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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.
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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.
We theoretically propose and experimentally demonstrate a nonclassicality test of single-mode field in phase space, which has an analogy with the nonlocality test proposed by Banaszek and Wodkiewicz [Phys. Rev. Lett. 82, 2009 (1999)]. Our approach to deriving the classical bound draws on the fact that the Wigner function of a coherent state is a product of two independent distributions as if the orthogonal quadratures (position and momentum) in phase space behave as local realistic variables. Our method detects every pure nonclassical Gaussian state, which can also be extended to mixed states. Furthermore, it sets a bound for all Gaussian states and their mixtures, thereby providing a criterion to detect a genuine quantum non-Gaussian state. Remarkably, our phase-space approach with invariance under Gaussian unitary operations leads to an optimized test for a given non-Gaussian state. We experimentally show how this enhanced method can manifest quantum non-Gaussianity of a state by simply choosing phase-space points appropriately, which is essentially equivalent to implementing a squeezing operation on a given state.
We search the BOOMERanG maps of the anisotropy of the Cosmic Microwave Background (CMB) for deviations from gaussianity. In this paper we focus on analysis techniques in pixel-space, and compute skewness, kurtosis and Minkowski functionals for the BOOMERanG maps and for gaussian simulations of the CMB sky. We do not find any significant deviation from gaussianity in the high galactic latitude section of the 150 GHz map. We do find deviations from gaussianity at lower latitudes and at 410 GHz, and we ascribe them to Galactic dust contamination. Using non-gaussian simulations of instrumental systematic effects, of foregrounds, and of sample non-gaussian cosmological models, we set upper limits to the non-gaussian component of the temperature field in the BOOMERanG maps. For fluctuations distributed as a 1 DOF $chi^2$ mixed to the main gaussian component our upper limits are in the few % range.
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.
Primordial gravitational waves (GWs) are said to be a smoking gun in cosmic inflation, while, even if they are detected, the specification of their origins are still required for establishing a true inflationary model. Testing non-Gaussianity in the tensor-mode anisotropies of the cosmic microwave background (CMB) is one of the most powerful ways to identify sources of GW signals. In this paper, we review studies searching for tensor non-Gaussianities employing the CMB bispectrum and forecast future developments. No significant signal has so far been found from temperature and E-mode polarization data, while orders-of-magnitude improvements in detection limits can be achieved by adding the information of B-mode polarization. There is already an established methodology for bispectrum estimation, which encourages a follow-up investigation with next-decadal CMB B-mode surveys.
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