Do wavelets really detect non-Gaussianity in the 4-year COBE data?

We investigate the detection of non-Gaussianity in the 4-year COBE data reported by Pando, Valls-Gabaud & Fang, using a technique based on the discrete wavelet transform. Their analysis was performed on the two DMR faces centred on the North and South Galactic poles, respectively, using the Daubechies 4 wavelet basis. We show that these results depend critically on the orientation of the data, and so should be treated with caution. For two distinct orientations of the data, we calculate estimates of the skewness, kurtosis and scale–scale correlation of the corresponding wavelet coefficients in all of the available scale domains of the transform. We obtain several detections of non-Gaussianity in the DMR-DSMB map at greater than the 99 per cent confidence level, but most of these occur on pixel–pixel scales and are therefore not cosmological in origin. Indeed, after removing all multipoles beyond ℓ=40 from the COBE maps, only one robust detection remains. Moreover, using Monte Carlo simulations, we find that the probability of obtaining such a detection by chance is 0.59. We repeat the analysis for the 53+90 GHz coadded COBE map. In this case, after removing ℓ>40 multipoles, two non-Gaussian detections at the 99 per cent level remain. Nevertheless, again using Monte Carlo simulations, we find that the probability of obtaining two such detections by chance is 0.28. Thus, we conclude the wavelet technique does not yield strong evidence for non-Gaussianity of cosmological origin in the 4-year COBE data.     

Non-Gaussianity detections in the Bianchi VIIh corrected WMAP one-year data made with directional spherical wavelets

Many of the current anomalies reported in the WMAP text ( WMAP ) one-year data disappear after 'correcting' for the best-fitting embedded Bianchi type VII _h component, albeit assuming no dark energy component. We investigate the effect of this Bianchi correction on the detections of non-Gaussianity in the WMAP data that we previously made using directional spherical wavelets. We confirm that the deviations from Gaussianity in the kurtosis of spherical Mexican hat wavelet coefficients are eliminated once the data are corrected for the Bianchi component, as previously discovered by Jaffe et al. This is due to the reduction of the cold spot at Galactic coordinates  ( l , b ) = (209°, −57°)  , which Cruz et al. claimed to be the sole source of non-Gaussianity introduced in the kurtosis. Our previous detections of non-Gaussianity observed in the skewness of spherical wavelet coefficients are not reduced by the Bianchi correction. Indeed, the most significant detection of non-Gaussianity made with the spherical real Morlet wavelet at a significant level of 98.4 per cent remains (using a very conservative method to estimate the significance). Furthermore, we perform preliminary tests to determine if foregrounds or systematics are the source of this non-Gaussian signal, concluding that it is unlikely that these factors are responsible. We make our code to simulate Bianchi-induced temperature fluctuations publicly available.     

A high-significance detection of non-Gaussianity in the Wilkinson Microwave Anisotropy Probe 1-yr data using directional spherical wavelets

A directional spherical wavelet analysis is performed to examine the Gaussianity of the Wilkinson Microwave Anisotropy Probe ( WMAP ) 1-yr data. Such an analysis is facilitated by the introduction of a fast directional continuous spherical wavelet transform. The directional nature of the analysis allows us to probe orientated structure in the data. Significant deviations from Gaussianity are detected in the skewness and kurtosis of spherical elliptical Mexican hat and real Morlet wavelet coefficients for both the WMAP and Tegmark, de Oliveira-Costa & Hamilton foreground-removed maps. The previous non-Gaussianity detection made by Vielva et al. using the spherical symmetric Mexican hat wavelet is confirmed, although their detection at the 99.9 per cent significance level is only made at the 95.3 per cent significance level using our most conservative statistical test. Furthermore, deviations from Gaussianity in the skewness of spherical real Morlet wavelet coefficients on a wavelet scale of 550 arcmin (corresponding to an effective global size on the sky of ∼26° and an internal size of ∼3°) at an azimuthal orientation of 72°, are made at the 98.3 per cent significance level, using the same conservative method. The wavelet analysis inherently allows us to localize on the sky those regions that introduce skewness and those that introduce kurtosis. Preliminary noise analysis indicates that these detected deviation regions are not atypical and have average noise dispersion. Further analysis is required to ascertain whether these detected regions correspond to secondary or instrumental effects, or whether in fact the non-Gaussianity detected is due to intrinsic primordial fluctuations in the cosmic microwave background.     

