We repeat the directional spherical real Morlet wavelet analysis, used to detect non-Gaussianity in the Wilkinson Microwave Anisotropy Probe (WMAP) 1-year and 3-year data (McEwen et al. 2005, 2006a), on the WMAP 5-year data. The non-Gaussian signal detected previously is present in the 5-year data at a slightly increased statistical significance of approximately 99%. Localised 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 localised regions detected in the 5-year data are excluded from the analysis the non-Gaussian signal is eliminated.
We study the SZ-effect-induced non-Gaussianity in the 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 as the galaxy and cluster fields. Using the WMAP data and 2MASS galaxy catalog 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 4^{th} order cross correlation between the wavelet variables of the WMAP maps and 2MASS clusters. The intensity of the 4^{th} order non-Gaussian f…
We repeat the directional spherical real Morlet wavelet analysis used to detect non-Gaussianity in the WMAP 1-year data (McEwen et al. 2005a), on the WMAP 3-year data. The non-Gaussian signal previously detected is indeed present in the 3-year data, although the significance of the detection is reduced. Using our most conservative method for constructing significance measures, we find the significance of the detection of non-Gaussianity drops from 98.3+/-0.4% to 94.9+/-0.7%; the significance drops from 99.3+/-0.3% to 97.2+/-0.5% using a method based on the $χ^2$ statistic. The wavelet analysis…
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…
A non-Gaussian detection in the WMAP 1-year data is reported. The detection has been found in the combined Q-V-W map proposed by the WMAP team (Komatsu et al. 2003) after applying a wavelet technique based on the Spherical Mexican Hat Wavelet (SMHW). The skewness and the kurtosis of the SMHW coefficients are calculated at different scales. A non-Gaussian signal is detected at scales of the SMHW around 4 deg (size in the sky of around 10 deg). The right tail probability of the detection is approx. 0.4%. In addition, a study of Gaussianity is performed in each hemisphere. The northern hemisphere…
We present non-Gaussianity testing on recently-released derived maps from the first-year WMAP data by Tegmark, de Oliveria-Costa and Hamilton. Our test is based on a phase mapping technique which has the advantage of testing non-Gaussianity at separate multipole bands. We show that their foreground-cleaned map is against the random-phase hypothesis at all 4 multipole bands centered around l = 150, 290, 400 and 500. Their Wiener-filtered map, on the other hand, is Gaussian for l < 250, and marginally Gaussian for 224 < l < 350. However, we see the evidence of non-Gaussianity for l > 350 as we d…
Alfven turbulence caused by statistically isotropic and homogeneous primordial magnetic field induces correlations in the cosmic microwave background anisotropies. The correlations are specifically between spherical harmonic modes a_{l-1,m} and a_{l+1,m}. In this paper we approach this issue from phase analysis of the CMB maps derived from the WMAP data sets. Using circular statistics and return phase mapping we examine phase correlation of Δl=2 for the primordial non-Gaussianity caused by the Alfven turbulence at the epoch of recombination. Our analyses show that such specific features from t…
Many of the current anomalies reported in the Wilkinson Microwave Anisotropy Probe (WMAP) 1-year data disappear after `correcting' for the best-fit embedded Bianchi type VII_h component (Jaffe et al. 2005), 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 (McEwen et al. 2005a). As previously discovered by Jaffe et al. (2005), the deviations from Gaussianity in the kurtosis of spherical Mexican hat wavelet coefficients are eliminated on…
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 WMAP's 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…
We present an analysis of the Minkowski Functionals (MFs) describing the WMAP three-year temperature maps to place limits on possible levels of primordial non-Gaussianity. In particular, we apply perturbative formulae for the MFs to give constraints on the usual non-linear coupling constant fNL. The theoretical predictions are found to agree with the MFs of simulated CMB maps including the full effects of radiative transfer. The agreement is also very good even when the simulation maps include various observational artifacts, including the pixel window function, beam smearing, inhomogeneous no…
