The Bispectrum and the Trispectrum of the Ostriker and Vishniac Effect

Abstract

We present analytical expressions for the Fourier analog of the CMB three-point and four-point correlation functions, the spatial bispectrum and trispectrum, of the Ostriker and Vishniac effect in the linear and mildly nonlinear regime. Through this systematic study, we illustrate a technique to tackle the calculation of such statistics making use of the effects of its small-angle and vector-like properties through the Limber approximation. Finally we discuss its configuration dependence and detectability in the context of Gaussian theories for the currently favored flat Lambda CDM cosmology.

22 pages, 6 figures. Version corrected from the original manuscript published in Phys.Rev.D67 [2003] with an accepted erratum (to be published in Phys.Rev.D70 [2004]). The conclusions remain the same

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