Measuring Primordial Non-Gaussianity in the Cosmic Microwave Background

By E. Komatsu, David N. Spergel, Benjamin Dan Wandelt. 2003

240 citations recorded by the source corpus.

We derive a fast way for measuring primordial non-Gaussianity in a nearly full-sky map of the cosmic microwave background. We find a cubic combination of sky maps combining bispectrum configurations to capture a quadratic term in primordial fluctuations. Our method takes only N3/2 operations rather than N5/2, as taken by the bispectrum analysis (1000 times faster for l = 512), retaining the same sensitivity. A key component is a map of the underlying primordial fluctuations, which can be more sensitive to the primordial non-Gaussianity than a temperature map. We also derive a fast and accurate statistic for measuring non-Gaussian signals from foreground point sources. The statistic is 106 times faster than the full bispectrum analysis and can be used to estimate contamination from the sources. Our algorithm has been successfully applied to the Wilkinson Microwave Anisotropy Probe sky maps by Komatsu and coworkers.

Subfields: Astronomy and Astrophysics, Computational Mechanics

View Paper: https://www.semanticscholar.org/paper/a715d3c9726c11dce00ef04634da47bbfb8f6409

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Citations in the corpus

Testing Inflation with Large Scale Structure: Connecting Hopes with Reality (2014, background): “Often these results are reported in terms of the local template [4, 5], f loc NL = 2.”
Signatures of Initial State Modifications on Bispectrum Statistics (2009, methodology): “Our sign convention for the non-Gaussian amplitude follows [24, 38], which is different from that used in [37].”
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).”
General CMB and primordial bispectrum estimation: Mode expansion, map making, and measures of F NL (2009, background): “The separable approach reduces the problem from one of O(l5 max) operations to a manageable O(l3 max) [9].”
SEVEN-YEAR WILKINSON MICROWAVE ANISOTROPY PROBE (WMAP) OBSERVATIONS: COSMOLOGICAL INTERPRETATION (2010, methodology): “Since then the limits have improved steadily as WMAP collect more years of data and the bispectrum method for estimating f localNL has improved (Komatsu et al. 2005; Creminelli et al. 2006, 2007; Spergel et al. 2007; Yadav & Wandelt 2008; Komatsu et al. 2009a; Smith et al. 2009).35 35 For…”
Planck 2015 results: XIX. Constraints on primordial magnetic fields (2015, unknown): “Thus, the bispectrum estimator remains factorizable like in the usual KSW approach (Komatsu et al. 2005).”
Primordial Non-Gaussianity and Bispectrum Measurements in the Cosmic Microwave Background and Large-Scale Structure (2010, methodology): “in [77] in the context of local fNL estimation and applied to the estimation of WMAP 1-year data by the WMAP team by Komatsu et al.”
Primordial Non-Gaussianities from Inflation Models (2010, background): “In typical data analyses [66–70], the estimator involves a triple integral of the bispectrum over the three momenta ki.”
Algorithms for bispectra: Forecasting, optimal analysis, and simulation (2006, methodology): “This generalizes the estimator proposed by Komatsu, Spergel and Wandelt (Komatsu et al. 2005) to arbitrary factorizable bispectra, and also improves it in the case of inhomogenous noise, by including the linear term in the estimator proposed in Creminelli et al. (2006).”
Non-Gaussianities in single field inflation and their optimal limits from the WMAP 5-year data (2009, background): “Since the relevant bispectra are factorizable in k1, k2, k3, the optimal estimators can be written down in a straightforward way following [30, 13, 32].”
Planck 2015 results. XVII. Constraints on primordial non-Gaussianity (2015, unknown): “…bispectrum and mixed bispectra because of the cross-correlation between isocurvature and adiabatic perturbations (Komatsu 2002; Bartolo et al. 2002; Komatsu et al. 2005; Kawasaki et al. 2008, 2009; Langlois et al. 2008; Hikage et al. 2009; Langlois & Lepidi 2011; Langlois & van Tent 2011, 2012;…”