We look for a non-Gaussian signal in the WMAP 5-year temperature anisotropy maps by performing a needlet-based data analysis. We use the foreground-reduced maps obtained by the WMAP team through the optimal combination of the W, V and Q channels, and perform realistic non-Gaussian simulations in order to constrain the non-linear coupling parameter $\fnl$. We apply a third-order estimator of the needlet coefficients skewness and compute the $χ^2$ statistics of its distribution. We obtain $-80<\fnl<120$ at 95% confidence level, which is consistent with a Gaussian distribution and comparable to p…
We present a search for non-Gaussianity in the WMAP first-year data using the two-point correlation function of maxima and minima in the temperature map. We find evidence for non-Gaussianity on large scales, whose origin appears to be associated with unsubstracted foregrounds, but which is not entirely clear. The signal appears to be associated most strongly with cold spots, and is more pronounced in the Southern galactic hemisphere. Removal of the region of sky near the galactic plane, or filtering out large-scale modes removes the signal. Analysis of individual frequency maps shows strongest…
We present a comparison between three approaches to test non-Gaussianity of cosmic microwave background data. The Minkowski functionals, the empirical process method and the skewness of wavelet coefficients are applied to maps generated from non-standard inflationary models and to Gaussian maps with point sources included. We discuss the different power of the pixel, harmonic and wavelet space methods on these simulated almost full-sky data (with Planck like noise). We also suggest a new procedure consisting of a combination of statistics in pixel, harmonic and wavelet space.
We cross correlate the Wilkinson Microwave Anisotropy Probe (WMAP) first year data and the diffuse gamma-ray intensity maps from the Energetic Gamma Ray Experiment Telescope (EGRET) using spherical wavelet approaches. Correlations at 99.7% significance level have been detected, at scales around $15^{\circ}$ in the WMAP foreground cleaned W-band and Q-band maps, based on data from regions that are outside the most conservative WMAP foreground mask; no significant correlation is found with the Tegmark cleaned map. The detected correlation is most likely of Galactic origin, and thus can help us p…
We perform multi-scale non-Gaussianity detection and localization to the Wilkinson Microwave Anisotropy Probe (WMAP) first-year data in both wavelet and real spaces. Such an analysis is facilitated by spherical wavelet transform and inverse transform techniques developed by the YAWtb team. Skewness and kurtosis as test statistics are calculated on scales from about $1^{\circ}$ to $30^{\circ}$ on the sky as well as toward different directions using anisotropic spherical Morlet wavelet (SMW). A maximum deviation from Gaussian simulations with a right tail probability of $\sim 99.9%$ is detected …
We investigate the Gaussianity of the 4-year COBE-DMR data (in HEALPix pixelisation) using an analysis based on spherical Haar wavelets. We use all the pixels lying outside the Galactic cut and compute the skewness, kurtosis and scale-scale correlation spectra for the wavelet coefficients at each scale. We also take into account the sensitivity of the method to the orientation of the input signal. We find a detection of non-Gaussianity at $> 99$ per cent level in just one of our statistics. Taking into account the total number of statistics computed, we estimate that the probability of obtaini…
A directional spherical wavelet analysis is performed to examine the Gaussianity of the WMAP 1-year data. Such an analysis is facilitated by the introduction of a fast directional continuous spherical wavelet transform. The directional nature of the analysis allows one 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 et al. (2003) foreground-removed maps. The previous non-Gaussianity detection made by Vielva et al. (2…
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…
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 signal's local features. In the present work, the non-Gaussianity of the WMAP temperature data of the cosmic microwave background (CMB) is analyzed in terms of the first four moments of the statistically isotropic random fields associated with these local morphological measures, at wavelet scales corresponding to angular sizes between 27.5 arcminutes and 30 degrees on the celestial sphere. While no detect…
ABRIDGED: We introduce and analyze a method for testing statistical isotropy and Gaussianity and apply it to the WMAP CMB foreground reduced, temperature maps, and cross-channel difference maps. We divide the sky into regions of varying size and shape and measure the first four moments of the one-point distribution within these regions, and using their simulated spatial distributions we test the statistical isotropy and Gaussianity hypotheses. By randomly varying orientations of these regions, we sample the underlying CMB field in a new manner, that offers a richer exploration of the data cont…
