Algorithms for bispectra: Forecasting, optimal analysis, and simulation

By Kendrick M. Smith, M. Zaldarriaga. 2006

146 citations recorded by the source corpus.

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 cosmic microwave background (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 integrated Sachs–Wolfe (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.

Subfields: Finance, Statistical and Nonlinear Physics, Signal Processing

View Paper: https://www.semanticscholar.org/paper/f53c47106f4a80442088f726a01f45ce2e397ea1

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Citations in the corpus

NINE-YEAR WILKINSON MICROWAVE ANISOTROPY PROBE (WMAP) OBSERVATIONS: FINAL MAPS AND RESULTS (2012, methodology): “We constrain the fNL parameters using the optimal (i.e. minimum variance unbiased) bispectrum estimator implemented in Smith et al. (2009), which builds on previous work (Komatsu et al. 2005; Creminelli et al. 2006; Smith & Zaldarriaga 2011).”
Shape of primordial non-Gaussianity and the CMB bispectrum (2008, background): “[13] for the DBI model, the only direct calculation elsewhere of a non-separable case).”
Primordial Non-Gaussianity and Bispectrum Measurements in the Cosmic Microwave Background and Large-Scale Structure (2010, methodology): “Like single field slow-roll inflation, the predicted ‘non-local’ shape function is a combination of a dominant local shape (II.13) and an equilateral shape (III.53) (see, for example, Barnaby & Cline, 2008; Halliwell, 1993; Seery et al., 2008; Zaldarriaga, 2004).”
General CMB and primordial bispectrum estimation: Mode expansion, map making, and measures of F NL (2009, result): “[3, 25, 31]), which enables a useful comparison between the outcome of our numerical pipelines and previously published results for the equilateral shape.”
Signatures of Initial State Modifications on Bispectrum Statistics (2009, background): “fore such a denominator would not be allowed, since a function with such a denominator can not be split up into functions of individual comoving momenta k 1;k 2 and k 3. There exists another approach [58], in which such a denominator is written as follows 1 (k 1 k 2 k 3)2 = Z 1 0 te t(k 1 k 2 k 3)dt”
Non-Gaussianities in single field inflation and their optimal limits from the WMAP 5-year data (2009, methodology): “where the optimal estimator found in [13] was implemented with the pipeline developed in [14].”