Transient events in the COBE database simultaneous with gamma ray bursts

We are investigating the COBE DMR data at instances of known -ray bursts (GRBs) when any of the six DMR horn directions was coincident with the direction of a burst. The BATSE instrument on board GRO has detected 207 bursts during the eight-month period of overlap corresponding to the current release of COBE data. The odds of a GRB occurring within the DMR field of view are near one coincidence per year. Here we report on one such serendipitous observation in 1991, GRB 911226, for which a detailed analysis is currently in progress.     

COBE observations of the microwave counterpart of GRBs

We have used the data from the COBE satellite to search for delayed microwave emission (31 - 90 GHz) from Gamma Ray Bursts (GRBs). The large 7° beam of COBE is well matched to the large positional uncertainties in the GRB locations, although it also means that fluxes from (point source) GRB objects will be diluted. In view of this we are doing a statistical search of the GRBs which occurred during the currently released COBE DMR data (years 1990 and 1991), which overlap 200 GRBs recorded by GRO. Here we concentrate on just the top 10 GRBs (in peak counts/second). We obtain the limits on the emission by comparing the COBE fluxes before and after the GRB at the GRB location. Since it is thought that the microwave emission should lag the GRB event, we have searched the GRB position for emission in the few months following the GRB occurrence.     

Present limits to cosmic bubbles from the COBE-DMR three-point correlation function

The existence of large-scale voids in several galaxy surveys suggests the occurrence of an inflationary first-order phase transition. This process generates primordial bubbles that, before evolving into the present voids, leave at decoupling a non-Gaussian imprint on the cosmic microwave background.
In this paper we evaluate an analytical expression of the collapsed three-point correlation function from the bubble temperature fluctuations. Comparing the results with COBE -DMR measures, we obtain upper limits on the allowed non-Gaussianity and hence on the bubble parameters.     

Cross-correlation between WMAP and 2MASS: non-Gaussianity induced by the SZ effect

We study the non-Gaussianity induced by the Sunyaev–Zel'dovich (SZ) effect in cosmic microwave background (CMB) fluctuation maps. If a CMB map is contaminated by the SZ effect of galaxies or galaxy clusters, the CMB maps should have similar non-Gaussian features to the galaxy and cluster fields. Using the WMAP data and 2MASS galaxy catalogue, we show that the non-Gaussianity of the 2MASS galaxies is imprinted on WMAP maps. The signature of non-Gaussianity can be seen with the fourth-order cross-correlation between the wavelet variables of the WMAP maps and 2MASS clusters. The intensity of the fourth-order non-Gaussian features is found to be consistent with the contamination of the SZ effect of 2MASS galaxies. We also show that this non-Gaussianity can not be seen by the high-order autocorrelation of the WMAP . This is because the SZ signals in the autocorrelations of the WMAP data generally are weaker than the WMAP –2MASS cross-correlations by a factor f ², which is the ratio between the powers of the SZ-effect map and the CMB fluctuations on the scale considered. Therefore, the ratio of high-order autocorrelations of CMB maps to cross-correlations of the CMB maps and galaxy field would be effective to constrain the powers of the SZ effect on various scales.     

Automated Detection of Coronal Loops Using a Wavelet Transform Modulus Maxima Method

We propose and test a wavelet transform modulus maxima method for the automated detection and extraction of coronal loops in extreme ultraviolet images of the solar corona. This method decomposes an image into a number of size scales and tracks enhanced power along each ridge corresponding to a coronal loop at each scale. We compare the results across scales and suggest the optimum set of parameters to maximize completeness, while minimizing detection of noise. For a test coronal image, we compare the global statistics (e.g. number of loops at each length) to previous automated coronal-loop detection algorithms.     

A high-significance detection of non-Gaussianity in the WMAP 5-yr data using directional spherical wavelets

We repeat the directional spherical real Morlet wavelet analysis, used previously to detect non-Gaussianity in the Wilkinson Microwave Anisotropy Probe ( WMAP ) 1- and 3-yr data, on the WMAP 5-yr data. The non-Gaussian signal detected previously is present in the 5-yr data at a slightly increased statistical significance of approximately 99 per cent. Localized regions that contribute most strongly to the non-Gaussian signal are found to be very similar to those detected in the previous releases of the WMAP data. When the localized regions detected in the 5-yr data are excluded from the analysis, the non-Gaussian signal is eliminated.     