We present an analysis of the Gaussianity of the 4-year COBE-DMR data (in HEALPix pixelisation) based on spherical wavelets. The skewness, kurtosis and scale-scale correlation spectra are computed from the detail wavelet coefficients at each scale. The sensitivity of the method to the orientation of the data is also taken into account. We find a single detection of non-Gaussianity at the $>99%$ confidence level in one of our statistics. We use Monte-Carlo simulations to assess the statistical significance of this detection and find that the probability of obtaining such a detection by chance f…
We investigate the power of wavelet techniques in detecting non-Gaussianity in the cosmic microwave background (CMB). We use the method to discriminate between an inflationary and a cosmic strings model using small simulated patches of the sky. We show the importance of the choice of a good test statistic in order to optimise the discriminating power of the wavelet technique. In particular, we construct the Fisher discriminant function, which combines all the information available in the different wavelet scales. We also compare the performance of different decomposition schemes and wavelet ba…
We investigate the use of wavelet transforms in detecting and characterising non-Gaussian structure in maps of the cosmic microwave background (CMB). We apply the method to simulated maps of the Kaiser-Stebbins effect due to cosmic strings onto which Gaussian signals of varying amplitudes are superposed. We find 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 partic…
We perform a wavelet analysis of the temperature and polarization maps of the Cosmic Microwave Background (CMB) delivered by the WMAP experiment in search for a parity violating signal. Such a signal could be seeded by new physics beyond the standard model, for which the Lorentz and CPT symmetries may not hold. Under these circumstances, the linear polarization direction of a CMB photon may get rotated during its cosmological journey, a phenomenon also called cosmological birefringence. Recently, Feng et al. have analyzed a subset the WMAP and BOOMERanG 2003 angular power spectra of the CMB, d…
We systematically analyze the primordial non-Gaussianity estimator used by the Wilkinson Microwave Anisotropy Probe (WMAP) science team with the basic ideas of estimation theory in order to see if the limited Cosmic Microwave Background (CMB) data is being optimally utilized. The WMAP estimator is based on the implicit assumption that the CMB bispectrum, the harmonic transform of the three-point correlation function, contains all of the primordial non-Gaussianity information in a CMB map. We first demonstrate that the Signal-to-Noise (S/N) of an estimator based on CMB three-point correlation f…
The first year Wilkinson Microwave Anisotropy Probe (WMAP) set quantitative constraints on the amplitude of any primordial non-Gaussianity. We run a series of dark matter-only N-body simulations with the WMAP constraints to investigate the effect of the presence of primordial non-Gaussianity on large scale structures. The model parameters can be constrained using the observations of protoclusters associated with Ly-$α$ emitters at high redshift ($2 \leq z \leq 4$), assuming the galaxy velocity bias can be modelled properly. High redshift structure formation potentially provides a more powerful…
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…
The spherical Mexican Hat wavelet is introduced in this paper, with the aim of testing the Gaussianity of the Cosmic Microwave Background temperature fluctuations. Using the information given by the wavelet coefficients at several scales, we have performed several statistical tests on the COBE-DMR maps to search for evidence of non-Gaussianity. Skewness, kurtosis, scale-scale correlations (for two and three scales) and Kolmogorov-Smirnov tests indicate that the COBE-DMR data are consistent with a Gaussian distribution. We have extended the analysis to compare temperature values provided by COB…
We investigate the performance of spherical wavelets in discriminating between standard inflationary models (Gaussian) and non-Gaussian models. For the later we consider small perturbations of the Gaussian model in which an artificially specified skewness or kurtosis is introduced through the Edgeworth expansion. By combining all the information present in all the wavelet scales with the Fisher discriminant, we find that the spherical Mexican Hat wavelets are clearly superior to the spherical Haar wavelets. The former can detect levels of the skewness and kurtosis of ~1% for 33' resolution, an…
