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تسجيل مستخدم جديدA Statistically Robust 3-Sigma Detection of Non-Gaussianity in the WMAP Data Using Hot and Cold Spots
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We present a careful frequentist analysis of one- and two-point statistics of the hot and cold spots in the cosmic microwave background (CMB) data obtained by the Wilkinson Microwave Anisotropy Probe (WMAP). Our main result is the detection of a new anomaly at the 3-sigma level using temperature-weighted extrema correlation functions. We obtain this result using a simple hypothesis test which reduces the maximum risk of a false detection to the same level as the claimed significance of the test. We further present a detailed study of the robustness of our earlier claim (Larson and Wandelt 2004) under variations in the noise model and in the resolution of the map. Free software which implements our test is available online.
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This paper presents a frequentist analysis of the hot and cold spots of the cosmic microwave background data collected by the Wilkinson Microwave Anisotropy Probe (WMAP). We compare the WMAP temperature statistics of extrema (number of extrema, mean
excursion, variance, skewness and kurtosis of the excursion) to Monte-Carlo simulations. We find that, on average, the local maxima (high temperatures in the anisotropy) are too cold and the local minima are too warm. In order to quantify this claim we describe a two-sided statistical hypothesis test which we advocate for other investigations of the Gaussianity hypothesis. Using this test we reject the isotropic Gaussian hypothesis at more than 99% confidence in a well-defined way. Our claims are based only on regions that are outside the most conservative WMAP foreground mask. We perform our test separately on maxima and minima, and on the north and south ecliptic and Galactic hemispheres and reject Gaussianity at above 95% confidence for almost all tests of the mean excursions. The same test also shows the variance of the maxima and minima to be low in the ecliptic north (99% confidence), but consistent in the south; this effect is not as pronounced in the Galactic north and south hemispheres.
We introduce the numbers of hot and cold spots, $n_h$ and $n_c$, of excursion sets of the CMB temperature anisotropy maps as statistical observables that can discriminate different non-Gaussian models. We numerically compute them from simulations of
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We present evidence for the detection of primordial non-Gaussianity of the local type (fNL), using the temperature information of the Cosmic Microwave Background (CMB) from the WMAP 3-year data. We employ the bispectrum estimator of non-Gaussianity d
escribed in (Yadav et al. 2007) which allows us to analyze the entirety of the WMAP data without an arbitrary cut-off in angular scale. Using the combined information from WMAPs two main science channels up to lmax=750 and the conservative Kp0 foreground mask we find 27 < fNL < 147 at 95% C.L., with a central value of fNL=87. This corresponds to a rejection of fNL=0 at more than 99.5% significance. We find that this detection is robust to variations in lmax, frequency and masks, and that no known foreground, instrument systematic, or secondary anisotropy explains our signal while passing our suite of tests. We explore the impact of several analysis choices on the stated significance and find 2.5 sigma for the most conservative view. We conclude that the WMAP 3-year data disfavors canonical single field slow-roll inflation.
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The decomposition of a signal on the sphere with the steerable wavelet constructed from the second Gaussian derivative gives access to the orientation, signed-intensity, and elongation of the signals local features. In the present work, the non-Gauss
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