An improved calculation of the non-Gaussian halo mass function

Abstract

The abundance of collapsed objects in the universe, or halo massfunction, is an important theoretical tool in studying the effects ofprimordially generated non-Gaussianities on the large scalestructure. The non-Gaussian mass function has been calculated byseveral authors in different ways, typically by exploiting thesmallness of certain parameters which naturally appear in thecalculation, to set up a perturbative expansion. We improve upon theexisting results for the mass function by combining path integralmethods and saddle point techniques (which have been separatelyapplied in previous approaches). Additionally, we carefully accountfor the various scale dependent combinations of small parameters which appear. Some of these combinations in fact become of order unity forlarge mass scales and at high redshifts, and must therefore be treatednon-perturbatively. Our approach allows us to do this, and also toaccount for multi-scale density correlations which appear in thecalculation. We thus derive an accurate expression for the massfunction which is based on approximations that are valid over a larger range of mass scales andredshifts than those of other authors. By tracking the terms ignoredin the analysis, we estimate theoretical errors for our result andalso for the results of others. We also discuss the complicationsintroduced by the choice of smoothing filter function, which we taketo be a top-hat in real space, and which leads to the dominant errorsin our expression. Finally, we present a detailed comparison betweenthe various expressions for the mass functions, exploring the accuracyand range of validity of each.