Journal Article

Conditional probabilities in the excursion set theory: generic barriers and non-Gaussian initial conditions

Andrea De Simone, Michele Maggiore and Antonio Riotto

in Monthly Notices of the Royal Astronomical Society

Published on behalf of The Royal Astronomical Society

Volume 418, issue 4, pages 2403-2421
Published in print December 2011 | ISSN: 0035-8711
Published online December 2011 | e-ISSN: 1365-2966 | DOI:
Conditional probabilities in the excursion set theory: generic barriers and non-Gaussian initial conditions

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The excursion set theory, where density perturbations evolve stochastically with the smoothing scale, provides a method for computing the dark matter halo mass function. The computation of the mass function is mapped into the so-called first-passage time problem in the presence of a moving barrier. The excursion set theory is also a powerful formalism to study other properties of dark matter haloes such as halo bias, accretion rate, formation time, merging rate and the formation history of haloes. This is achieved by computing conditional probabilities with non-trivial initial conditions, and the conditional two-barrier first-crossing rate. In this paper we use the path integral formulation of the excursion set theory to calculate analytically these conditional probabilities in the presence of a generic moving barrier, including the one describing the ellipsoidal collapse, and for both Gaussian and non-Gaussian initial conditions. While most of our analysis associated with Gaussian initial conditions assumes Markovianity (top-hat in momentum space smoothing, rather than generic filters), the non-Markovianity of the random walks induced by non-Gaussianity is consistently accounted for. We compute, for a generic barrier, the first two scale-independent halo bias parameters, the conditional mass function and the halo formation time probability, including the effects of non-Gaussianities. We also provide the expression for the two-constant-barrier first-crossing rate when non-Markovian effects are induced by a top-hat filter function in real space.

Keywords: cosmology: theory; large-scale structure of Universe

Journal Article.  11376 words.  Illustrated.

Subjects: Astronomy and Astrophysics

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