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Register a new userDetection of primordial non-Gaussianity (fNL) in the WMAP 3-year data at above 99.5% confidence
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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 described 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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We constrain the amplitude of primordial non-Gaussianity in the CMB data taking into account the presence of foreground residuals in the maps. We generalise the needlet bispectrum estimator marginalizing over the amplitudes of thermal dust, free-free and synchrotron templates. We apply our procedure to WMAP 5 year data, finding fNL= 38pm 47 (1 sigma), while the analysis without marginalization provides fNL= 35pm 42. Splitting the marginalization over each foreground separately, we found that the estimates of fNL are positively cross correlated of 17%, 12% with the dust and synchrotron respectively, while a negative cross correlation of about -10% is found for the free-free component.
We present skeleton studies of non-Gaussianity in the CMB temperature anisotropy observed in the WMAP5 data. The local skeleton is traced on the 2D sphere by cubic spline interpolation which leads to more accurate estimation of the intersection positions between the skeleton and the secondary pixels than conventional linear interpolation. We demonstrate that the skeleton-based estimator of non-Gaussianity of the local type (f_NL) - the departure of the length distribution from the corresponding Gaussian expectation - yields an unbiased and sufficiently converged f_NL-likelihood. We analyse the skeleton statistics in the WMAP5 combined V- and W-band data outside the Galactic base-mask determined from the KQ75 sky-coverage. The results are consistent with Gaussian simulations of the the best-fitting cosmological model, but deviate from the previous results determined using the WMAP1 data. We show that it is unlikely that the improved skeleton tracing method, the omission of Q-band data, the modification of the foreground-template fitting method or the absence of 6 extended regions in the new mask contribute to such a deviation. However, the application of the Kp0 base-mask in data processing does improve the consistency with the WMAP1 results. The f_NL-likelihoods of the data are estimated at 9 different smoothing levels. It is unexpected that the best-fit values show positive correlation with the smoothing scales. Further investigation argues against a point-source or goodness-of-fit explanation but finds that about 30% of either Gaussian or f_NL samples having better goodness-of-fit than the WMAP5 show a similar correlation. We present the estimate f_NL=47.3+/-34.9 (1sigma error) determined from the first four smoothing angles and f_NL=76.8+/-43.1 for the combination of all nine. The former result may be overestimated at the 0.21sigma-level because of point sources.
We present a Gaussianity analysis of the WMAP 5-year Cosmic Microwave Background (CMB) temperature anisotropy data maps. We use several third order estimators based on the spherical Mexican hat wavelet. We impose constraints on the local non-linear coupling parameter fnl using well motivated non-Gaussian simulations. We analyse the WMAP maps at resolution of 6.9 arcmin for the Q, V, and W frequency bands. We use the KQ75 mask recommended by the WMAP team which masks out 28% of the sky. The wavelet coefficients are evaluated at 10 different scales from 6.9 to 150 arcmin. With these coefficients we compute the third order estimators which are used to perform a chi-squared analysis. The chi-squared statistic is used to test the Gaussianity of the WMAP data as well as to constrain the fnl parameter. Our results indicate that the WMAP data are compatible with the Gaussian simulations, and the fnl parameter is constrained to -8 < fnl < +111 at 95% CL for the combined V+W map. This value has been corrected for the presence of undetected point sources, which add a positive contribution of Delta_fnl = 3+-5 in the V+W map. Our results are very similar to those obtained by Komatsu et al (2008) using the bispectrum.
Higher Criticism is a recently developed statistic for non-Gaussian detection, proposed in Donoho & Jin 2004. We find that Higher Criticism is useful for two purposes. First, Higher Criticism has competitive detection power, and non-Gaussianity is detected at the level 99% in the first year WMAP data. We find that the Higher Criticism value of WMAP is outside the 99% confidence region at a wavelet scale of 5 degrees (99.46% of Higher Criticism values based on simulated maps are below the values for WMAP). Second, Higher Criticism offers a way to locate a small portion of data that accounts for the non-Gaussianity. Using Higher Criticism, we have successfully identified a ring of pixels centered at (lapprox 209 deg, bapprox -57 deg), which seems to account for the observed detection of non-Gaussianity at the wavelet scale of 5 degrees. Note that the detection is achieved in wavelet space first. Second, it is always possible that a fraction of pixels within the ring might deviate from Gaussianity even if they do not appear to be above the 99% confidence level in wavelet space. The location of the ring coincides with the cold spot detected in Vielva et al. 2004 and Cruz et al. 2005.
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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