arXiv subjects

O. Forni

Publications and source records attributed to O. Forni.

134 records · Page 8Linked to original sources

arXiv2005

Cosmological non-Gaussian Signature Detection: Comparing Performance of Different Statistical Tests

Currently, it appears that the best method for non-Gaussianity detection in the Cosmic Microwave Background (CMB) consists in calculating the kurtosis of the wavelet coefficients. We know that wavelet-kurtosis outperforms other methods such as the bispectrum, the genus, ridgelet-kurtosis and curvelet-kurtosis on an empirical basis, but relatively few studies have compared other transform-based statistics, such as extreme values, or more recent tools such as Higher Criticism (HC), or proposed `best possible' choices for such statistics. In this paper we consider two models for transform-domain coefficients: (a) a power-law model, which seems suited to the wavelet coefficients of simulated cosmic strings; and (b) a sparse mixture model, which seems suitable for the curvelet coefficients of filamentary structure. For model (a), if power-law behavior holds with finite 8-th moment, excess kurtosis is an asymptotically optimal detector, but if the 8-th moment is not finite, a test based on extreme values is asymptotically optimal. For model (b), if the transform coefficients are very sparse, a recent test, Higher Criticism, is an optimal detector, but if they are dense, kurtosis is an optimal detector. Empirical wavelet coefficients of simulated cosmic strings have power-law character, infinite 8-th moment, while curvelet coefficients of the simulated cosmic strings are not very sparse. In all cases, excess kurtosis seems to be an effective test in moderate-resolution imagery.

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arXiv2004

Separating the kinetic SZ effect from primary CMB fluctuations

In the present work, we propose a new method aiming at extracting the kinetic Sunyaev-Zel'dovich (KSZ) temperature fluctuations embedded in the primary anisotropies of the cosmic microwave background (CMB). We base our study on simulated maps without noise and we consider very simple and minimal assumptions. Our method essentially takes benefit from the spatial correlation between KSZ and the Compton parameter distribution associated with the thermal Sunyaev-Zel'dovich (TSZ) effect of the galaxy clusters, the later can be obtained by means of multi-frequency based component separation techniques. We reconstruct the KSZ signal by interpolating the CMB fluctuations without making any hypothesis besides the CMB fluctuations are Gaussian distributed. We present two ways of estimating the KSZ fluctuations, after the interpolation step. In the first way we use a blind technique based on canonical Principal Component Analysis, while the second uses a minimisation criterion based on the fact that KSZ dominates a small angular scales and that it follows a non-Gaussian distribution. We show using the correlation between the input and reconstructed KSZ map that the latter can be reconstructed in a very satisfactory manner (average correlation coefficient between 0.62 and 0.90), furthermore both the retrieved KSZ power spectrum and temperature fluctuation distribution are in quite good agreement with the original signal. The ratio between the input and reconstructed power spectrum is indeed very close to one up to a multipole $\ell\sim 200$ in the best case. The method presented here can be considered as a promising starting point to identify in CMB observations the temperature fluctuation associated with the KSZ effect.

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arXiv2003

Detection and discrimination of cosmological non-Gaussian signatures by multi-scale methods

Recent Cosmic Microwave Background (CMB) observations indicate that the temperature anisotropies arise from quantum fluctuations in the inflationary scenario. In the simplest inflationary models, the distribution of CMB temperature fluctuations should be Gaussian. However, non-Gaussian signatures can be present. They might have different origins and thus different statistical and morphological characteristics. In this context and motivated by recent and future CMB experiments, we search for, and discriminate between, different non-Gaussian signatures. We analyse simulated maps of three cosmological sources of temperature anisotropies: Gaussian distributed CMB anisotropies from inflation, temperature fluctuations from cosmic strings and anisotropies due to the kinetic Sunyaev-Zel'dovich (SZ) effect both showing a non-Gaussian character. We use different multi-scale methods, namely, wavelet, ridgelet and curvelet transforms. The sensitivity and the discriminating power of the methods is evaluated using simulated data sets. We find that the bi-orthogonal wavelet transform is the most powerful for the detection of non-Gaussian signatures and that the curvelet and ridgelet transforms characterise quite precisely and exclusively the cosmic strings. They allow us thus to detect them in a mixture of CMB + SZ + cosmic strings. We show that not one method only should be applied to understand non-Gaussianity but rather a set of different robust and complementary methods should be used.

