Measuring the Three Point Correlation Function of the Cosmic Microwave Background

Abstract

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 both on 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 Anisotropy Probe. We estimate 336 cross-correlations of any triplet of maps from the 8 differential assemblies, scanning altogether 2.6 million triangular configurations. Estimating covariances from 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 for three-point measurements. This confirms that the data are consistent with Gaussianity at better than 1-$\sigma$ level when jointly considering all configurations. We constrain a specific non-Gaussian model using the quadratic approximation of weak non-Gaussianities in terms of the $f_{NLT}$ parameter, for which we construct an estimator from the 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 $f_{NLT}=-110\pm 150$ assuming a $\Lambda$CDM concordance model.

20 pages, 5 figures

References in corpus (31)

• First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Determination of Cosmological Parameters
• First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Preliminary Maps and Basic Results
• MASTER of the CMB Anisotropy Power Spectrum: A Fast Method for Statistical Analysis of Large and Complex CMB Data Sets
• First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Tests of Gaussianity
• The significance of the largest scale CMB fluctuations in WMAP
• Detection of non-Gaussianity in the WMAP 1-year data using spherical wavelets
• Multipole Vectors--a new representation of the CMB sky and evidence for statistical anisotropy or non-Gaussianity at 2<=l<=8
• Measuring primordial non-Gaussianity in the cosmic microwave background
• Non-Gaussian Signatures in the Temperature Fluctuation Observed by the Wilkinson Microwave Anisotropy Probe
• First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Data Processing Methods and Systematic Errors Limits
• Controlling the False Discovery Rate in Astrophysical Data Analysis
• A new source detection algorithm using FDR
• Measurement of the cosmic microwave background bispectrum on the COBE DMR sky maps
• A high-significance detection of non-Gaussianity in the WMAP 1-year data using directional spherical wavelets
• Higher Criticism Statistic: Detecting and Identifying Non-Gaussianity in the WMAP First Year Data
• Wavelets and WMAP non-Gaussianity
• Assessing the effects of foregrounds and sky removal in WMAP
• The N-point correlation functions of the first-year Wilkinson Microwave Anisotropy Probe sky maps
• Three-point Correlation Functions of SDSS Galaxies in Redshift Space: Morphology, Color, and Luminosity Dependence
• The 3-point function in the large scale structure: I. The weakly non-linear regime in N-body simulations
• Three-Point Statistics from a New Perspective
• Cosmic Statistics of Statistics
• 3-point temperature anisotropies in WMAP: Limits on CMB non-Gaussianities and non-linearities
• Fast n-point correlation functions and three-point lensing application
• Statistics of phase correlations as a test for non-Gaussianity of the CMB maps
• Experimental Cosmic Statistics II: Distribution
• Fast Edge Corrected Measurement of the Two-Point Correlation Function and the Power Spectrum
• N-point correlations in CDM and $\Omega$CDM Simulations
• Non-Gaussianity due to Possible Residual Foreground Signals in WMAP 1st-year Data Using Spherical Wavelet Approaches
• The Angular Power Spectrum of the First-Year WMAP Data Reanalysed
• Conditional Cumulants in Weakly Non-linear Regime

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• A roadmap to cosmological parameter analysis with third-order shear statistics III: Efficient estimation of third-order shear correlation functions and an application to the KiDS-1000 data
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