Cosmic microwave background bispectrum and slow-roll inflation

Recent tentative findings of non-Gaussian structure in the COBE -DMR data set have triggered renewed attention on candidate models from which such intrinsic signature could arise. In the framework of slow-roll inflation with built-in non-linearities in the inflaton field evolution, we present expressions for both the cosmic microwave background (CMB) skewness and the full angular bispectrum _ℓ1ℓ₂ℓ₃ in terms of the slow-roll parameters. We use an estimator for the angular bispectrum recently proposed in the literature and calculate its variance for an arbitrary ℓ _i multipole combination. We stress that a real detection of non-Gaussianity in the CMB would imply that an important component of the anisotropies arises from processes other than primordial quantum fluctuations. We further investigate the behaviour of the signal-to-(theoretical) noise ratio and demonstrate for generic inflationary models that it decreases in the limited range of small ℓs considered for increasing multipole ℓ, while the opposite applies for the standard _ℓs.     

Multi-Conjugate Adaptive Optics with laser guide stars: performance in the infrared and visible

The assumption of the Gaussianity of primordial perturbations plays an important role in modern cosmology. The most direct test of this hypothesis consists of testing the Gaussianity of cosmic microwave background (CMB) maps. Counting the pixels with the temperatures in given ranges and thus estimating the one-point probability function of the field is the simplest of all the tests. Other usually more complex tests of Gaussianity generally use a great deal of the information already contained in the probability function. However, the most interesting outcome of such a test would be the signal of non-Gaussianity independent of the probability function. It is shown that the independent information has purely morphological character i.e. it depends on the geometry and topology of the level contours only. As an example we discuss in detail the quadratic model   v = u + α ( u ²-1)  ( u is a Gaussian field with   u¯ =0  and  〈 u ²〉=1  , α is a parameter) that may arise in slow-roll or two-field inflation models. We show that in the limit of small amplitude α the full information about the non-Gaussianity is contained in the probability function. If other tests are performed on this model they simply recycle the same information. A simple procedure allowing us to assess the sensitivity of any statistics to the morphological information is suggested. We provide an analytic estimate of the statistical limit for detecting the quadratic non-Gaussianity α _c as a function of the map size in the ideal situation when the scale of the field is resolved. This estimate is in a good agreement with the results of the Monte Carlo simulations of 256² and 1024² maps. The effect of resolution on the detection quadratic non-Gaussianity is also briefly discussed.     

The effects of primordial non-Gaussianity on the cosmological reionization

We investigate the effects of non-Gaussianity in the primordial density field on the reionization history. We rely on a semi-analytic method to describe the processes acting on the intergalactic medium (IGM), relating the distribution of the ionizing sources to that of dark matter haloes. Extending previous work in the literature, we consider models in which the primordial non-Gaussianity is measured by the dimensionless non-linearity parameter f _NL, using the constraints recently obtained from cosmic microwave background data. We predict the ionized fraction and the optical depth at different cosmological epochs assuming two different kinds of non-Gaussianity characterized by a scale-independent and a scale-dependent f _NL and comparing the results to those for the standard Gaussian scenario. We find that a positive f _NL enhances the formation of high-mass haloes at early epochs when reionization begins, and, as a consequence, the IGM ionized fraction can grow by a factor of up to 5 with respect to the corresponding Gaussian model. The increase of the filling factor has a small impact on the reionization optical depth and is of the order of ∼10 per cent if a scale-dependent non-Gaussianity is assumed. Our predictions for non-Gaussian models are in agreement with the latest Wilkinson Microwave Anisotropy Probe results within the error bars, but a higher precision is required to constrain the scale dependence of non-Gaussianity.     

