Wavelet analysis of cosmic microwave background anisotropy

Abstract

The cosmic microwave background (CMB) temperature anisotropy is a random field on the spherical sky whose statistical properties keep the information of the universe, especially the early universe. The study of its Gaussian statistics, namely the search for non-Gaussian signatures, is hopefully a way complementary to others in cosmology. In this thesis, we review the search for non-Gaussianity on the WMAP (Wilkinson Microwave Anisotropy Probe) first-year CMB data using the spherical Mexican hat wavelet of Vielva et al. (2004) and Mukherjee and Wang (2004). Their results are positive; the non-Gaussian signal was found at the wavelet scale around 4” (~ 10° in the sky) in the southern Galactic hemisphere. In addition, the nonlinear coupling parameter f[subscript NL], Which reflects the degree of non-Gaussianity in the form of the quadratic term in the Bardeen’s curvature perturbations, was constrained in Mukherjee and Wang using the skewness at all wavelet scales. Their results constrained f[subscript NL] to be 50±80 at 68% confidence, and less than 280 at 99% confidence.