Some analyses of recent cosmic microwave background (CMB) data have provided hints that there are deviations from Gaussianity in the WMAP CMB temperature fluctuations. Given the far reaching consequences of such a non-Gaussianity for our understanding of the physics of the early universe, it is important to employ alternative indicators in order to determine whether the reported non-Gaussianity is of cosmological origin, and/or extract further information that may be helpful for identifying its causes. We propose two new non-Gaussianity indicators, based on skewness and kurtosis of large-angle…
We use the local curvature to investigate the possible existence of non-Gaussianity/asymmetry in the WMAP data. Considering the full sky we find results which are consistent with the Gaussian assumption. However, strong non-Gaussian features emerge when considering the northern and southern galactic hemisphere separately, particularly on scales between 1 and 5 degrees. Quite interestingly, the maximum non-Gaussianity is found for hemispheres centered near the ecliptic poles, which might suggest the presence of some systematic effect. The direction of the asymmetry seems consistent with the fin…
Using local morphological measures on the sphere defined through a steerable wavelet analysis, we examine the three-year WMAP and the NVSS data for correlation induced by the integrated Sachs-Wolfe (ISW) effect. The steerable wavelet constructed from the second derivative of a Gaussian allows one to define three local morphological measures, namely the signed-intensity, orientation and elongation of local features. Detections of correlation between the WMAP and NVSS data are made with each of these morphological measures. The most significant detection is obtained in the correlation of the sig…
We investigate the detection of non-Gaussianity in the 4-year COBE data reported by Pando, Valls-Gabaud & Fang (1998), 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 unbiased estimates of the skewness, kurtosis and scale-scale correlation of the corresponding wavelet …
Using a discrete wavelet based space-scale decomposition (SSD), the spectrum of the skewness and kurtosis is developed to describe the non-Gaussian signatures in cosmologically interesting samples. Because the basis of the discrete wavelet is compactly supported, the one-point distribution of the father function coefficients (FFCs) taken from one realization is a good estimate of the probability distribution function of the density if the ``fair sample hypothesis" holds. These FFC one-point distributions can also avoid the constraints of the central limit theorem on the detection of non-Gaussi…
We present limits to the amplitude of non-Gaussian primordial fluctuations in the WMAP 1-year cosmic microwave background sky maps. A non-linear coupling parameter, f_NL, characterizes the amplitude of a quadratic term in the primordial potential. We use two statistics: one is a cubic statistic which measures phase correlations of temperature fluctuations after combining all configurations of the angular bispectrum. The other uses the Minkowski functionals to measure the morphology of the sky maps. Both methods find the WMAP data consistent with Gaussian primordial fluctuations and establish l…
In the context of the present and future Cosmic Microwave Background (CMB) experiments, going beyond the information provided by the power spectrum has become necessary in order to tightly constrain the cosmological model. The non-Gaussian signatures in the CMB represent a very promising tool to probe the early universe and the structure formation epoch. We present the results of a comparison between two families of non-Gaussian estimators: The first act on the wavelet space (skewness and excess kurtosis of the wavelet coefficients) and the second group on the Fourier space (bi- and trispectru…
We study the statistical properties of the 1st year WMAP data on different scales using the spherical mexican hat wavelet transform. Consistent with the results of Vielva et al. (2003) we find a deviation from Gaussianity in the form of kurtosis of wavelet coefficients on $3-4^\circ$ scales in the southern Galactic hemisphere. This paper extends the work of Vielva et al. as follows. We find that the non-Gaussian signal shows up more strongly in the form of a larger than expected number of cold pixels and also in the form of scale-scale correlations amongst wavelet coefficients. We establish th…
The issue of non-Gaussianity is not only related to distinguishing the theories of the origin of primordial fluctuations, but also crucial for the determination of cosmological parameters in the framework of inflation paradigm. We present an advenced method for testing non-Gaussianity on the whole-sky CMB anisotropies. This method is based on the Kuiper's statistic to probe the two-dimensional uniformity on a periodic mapping square associating phases: return mapping of phases of the derived CMB (similar to auto correlation) and cross correlations between phases of the derived CMB and foregrou…
