STATISTICS OF MICROWAVE BACKGROUND FLUCTUATIONS INDUCED BY TOPOLOGICAL DEFECTS

We use the analytical model recently introduced by the author to investigate the statistics of temperature fluctuations on the cosmic microwave background induced by topological defects. The cases of cosmic strings and textures are studied. We derive analytically the characteristic function of the probability distribution for deltaT/T and use it to obtain the lowest twelve moments including the skewness and the kurtosis. The distribution function is also obtained and it is compared with the Gaussian distribution thus identifying long non-Gaussian tails. We show that for both cosmic strings and textures all odd moments (including skewness) vanish while the relative deviation from the Gaussian for even moments increases with the order of the moment. The non-Gaussian signatures of collapsing texture knots, derived from the distribution function and the moments, are found to be more prominent than the corresponding signatures for strings. We discuss the physical origin of this result.