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arXiv2003

Non-Gaussianity: Comparing wavelet and Fourier based methods

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 trispectrum). We compare the relative sensitivities of these estimators by applying them to three different data sets meant to reproduce the majority of possible non-Gaussian contributions to the CMB. We find that the skewness in the wavelet space is slightly more sensitive than the bispectrum. For the four point estimators, we find that the excess kurtosis of the wavelet coefficients has very similar capabilities than the diagonal trispectrum while a near-diagonal trispectrum seems to be less sensitive to non-Gaussian signatures.

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arXiv2000

Using the COBE/DMR data as a test-bed for normality assessments

A very important property of a statistical distribution is to know whether it obeys Gaussian statistics or not. On the one hand, it is of paramount importance in the context of CMB anisotropy studies, since deviations from a Gaussian distribution could indicate the presence of uncorrected measurement systematics, of remaining fluctuations contributed by foregrounds, of deviations from the simplest models of inflation or of topological defects. On the other hand, looking for a non-Gaussian signal is a very ill-defined task and performances of various assessment methods may differ widely when applied in different contexts. In previous studies, we introduced a sensitive wavelet-based method which we apply here to the COBE/DMR data set, already extensively studied, using different approaches. This provides an objective way to compare methods. It turns out that our multi-scale wavelet decomposition is a sensitive method. Yet we show that the results are rather sensitive to the choice of both the decomposition scheme and the wavelet basis. We find that the detection of the non-Gaussian signature is ``marginal'' with a probability of at most 99%.

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arXiv2000

Non-Gaussian signature induced by the SZ effect of galaxy clusters

We apply statistical tests, based on the study of thecoefficients in a wavelet decomposition, to a cosmological signal: the Cosmic Microwave Background (CMB) anisotropies. The latter represent the superposition of primary anisotropy imprints of the initial density perturbations and secondary anisotropies due to photon interactions after recombination. In an inflationary scenario with Gaussian distributed fluctuations, we study the statistical signature of the secondary effects. More specifically, we investigate the dominant effects arising from the Sunyaev-Zel'dovich effect of galaxy clusters. Our study predicts the non-Gaussian signature of these secondary anisotropies and its detectability in the context of the future CMB satellite Planck Surveyor.

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arXiv1999

Searching for the non-gaussian signature of the CMB secondary anisotropies

In a first paper (Forni & Aghanim 1999), we developed several statistical discriminators to test the non-gaussian nature of a signal. These tests are based on the study of the coefficients in a wavelet decomposition basis. In this paper, we apply them in a cosmological context, to the study of the nature of the Cosmic Microwave Background (CMB) anisotropies. The latter represent the superposition of primary anisotropy imprints of the initial density perturbations and secondary ones due to photon interactions after recombination. In an inflationary scenario (standard Cold Dark Matter) with gaussian distributed fluctuations, we study the statistical signature of the secondary effects. More specifically, we investigate the dominant effects arising from the Compton scattering of CMB photons in ionised regions of the Universe: the Sunyaev-Zel'dovich effect of galaxy clusters and the effects of a spatially inhomogeneous re-ionisation of the Universe. Our study specifies and predicts the non-gaussian signature of the secondary anisotropies induced by these scattering effects. We find that our statistical discriminators allow us to distinguish and highlight the non-gaussian signature of a process even if it is combined with a larger gaussian one. We investigate the detectability of the secondary anisotropy non-gaussian signature in the context of the future CMB satellites (MAP and Planck Surveyor).

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arXiv1999

Searching for non-gaussianity: Statistical tests

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 distribution is a rather weak discriminator, the search for the statistical signature of non-gaussianity relies on the study of the coefficient distribution of an image in the wavelet decomposition basis which is much more sensitive. We develop two statistical tests for non-gaussianity. In order to test their reliability, we apply them to sets of test maps representing a combination of gaussian and non-gaussian signals. We deliberately choose a signal with a weak non-gaussian signature and we find that such a non-gaussian signature is easily detected using our statistical discriminators. In a second paper, we apply the tests in a cosmological context.

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