An extremely cold and big spot in the WMAP 1-year data is analyzed. Our work is a continuation of a previous paper (Vielva et al. 2004) where non-Gaussianity was detected, with a method based on the Spherical Mexican Hat Wavelet (SMHW) technique. We study the spots at different thresholds on the SMHW coefficient maps, considering six estimators, namely number of maxima, number of minima, number of hot and cold spots, and number of pixels of the spots. At SMHW scales around 4 degrees (10 degrees on the sky), the data deviate from Gaussianity. The analysis is performed on all sky, the northern a…
In the curvaton model of inflation, where a second scalar field, the "curvaton", is responsible for the observed inhomogeneity, a non-zero neutrino degeneracy may lead to a characteristic pattern of isocurvature perturbations in the neutrino, cold dark matter and baryon components. We find the current data can only place upper limits on the level of isocurvature perturbations. These can be translated into upper limits on the neutrino degeneracy parameter. In the case that lepton number is created before curvaton decay, we find that the limit on the neutrino degeneracy parameter is comparable w…
We perform a frequentist analysis of the bispectrum of WMAP first year data. We find clear signal domination up to l=200, with overall consistency with Gaussianity except for the following features. There is a flat patch (i.e. a low chi-squared region) in the same-l components of the bispectrum spanning the range l=32-62; this may be interpreted as ruling out Gaussianity at the 99.6% confidence level. There is also an asymmetry between the North and South inter-l bispectrum components at the 99% confidence level. The preferred asymmetry axis correlates well with the (l,b)=(57,10) direction quo…
We study the effect of primordial isocurvature perturbations on non-Gaussian properties of CMB temperature anisotropies. We consider generic forms of the non-linearity of isocurvature perturbations which can be applied to a wide range of theoretical models. We derive analytical expressions for the bispectrum and the Minkowski Functionals for CMB temperature fluctuations to describe the non-Gaussianity from isocurvature perturbations. We find that the isocurvature non-Gaussianity in the quadratic isocurvature model, where the isocurvature perturbation S is written as a quadratic function of the…
Motivated by the success of the Bianchi VII_h model in addressing many of the anomalies observed in the WMAP data (Jaffe et al.), we present calculations in real and in wavelet space of the Higher Criticism statistic of the Bianchi corrected Wilkinson Microwave Anisotropy Probe (WMAP) first year data. At the wavelet scale of 5 degrees the Higher Criticism of the WMAP map drops from a value above the 99% c.l. to a value below the 68% c.l. when corrected by the Bianchi template. An important property of the Higher Criticism statistic is its ability to locate the pixels that account for the devia…
We propose a fast and efficient bispectrum statistic for Cosmic Microwave Background (CMB) temperature anisotropies to constrain the amplitude of the primordial non-Gaussian signal measured in terms of the non-linear coupling parameter f_NL. We show how the method can achieve a remarkable computational advantage by focussing on subsets of the multipole configurations, where the non-Gaussian signal is more concentrated. The detection power of the test, increases roughly linearly with the maximum multipole, as shown in the ideal case of an experiment without noise and gaps. The CPU-time scales a…
We investigate the Statistical Isotropy and Gaussianity of the CMB fluctuations, using a set of multipole vector functions capable of separating these two issues. In general a multipole is broken into a frame and $2\ell-3$ ordered invariants. The multipole frame is found to be suitably sensitive to galactic cuts. We then apply our method to real WMAP datasets; a coadded masked map, the Internal Linear Combinations map, and Wiener filtered and cleaned maps. Taken as a whole, multipoles in the range $\ell=2-10$ or $\ell=2-20$ show consistency with statistical isotropy, as proved by the Kolmogoro…
We analyze the 3-year WMAP data and look for a deviation from Gaussianity in the form of a 3-point function that has either of the two theoretically motivated shapes: local and equilateral. There is no evidence of departure from Gaussianity and the analysis gives the presently tightest bounds on the parameters f_ NL^local and f_NL^equil., which define the amplitude of respectively the local and the equilateral non-Gaussianity: -36 < f_NL^local < 100, -256 < f_NL^equil. < 332 at 95% C.L.
