2005/08/15 by Gang Chen, Istvan Szapudi · 24 citations
Computer Science · Physics and Astronomy · #CMB cold spot #Computational Physics and Python Applications #Correlation function (quantum field theory) #Cosmic background radiation #Cosmic microwave background #Cosmic variance #Cosmology and Gravitation Theories #Estimator #Kurtosis #Logarithm #Particle physics theoretical and experimental studies #Scaling #Skewness #astro-ph
paper · pdf · doi:10.1086/497619
published in The Astrophysical Journal 635(2), 743-749 (IOP Publishing) · 20 pages, 5 figures
arxiv created 2005/08/15 · openalex publication_date 2005/12/15 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We present a new method to estimate three-point correlations in cosmic microwave background maps. Our fast Fourier transform-based implementation estimates three-point functions using all possible configurations (triangles) at a controlled resolution. The speed of the technique depends on both the resolution and the total number of pixels N . The resulting N log N scaling is substantially faster than naive methods with prohibitive N 3 scaling. As an initial application, we measure three-point correlation functions in the first-year data release of the Wilkinson Microwave Anisotropy Probe ( WMAP ). We estimate 336 cross-correlations of any triplet of maps from the eight differential assemblies, scanning altogether 2.6 million triangular configurations. Using Gaussian signal plus realistic noise simulations, we perform a null hypothesis testing with regards to the Gaussianity of the cosmic microwave background. Our main result is that at the three-point level, WMAP is fully consistent with Gaussianity. To quantify the level of possible deviations, we introduce false discovery rate analysis, a novel statistical technique to analyze three-point measurements. This confirms that the data are consistent with Gaussianity at better than the 1 σ level when jointly considering all configurations. We constrain a specific non-Gaussian model using a quadratic expansion of the temperature field in terms of the f NLT parameter, Δ T / T = (Δ T / T ) L + f NLT [(Δ T / T ) - ⟨(Δ T / T ) ⟩], for which we construct an estimator from the three-point function. We find that using the skewness alone is more constraining than a heuristic suboptimal combination of all our results; our best estimate is f NLT = -110 ± 150, assuming a ΛCDM concordance model.