Multiple Methods for Estimating the Bispectrum of the Cosmic Microwave Background with Application to the MAXIMA Data
arXiv:astro-ph/0211123 · doi:10.1046/j.1365-8711.2003.06438.x
Abstract
We describe different methods for estimating the bispectrum of Cosmic Microwave Background data. In particular we construct a minimum variance estimator for the flat-sky limit and compare results with previously-studied frequentist methods. Application to the MAXIMA dataset shows consistency with primordial Gaussianity. Weak quadratic non-Gaussianity is characterised by a tunable parameter , corresponding to non-Gaussianity at a level (ratio of non-Gaussian to Gaussian terms), and we find limits of for the minimum-variance estimator and for the usual frequentist estimator. These are the tightest limits on primordial non-Gaussianity which include the full effects of the radiation transfer function.
24 pages, 13 figures
References in corpus (43)
- A Flat Universe from High-Resolution Maps of the Cosmic Microwave Background Radiation
- A Line of Sight Approach to Cosmic Microwave Background Anisotropies
- Cosmological Perturbation Theory in the Synchronous vs. Conformal Newtonian Gauge
- Cosmological Perturbation Theory in the Synchronous and Conformal Newtonian Gauges
- Generating the curvature perturbation without an inflaton
- MAXIMA-1: A Measurement of the Cosmic Microwave Background Anisotropy on angular scales of 10 arcminutes to 5 degrees
- 4-Year COBE DMR Cosmic Microwave Background Observations: Maps and Basic Results
- Acoustic Signatures in the Primary Microwave Background Bispectrum
- DASI First Results: A Measurement of the Cosmic Microwave Background Angular Power Spectrum
- The Three--Point Correlation Function of the Cosmic Microwave Background in Inflationary Models
- Weak Lensing of the CMB: A Harmonic Approach
- Estimating the Power Spectrum of the Cosmic Microwave Background
- How to measure CMB power spectra without losing information
- Large-scale structure, the cosmic microwave background, and primordial non-gaussianity
- Cosmological implications of the MAXIMA-I high resolution Cosmic Microwave Background anisotropy measurement
- The Angular Trispectrum of the CMB
- Non-Gaussianity from Inflation
- The Angular Dependence of the Three-Point Correlation Function of the Cosmic Microwave Background Radiation as Predicted by Inflationary Cosmologies
- The Microwave Background Bispectrum, Paper II: A Probe of the Low Redshift Universe
- The Cosmic Microwave Background Bispectrum and Inflation
- The Bispectrum of IRAS Galaxies
- Evidence for non-Gaussianity in the COBE DMR Four Year Sky Maps
- The Microwave Background Bispectrum, Paper I: Basic Formalism
- Interferometric Observation of Cosmic Microwave Background Anisotropies
- Measurement of the cosmic microwave background bispectrum on the COBE DMR sky maps
- Constraints on Galaxy Bias, Matter Density, and Primordial Non--Gausianity from the PSCz Galaxy Redshift Survey
- Estimating non-gaussianity in the microwave background
- Imprint of Reionization on the Cosmic Microwave Background Bispectrum
- Higher-Order Gravitational Perturbations of the Cosmic Microwave Background
- A Measurement of the Angular Power Spectrum of the Microwave Background Made from the High Chilean Andes
- Conformal Invariance and Cosmic Background Radiation
- The Angular Bispectrum of The Cosmic Microwave Background
- Tests for Gaussianity of the MAXIMA-1 CMB Map
- On the APM power spectrum and the CMB anisotropy: Evidence for a phase transition during inflation?
- Reproducing Cosmic Microwave Background anisotropies with mixed isocurvature perturbations
- Estimate of the Cosmological Bispectrum from the MAXIMA-1 Cosmic Microwave Background Map
- The Trispectrum of the 4 Year COBE-DMR data
- Best Unbiased Estimators for the Three-Point Correlators of the Cosmic Microwave Background Radiation
- Quasi-Linear Evolution of Compensated Cosmological Perturbations: The Nonlinear Sigma Model
- CMB Bispectrum from Active Models of Structure Formation
- Generating non-Gaussian maps with a given power spectrum and bispectrum
- Photographing the wave function of the Universe
- Statistical Tests for the Gaussian Nature of Primordial Fluctuations Through CBR Experiments
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- Non-Gaussianity from Inflation: Theory and Observations
- First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Tests of Gaussianity
- Multipole Vectors--a new representation of the CMB sky and evidence for statistical anisotropy or non-Gaussianity at 2<=l<=8
- Multifrequency analysis of 21 cm fluctuations from the Era of Reionization
- Measuring primordial non-Gaussianity in the cosmic microwave background
- Non-Gaussian Signatures in the Temperature Fluctuation Observed by the Wilkinson Microwave Anisotropy Probe
- Weak lensing analysis in three dimensions
- Optimal Estimation of Non-Gaussianity
- Wavelets and WMAP non-Gaussianity
- Measuring dark energy properties with 3D cosmic shear
- Primordial Non-Gaussianity in the Cosmic Microwave Background
- A New Approach to Probing Primordial Non-Gaussianity
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- High-Resolution Simulations of Cosmic Microwave Background non-Gaussian Maps in Spherical Coordinates
- Cosmology Without Window Functions: Cubic Estimators for the Galaxy Bispectrum
- Detecting Bispectral Acoustic Oscillations from Inflation Using a New Flexible Estimator
- New Optimised Estimators for the Primordial Trispectrum
- Improved constraints on primordial non-Gaussianity for the Wilkinson Microwave Anisotropy Probe 5-yr data
- Primordial non-Gaussianity: local curvature method and statistical significance of constraints on f_NL from WMAP data
- Non-Gaussianity: Comparing wavelet and Fourier based methods
- The integrated bispectrum as a test of CMB non-Gaussianity: detection power and limits on f_NL with WMAP data
- Secondary non-Gaussianity and Cross-Correlation Analysis
- New Approaches to Probing Minkowski Functionals
- BOOMERanG Constraints on Primordial Non-Gaussianity from Analytical Minkowski Functionals
- Constraints on general primordial non-Gaussianity using wavelets for the Wilkinson Microwave anisotropy probe 7-year data
- MAXIMA: A Balloon-Borne Cosmic Microwave Background Anisotropy Experiment
- Estimating the bispectrum of the Very Small Array data
- Optimal Estimation of the Binned Mask-Free Power Spectrum, Bispectrum, and Trispectrum on the Full Sky: Scalar Edition
- Primordial Non-Gaussianity from a Joint Analysis of Cosmic Microwave Background Temperature and Polarization
- Searching for non-Gaussianity in the VSA data
- On the optimality of the spherical Mexican hat wavelet estimator for the primordial non-Gaussianity
- Goodness-of-Fit Tests to study the Gaussianity of the MAXIMA data
- Recent Results from the MAXIMA Experiment
- Non-Gaussianity of diffuse Galactic synchrotron emission at 408 MHz
- Separating the kinetic SZ effect from primary CMB fluctuations
- Investigating non-Gaussianity in Cosmic Microwave Background Temperature Maps using Spherical Harmonic Phases