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Register a new userWavelet analysis and the detection of non-Gaussianity in the CMB
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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 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 five times the rms amplitude of the original cosmic string map. We also find that the wavelet technique is useful in characterising the angular scales at which the non-Gaussian signal occurs.
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The non-Gaussianity of inflationary perturbations, as encoded in the bispectrum (or 3-point correlator), has become an important additional way of distinguishing between inflation models, going beyond the linear Gaussian perturbation quantities of the power spectrum. This habilitation thesis provides a review of my work on both the theoretical and the observational aspects of these non-Gaussianities. In the first part a formalism is described, called the long-wavelength formalism, that provides a way to compute the non-Gaussianities in multiple-field inflation. Applications of this formalism to various classes of models, as well as its extensions, are also treated. In the second part an estimator is described, called the binned bispectrum estimator, that allows the extraction of information about non-Gaussianities from data of the cosmic microwave background radiation (CMB). It was in particular one of the three estimators applied to the data of the Planck satellite to provide the currently best constraints on primordial non-Gaussianity. Various extensions of the estimator and results obtained are also discussed.
Tensor non-Gaussianities are a key ingredient to test the symmetries and the presence of higher spin fields during the inflationary epoch. Indeed, the shape of the three point correlator of the graviton is totally fixed by the symmetries of the de Sitter stage and, in the case of parity conservation, gets contributions only from the ordinary gravity action plus a higher derivative term called the (Weyl)$^3$ action. We discuss current and future bounds on the three point tensor contribution from the (Weyl)$^3$ term using cosmic microwave background (CMB) bispectra. Our results indicate that forthcoming experiments, such as LiteBIRD, CMB-S4 and CORE, will detect the presence of the (Weyl)$^3$ term if $M_p^4 L^4 sim 10^{17} r^{-4}$, where $L$ parametrizes the strength of the (Weyl)$^3$ term and $r$ is the tensor-to-scalar ratio, which corresponds to $Lgtrsim 3.2 times 10^5 M_p^{-1}$, while the current upper limit is $M_p^4 L^4 = (1.1 pm 4.0) times 10^{19} r^{-4}$ (68%CL).
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 bases. For our case, we find that the Mallat and {it `a trous} algorithms are superior to the 2D-tensor wavelets. Using this technique, the inflationary and strings models are clearly distinguished even in the presence of a superposed Gaussian component with twice the rms amplitude of the original cosmic string map.
This paper reviews the application of a novel methodology for analysing the isotropy of the universe by probing the alignment of local structures in the CMB. The strength of the proposed methodology relies on the steerable wavelet filtering of the CMB signal. One the one hand, the filter steerability renders the computation of the local orientation of the CMB features affordable in terms of computation time. On the other hand, the scale-space nature of the wavelet filtering allows to explore the alignment of the local structures at different scales, probing possible different phenomena. We present the WMAP first-year data analysis recently performed by the same authors (Wiaux et al.), where an extremely significant anisotropy was found. In particular, a preferred plane was detected, having a normal direction with a northern end position close to the northern end of the CMB dipole axis. In addition, a most preferred direction was found in that plane, with a northern end direction very close to the north ecliptic pole. This result synthesised for the first time previously reported anomalies identified in the direction of the dipole and the ecliptic poles axes. In a forthcoming paper (Vielva et al.), we have extended our analysis to the study of individual frequency maps finding first indications for discarding foregrounds as the origin of the anomaly. We have also tested that the preferred orientations are defined by structures homogeneously distributed in the sky, rather than from localised regions. We have also analysed the WMAP 3-year data, finding the same anomaly pattern, although at a slightly lower significance level.
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-Gaussianity. Thus the FFC one-point distributions are effective in detecting non-Gaussian behavior in samples such as non-Gaussian clumps embedded in a Gaussain background, regardless of the number or density of the clumps. We demonstrate that the non-Gaussianity can reveal not only the magnitudes but also the scales of non-Gaussianity. Also calculated are the FFC one-point distributions, skewness and kurtosis spectra for real data and linearly simulated samples of QSO Ly$alpha$ forests. When considering only second and lower order of statistics, such as the number density and two-point correlation functions, the simulated data show the same features as the real data. However, the the kurtosis spectra of samples given by different models are found to be different. On the other hand, the spectra of skewness and kurtosis for independent observational data sets are found to be the same. Moreover, the real data are significantly different from the non-Gaussianity spectrum of various posssible random samples. Therefore the non-Gaussain spectrum is necessary and valuable for model discrimination.
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