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Register a new userThe discriminating power of wavelets to detect non-Gaussianity in the CMB
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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.
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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.
Observations of the Cosmic Microwave Background (CMB) provide increasingly accurate information about the structure of the Universe at the recombination epoch. Most of this information is encoded in the angular power spectrum of the CMB. The aim of this work is to propose a versatile and powerful method for spectral estimation on the sphere which can easily deal with non-stationarity, foregrounds and multiple experiments with various specifications. In this paper, we use needlets (wavelets) on the sphere to construct natural and efficient spectral estimators for partially observed and beamed CMB with non stationary noise. In the case of a single experiment, we compare this method with Pseudo-$C_ell$ methods. The performance of the needlet spectral estimators (NSE) compares very favorably to the best Pseudo--$C_ell$ estimators, over the whole multipole range. On simulations with a simple model (CMB + uncorrelated noise with known variance per pixel + mask), they perform uniformly better. Their distinctive ability to aggregate many different experiments, to control the propagation of errors and to produce a single wide-band error bars is highlighted. The needlet spectral estimator is a powerful, tunable tool which is very well suited to angular power spectrum estimation of spherical data such as incomplete and noisy CMB maps.
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 for an underlying Gaussian field is as high as 0.69. Therefore, our analysis does not show evidence of non-Gaussianity in the COBE-DMR data.
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.
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).
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