Bayesian Analysis of Hemispherical Power Asymmetry in the Cosmic Microwave Background

Abstract

The cosmic microwave background (CMB) radiation at 2.7 K is the leftover radiation from the Big Bang. By studying this radiation we can extract much information about the universe we live in. CMB experiments over the last twenty years have given us the cosmological concordance model. The main features of this (LCDM) model are that the universe is isotropic, homogeneous and filled with random Gaussian fluctuations, which were created during inflation. These fluctuations are nearly scale-invariant. The currently best available data come from WMAP, and have confirmed the LCDM model. But after the first-year release of the WMAP data, some unexpected properties were found in the radiation. Several detailed analyses showed strong hints of non-Gaussianity and violation of statistical isotropy. One of the studies showed that the large-scale power is unevenly distributed on the sky, i.e., the temperature fluctuations on large scales were greater in one part of the sky than in the opposing direction. This raise the question on statistical isotropy in the CMB. In order to quantify the statistical significance of this observed dipolar distribution, I adopt a parametric model for the observed data. In this model, the isotropic, Gaussian random field is modulated by a dipole field which dependents on an amplitude and direction. Using a Bayesian framework, I use the five-year WMAP data to estimate the three parameters of the dipole field for smaller scales than previously considered.