Statistics and Topology of the COBE DMR First Year Maps

Abstract

We use statistical and topological quantities to test the COBE-DMR first year sky maps against the hypothesis that the observed temperature fluctuations reflect Gaussian initial density perturbations with random phases. Recent papers discuss specific quantities as discriminators between Gaussian and non-Gaussian behavior, but the treatment of instrumental noise on the data is largely ignored. The presence of noise in the data biases many statistical quantities in a manner dependent on both the noise properties and the unknown CMB temperature field. Appropriate weighting schemes can minimize this effect, but it cannot be completely eliminated. Analytic expressions are presented for these biases, and Monte Carlo simulations used to assess the best strategy for determining cosmologically interesting information from noisy data. The genus is a robust discriminator that can be used to estimate the power law quadrupole-normalized amplitude independently of the 2-point correlation function. The genus of the DMR data are consistent with Gaussian initial fluctuations with Q_rms = 15.7 +/- 2.2 - (6.6 +/- 0.3)(n - 1) uK where n is the power law index. Fitting the rms temperature variations at various smoothing angles gives Q_rms = 13.2 +/- 2.5 uK and n = 1.7 +0.3 -0.6. While consistent with Gaussian fluctuations, the first year data are only sufficient to rule out strongly non-Gaussian distributions of fluctuations.

17 pages post script

Cited by in corpus (40)

• 4-Year COBE DMR Cosmic Microwave Background Observations: Maps and Basic Results
• Cosmology with a Primordial Scaling Field
• Structure formation with a self-tuning scalar field
• Multipole Vectors--a new representation of the CMB sky and evidence for statistical anisotropy or non-Gaussianity at 2<=l<=8
• Beyond genus statistics: a unifying approach to the morphology of cosmic structure
• Tests for Non-Gaussian Statistics in the DMR Four-Year Sky Maps
• Non-Gaussian Signatures in the Cosmic Background Radiation from Warm Inflation
• Non-Gaussian statistics of critical sets in 2 and 3D: Peaks, voids, saddles, genus and skeleton
• Tests for Gaussianity of the MAXIMA-1 CMB Map
• Minkowski Functional Description of Microwave Background Gaussianity
• Wavelet analysis and the detection of non-Gaussianity in the CMB
• On the Non-Gaussianity Observed in the COBE-DMR Sky Maps
• Is the cosmic microwave background really non-Gaussian?
• Topology of structure in the Sloan Digital Sky Survey: model testing
• On the trispectrum as a gaussian test for cosmology
• Gaussianity of Degree-Scale Cosmic Microwave Background Anisotropy Observations
• The correlation of peaks in the microwave background
• Topology of Neutral Hydrogen Within the Small Magellanic Cloud
• Two Dimensional Topology of Large Scale Structure in the Las Campanas Redshift Survey
• Best Unbiased Estimators for the Three-Point Correlators of the Cosmic Microwave Background Radiation
• Statistical Power, the Bispectrum and the Search for Non-Gaussianity in the CMB Anisotropy
• General Statistical properties of the CMB Polarization field
• Topology of the Galaxy Distribution in the Hubble Deep Fields
• Long range correlation in cosmic microwave background radiation
• A Bayesian estimate of the skewness of the Cosmic Microwave Background
• Probing CMB Non-Gaussianity Using Local Curvature
• Topology from the Simulated Sloan Digital Sky Survey
• Full-sky correlations of peaks in the microwave background
• Weakly non-Gaussian formula for the Minkowski functionals in general dimensions
• Characteristic Angular Scales in Cosmic Microwave Background Radiation
• The Topology of Large Scale Structure in the 1.2 Jy IRAS Redshift Survey
• Effects of Foreground Contamination on the Cosmic Microwave Background Anisotropy Measured by MAP
• Kolmogorov Complexity, Cosmic Microwave Background Maps and the Curvature of the Universe
• Analysing large scale structure: II. Testing for primordial non-Gaussianity in CMB maps using surrogates
• Toward High-Precision Measures of Large-Scale Structure
• Two cosmological models for clusters of galaxies
• Statistics of the excursion sets in models with local primordial non-Gaussianity
• Primordial Feature at the Scale of Superclusters of Galaxies
• The topology of weak lensing field in the neighborhood of MS1054-03
• Searching for Long Strings in CMB Maps