Algorithms for bispectra: forecasting, optimal analysis and simulation

Abstract

We propose a factorizability ansatz for angular bispectra which permits fast algorithms for forecasting, analysis, and simulation, yet is general enough to encompass many interesting CMB bispectra. We describe a suite of general algorithms which apply to any bispectrum which can be represented in factorizable form. First, we present algorithms for Fisher matrix forecasts and the related problem of optimizing the factorizable representation, giving a Fisher forecast for Planck as an example. We show that the CMB can give independent constraints on the amplitude of primordial bispectra of both local and equilateral shape as well as those created by secondary anisotropies. We also show that the ISW-lensing bispectrum should be detected by Planck and could bias estimates of the local type of non-Gaussianity if not properly accounted for. Second, we implement a bispectrum estimator which is fully optimal in the presence of sky cuts and inhomogeneous noise, extends the generality of fast estimators which have been limited to a few specific forms of the bispectrum, and improves the running time of existing implementations by several orders of magnitude. Third, we give an algorithm for simulating random, weakly non-Gaussian maps with prescribed power spectrum and factorizable bispectrum.