We present a model-independent method to test for scale-dependent non-Gaussianities in combination with scaling indices as test statistics. Therefore, surrogate data sets are generated, in which the power spectrum of the original data is preserved, while the higher order correlations are partly randomized by applying a scale-dependent shuffling procedure to the Fourier phases. We apply this method to the Wilkinson Microwave Anisotropy Probe data of the cosmic microwave background and find signatures for non-Gaussianities on large scales. Further tests are required to elucidate the origin of the detected anomalies.
We continue the analysis of non‐Gaussianities in the cosmic microwave background by means of the scaling index method by applying this method on the single Q, V, W bands and the co‐added VW band of the five‐year data of the Wilkinson Microwave Anisotropy Probe. We compare each of the results with 1000 Monte Carlo simulations mimicking the Gaussian properties of the best fitting Λ cold dark matter model. Based on the scaling indices, scale‐dependent empirical probability distributions, moments of these distributions and χ2 combinations of them are calculated, obtaining similar results as in the former analysis of the three‐year data: we derive evidence for non‐Gaussianity with a probability of up to 97.3 per cent for the mean when regarding the KQ75‐masked full sky and summing up over all considered length‐scales by means of a diagonal χ2 statistics. Looking at only the northern or southern hemisphere of the galactic coordinate system, we obtain up to 98.5 or 96.6 per cent, respectively. For the standard deviation, these results appear as 95.6 per cent for the full sky (99.7 per cent north, 89.4 per cent south) and for a χ2 combination of both measurements as 97.4 per cent (99.1 per cent north, 95.5 per cent south). We obtain larger deviations from Gaussianity when looking at separate scale lengths. By performing an analysis of rotated hemispheres, we detect an obvious asymmetry in the data. In addition to these investigations, we present a method of filling the mask with Gaussian noise to eliminate boundary effects caused by the mask. With the help of this technique, we identify several local features on the map, of which the most significant one turns out to be the well‐known cold spot. When excluding all these spots from the analysis, the deviation from Gaussianity increases, which shows that the discovered local anomalies are not the reason of the global detection of non‐Gaussianity, but actually were damping the deviations on average. Our analyses per band and per year suggest, however, that it is very unlikely that the detected anomalies are due to foreground effects.
We present a model-independent investigation of the Wilkinson Microwave Anisotropy Probe (WMAP) data with respect to scale-independent and scale-dependent non-Gaussianities (NGs). To this end, we employ the method of constrained randomization. For generating so-called surrogate maps a well-specified shuffling scheme is applied to the Fourier phases of the original data, which allows us to test for the presence of higher order correlations (HOCs) also and especially on well-defined scales. Using scaling indices as test statistics for the HOCs in the maps we find highly significant signatures for NGs when considering all scales. We test for NGs in four different l-bands Δl, namely in the bands Δl=[2, 20], [20, 60], [60, 120] and [120, 300]. We find highly significant signatures for both NGs and ecliptic hemispherical asymmetries for the interval Δl=[2, 20] covering the large scales. We also obtain highly significant deviations from Gaussianity for the band Δl=[120, 300]. The result for the full l-range can then easily be interpreted as a superposition of the signatures found in the bands Δl=[2, 20] and [120, 300]. We find remarkably similar results when analysing different ILC-like maps based on the WMAP 3-, 5- and 7-year data. We perform a set of tests to investigate whether and to what extent the detected anomalies can be explained by systematics. While none of these tests can convincingly rule out the intrinsic nature of the anomalies for the low-l case, the ILC map making procedure and/or residual noise in the maps can also lead to NGs at small scales. Our investigations prove that there are phase correlations in the WMAP data of the cosmic microwave background. In the absence of an explanation in terms of Galactic foregrounds or known systematic artefacts, the signatures at low l must so far be taken to be cosmological at high significance. These findings would strongly disagree with predictions of isotropic cosmologies with single field slow roll inflation. The task is now to elucidate the origin of the phase correlations and to understand the physical processes leading to these scale-dependent NGs - if it turns out that systematics as a cause for them must be ruled out
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