The three Minkowski functionals and the recently defined length of the skeleton are estimated for the co-added first-year Wilkinson Microwave Anisotropy Probe (WMAP) data and compared with 5000 Monte Carlo simulations, based on Gaussian fluctuations with the a-priori best-fit running-index power spectrum and WMAP-like beam and noise properties. Several power spectrum-dependent quantities, such as the number of stationary points, the total length of the skeleton, and a spectral parameter, gamma, are also estimated. While the area and length Minkowski functionals and the length of the skeleton s…
The non--Gaussian cold spot in the 1-year WMAP data, described in Vielva et al. and Cruz et al., is analysed in detail in the present paper. First of all, we perform a more rigorous calculation of the significance of the non-zero kurtosis detected in WMAP maps by Vielva et al. in wavelet space, mainly generated by the Spot. We confirm the robustness of that detection, since the probability of obtaining this deviation by chance is 0.69%. Afterwards, the morphology of the Spot is studied by applying Spherical Mexican Hat Wavelets with different ellipticities. The shape of the Spot is found to be…
The non-Gaussian cold spot detected in wavelet space in the WMAP 1-year data, is detected again in the coadded WMAP 3-year data at the same position (b = -57, l = 209) and size in the sky (around 10 degrees). The present analysis is based on several statistical methods: kurtosis, maximum absolute temperature, number of pixels below a given threshold, volume and Higher Criticism. All these methods detect deviations from Gaussianity in the 3--year data set at a slightly higher confidence level than in the WMAP 1-year data. These small differences are mainly due to the new foreground reduction te…
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 th…
We review two powerful methods to test the Gaussianity of the cosmic microwave background (CMB): one based on the distribution of spherical wavelet coefficients and the other on smooth tests of goodness-of-fit. The spherical wavelet families proposed to analyse the CMB are the Haar and the Mexican Hat ones. The latter is preferred for detecting non-Gaussian homogeneous and isotropic primordial models containing some amount of skewness or kurtosis. Smooth tests of goodness-of-fit have recently been introduced in the field showing some interesting properties. We will discuss the smooth tests of …
We test the consistency of estimates of the non-linear coupling constant f_{NL} using non-Gaussian CMB maps generated by the method described in (Liguori, Matarrese and Moscardini 2003). This procedure to obtain non-Gaussian maps differs significantly from the method used in previous works on estimation of f_{NL}. Nevertheless, using spherical wavelets, we find results in very good agreement with (Mukherjee and Wang 2004), showing that the two ways of generating primordial non-Gaussian maps give equivalent results. Moreover, we introduce a new method for estimating the non-linear coupling cons…
Non-gaussianity represents the statistical signature of physical processes such as turbulence. It can also be used as a powerful tool to discriminate between competing cosmological scenarios. A canonical analysis of non-gaussianity is based on the study of the distribution of the signal in the real (or direct) space (e.g. brightness, temperature). This work presents an image processing method in which we propose statistical tests to indicate and quantify the non-gaussian nature of a signal. Our method is based on a wavelet analysis of a signal. Because the temperature or brightness distributio…
We present the analysis on the quadrupole phases of the Internal Linear Combination map, ILC(I) and (III) derived by the WMAP team (1 and 3-year data release). This approach allows us to see the global trend of non-Gaussianity of the quadrupoles for the ILC(III) map through phase correlations with the foregrounds. Significant phase correlations is found in between the ILC(III) quadrupole and the WMAP foregrounds phases for K-W band: the phases of the ILC(III) quadrupole xi_{2,1}, xi_{2,2} and those of the foregrounds at K-W bands Phi_{2,1}, Phi_{2,2} display significant symmetry: xi_{2,1}+Phi_…
Recent analysis of the WMAP three year data suggests $f_{NL}^{local}\simeq86.8$ in the WMAP convention. It is necessary to make sure whether general single field inflation can produce a large positive $f_{NL}$ before turning to other scenarios. We give some examples to generate a large positive $f_{NL}^{equil}$ in general single field inflation. Our models are different from ghost inflation. Due to the appearance of non-conventional kinetic terms, $f_{NL}^{equil}\gg1$ can be realized in single field inflation.
