Measuring primordial non-Gaussianity in the cosmic microwave background

Eiichiro Komatsu1, David N. Spergel1 and Benjamin D. Wandelt2

1. Department of Astrophysical Sciences, Princeton University, Princeton, NJ 08544, USA
2. Department of Physics, University of Illinois at Urbana-Champaign, Urbana, IL 61801-3080, USA


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 of the bispectrum analysis (1000 times faster for l=512), retaining the same sensitivity. A key component is a map of 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 et al. (2003).


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