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.Comment: 14 pages, 7 figures, in press in Astronomy & Astrophysics Supplement Serie

On the detectability of non-trivial topologies

We explore the main physical processes which potentially affect the topological signal in the Cosmic Microwave Background (CMB) for a range of toroidal universes. We consider specifically reionisation, the integrated Sachs-Wolfe (ISW) effect, the size of the causal horizon, topological defects and primordial gravitational waves. We use three estimators: the information content, the S/N statistic and the Bayesian evidence. While reionisation has nearly no effect on the estimators, we show that taking into account the ISW strongly decreases our ability to detect the topological signal. We also study the impact of varying the relevant cosmological parameters within the 2 sigma ranges allowed by present data. We find that only Omega_Lambda, which influences both ISW and the size of the causal horizon, significantly alters the detection for all three estimators considered here.Comment: 11 pages, 9 figure

The Maximum B-mode Polarization of the Cosmic Microwave Background from Inhomogeneous Reionization

We compute the B-mode polarization power spectrum of the CMB from an epoch of inhomogeneous reionization, using a simple model in which HII regions are represented by ionized spherical bubbles with a log normal distribution of sizes whose clustering properties are determined by large-scale structure. Both the global ionization fraction and the characteristic radius of HII regions are allowed to be free functions of redshift. Models that would produce substantial contamination to degree scale gravitational wave B-mode measurements have power that is dominated by the shot noise of the bubbles. Rare bubbles of >100 Mpc at z>20 can produce signals that in fact exceed the B-modes from gravitational lensing and are comparable to the maximal allowed signal of gravitational waves (~0.1uK) while still being consistent with global constraints on the total optical depth. Even bubbles down to 20 Mpc at z~15, or 40 Mpc at z~10 can be relevant (0.01uK) once the lensing signal is removed either statistically or directly. However, currently favored theoretical models that have ionization bubbles that only grow to such sizes at the very end of a fairly prompt and late reionization produce signals which are at most at these levels.Comment: 14 pages, 11 figures; published in ApJ; corrected Fig. 4 and updated reference