No Higher Criticism of the Bianchi-corrected Wilkinson Microwave Anisotropy Probe data

Higher Criticism (HC) has been proposed by Donoho & Jin as an effective statistic to detect deviations from Gaussianity. Motivated by the success of the Bianchi VII_h model in addressing many of the anomalies observed in the Wilkinson Microwave Anisotropy Probe ( WMAP ) data (Jaffe et al.), we present calculations in real and in wavelet space of the HC statistic of the Bianchi-corrected WMAP first-year data. At the wavelet scale of 5°, the HC of the WMAP map drops from a value above the 99 per cent confidence level (c.l.) to a value below the 68 per cent CL when corrected by the Bianchi template. An important property of the HC statistic is its ability to locate the pixels that account for the deviation from Gaussianity. The analysis of the uncorrected WMAP data pointed to a cold spot in the Southern hemisphere, centred at   l ∼ 209°, b ∼−57°  . The HC of the Bianchi-corrected map indicates that this spot remains prominent, albeit at a level completely consistent with Gaussian statistics. Consequently, it is debatable how much emphasis should be placed on this residual feature, but we consider the effect of modestly increasing the scaling of the template. A factor of only 1.2 renders the spot indistinguishable from the background level, with no noticeable impact on the results published in Jaffe et al. for the low- l anomalies, large-scale power asymmetry or wavelet kurtosis. A trivial interpretation would be that the Bianchi template may require a small enhancement of power on scales corresponding to the wavelet scale of 5°.     

Non-Gaussianity of peak statistics in contrasting spots of WMAP ILC

We study the statistics of isolated maxima and minima in the regions of three contrasting spots in the WMAP7 ILC data. A non-Gaussianity of signal distribution is detected in these regions. We demonstrate that non-Gaussian properties are related to the appearance of low harmonics (ℓ ≤20). Possible reasons of this non-Gaussianity are discussed.     

Non-Gaussian distribution and clustering of hot and cold pixels in the five-year WMAP sky

We present measurements of the clustering of hot and cold patches in the microwave background sky as measured from the Wilkinson Microwave Anisotropy Probe 5-year data. These measurements are compared with theoretical predictions which assume that the cosmological signal obeys Gaussian statistics. We find significant differences from the simplest Gaussian-based prediction. However, the measurements are sensitive to the fact that the noise is spatially inhomogeneous (e.g. because different parts of the sky were observed for different lengths of time). We show how to account for this spatial inhomogeneity when making predictions. Differences from the Gaussian-based expectation remain even after this more careful accounting of the noise. In particular, we note that hot and cold pixels cluster differently within the same temperature thresholds at few-degree scales. While these findings may indicate primordial non-Gaussianity, we discuss other plausible explanations for these discrepancies. In addition, we find some deviations from Gaussianity at sub-degree scales, especially in the W band, whose origin may be associated with extragalactic dust emission.     

Wavelet analysis and the detection of non-Gaussianity in the cosmic microwave background

We investigate the use of wavelet transforms in detecting and characterizing non-Gaussian structure in maps of the cosmic microwave background (CMB). We apply the method to simulated maps of the KaiserStebbins effect resulting from cosmic strings, on to which Gaussian signals of varying amplitudes are superposed. We find that the method significantly outperforms standard techniques based on measuring the moments of the pixel temperature distribution. We also compare the results with those obtained using techniques based on Minkowski functionals, and we again find the wavelet method to be superior. In particular, using the wavelet technique, we find that it is possible to detect non-Gaussianity even in the presence of a superposed Gaussian signal with 3 times the rms amplitude of the original cosmic string map. We also find that the wavelet technique is useful in characterizing the angular scales at which the non-Gaussian signal occurs.     

The complete bispectrum of COBE-DMR four-year maps

We extend a previous bispectrum analysis of the COBE -DMR four-year maps, allowing for the presence of correlations between all possible angular scales. For reasons of presentation we restrict ourselves to triplets of modes symmetrically arranged, but with larger and larger ℓ separation. We find that the non-Gaussian signal found earlier for bispectrum components including adjacent modes does not extend to triplets of modes with larger separations. Indeed for all separations Δℓ>1 we find that the COBE -DMR data are very Gaussian. The implication seems to be that the previously detected non-Gaussian scale–scale correlation falls off very quickly with mode separation.     

The cluster abundance in cosmic string models for structure formation

We use the present observed number density of large X-ray clusters to constrain the amplitude of matter density perturbations induced by cosmic strings on the scale of 8  h ⁻¹ Mpc ( σ ₈), in both open cosmologies and flat models with a non-zero cosmological constant. We find a slightly lower value of σ ₈ than that obtained in the context of primordial Gaussian fluctuations generated during inflation. This lower normalization of σ ₈ results from the mild non-Gaussianity on cluster scales, where the one-point probability distribution function is well approximated by a χ ² distribution and thus has a longer tail than a Gaussian distribution. We also show that σ ₈ normalized using cluster abundance is consistent with the COBE normalization.