We propose a framework for separating the information contained in the CMB multipoles, $a_{\ell m}$, into its algebraically independent components. Thus we cleanly separate information pertaining to the power spectrum, non-Gaussianity and preferred axis effects. The formalism builds upon the recently proposed multipole vectors (Copi, Huterer & Starkman 2003; Schwarz & al 2004; Katz & Weeks 2004), and we elucidate a few features regarding these vectors, namely their lack of statistical independence for a Gaussian random process. In a few cases we explicitly relate our proposed invariants to com…
A fast algorithm for Antoine and Vandergheynst's (1998) directional continuous spherical wavelet transform (CSWT) is presented. Computational requirements are reduced by a factor of O(\sqrt{N}), when N is the number of pixels on the sphere. The spherical Mexican hat wavelet Gaussianity analysis of the WMAP 1-year data performed by Vielva et al. (2003) is reproduced and confirmed using the fast CSWT. The proposed extension to directional analysis is inherently afforded by the fast CSWT algorithm.
We study non-Gaussianity in two distinct models of preheating: instant and tachyonic. In instant preheating non-Gaussianity is sourced by the local terms generated through the coupled perturbations of the two scalar fields. We find that the non-Gaussianity parameter is given by $f_{NL}^ϕ\sim 2g < O(1)$, where $g$ is a coupling constant, so that instant preheating is unlikely to be constrained by WMAP or Planck. In the case of tachyonic preheating non-Gaussianity arises solely from the instability of the tachyon matter and is found to be large. We find that for single field inflation the presen…
We have tested Very Small Array (VSA) observations of three regions of sky for the presence of non-Gaussianity, using high-order cumulants, Minkowski functionals, a wavelet-based test and a Bayesian joint power spectrum/non-Gaussianity analysis. We find the data from two regions to be consistent with Gaussianity. In the third region, we obtain a 96.7% detection of non-Gaussianity using the wavelet test. We perform simulations to characterise the tests, and conclude that this is consistent with expected residual point source contamination. There is therefore no evidence that this detection is o…
We develop a method to constrain the level of non-Gaussianity of density perturbations when the 3-point function is of the "equilateral" type. Departures from Gaussianity of this form are produced by single field models such as ghost or DBI inflation and in general by the presence of higher order derivative operators in the effective Lagrangian of the inflaton. We show that the induced shape of the 3-point function can be very well approximated by a factorizable form, making the analysis practical. We also show that, unless one has a full sky map with uniform noise, in order to saturate the Cr…
We consider a two component hybrid inflation model, in which two fields drive inflation. Our results show that this model generates an observable non-gaussian contribution to the curvature spectrum, within the limits allowed by the recent WMAP year 3 data. We show that if one field has a mass less than zero, and an initial field value less than 0.06Mpl while the other field has a mass greater than zero, and initial field value ranging between 0.5Mpl and Mpl then the non-gaussianity is observable with 1<fnl<1.5, but that fnl becomes much less than the observable limit should we take both masses…
