian initial conditions and for a window function which is a top-hat in wavenumber space. The expression of the halo mass function for the ellipsoidal collapse barrier and with non-Gaussianity is therefore obtained in a fully consistent way and it does not require the introduction of any form factor artificially derived from the Press-Schechter formalism based on the spherical collapse and usually adopted in the literature