A Quadratic Estimator for Statistical Anisotropy in the Cosmic Microwave Background

The standard model of cosmology has proven to be a great success. Through measurements of the Cosmic Microwave Background radiation, cosmologists have been able to constrain parameters such as the age and geometry of the universe, or the amounts of different types of energy, to high accuracy. The inflationary theory of the model states that the anisotropies in the background radiation should be distributed so that they follow statistical isotropy and homogeneity. However, the CMB maps detected by the WMAP satellite have shown to reveal possible deviations from this assumption. There have been claims of a hemispherical power asymmetry between two parts of the sky, where one part exhibits stronger fluctuations and the other weaker. This feature has been investigated since the first-year maps were released, and a number of independent studies have found consistent results, in particular regarding the preferred direction of the asymmetry. However, the methods have traditionally been limited computationally to only including the largest scales in the analysis. In a recent paper, Hanson & Lewis (2009) developed a Quadratic Maximum Likelihood estimator for analyzing the dipolar asymmetry, and found consistent results with previous studies but noted that the effect diminished with including higher l in the analysis. We present the Quadratic Maximum Likelihood estimator introduced by Hanson & Lewis, and re-implement it for our own analyses. We investigate the claims made by the WMAP team, in Bennett et al. (2011), that the reported dipolar asymmetry effect is a statistical fluke and that the previous claims found in the literature are insignificant. The WMAP team's claims are based on the QML estimator. The results we obtain are found to be consistent with previous studies, H&L and with Bennett et al., and the significance of the asymmetry is found to vary with the assumed modulation multipole l_mod. However, we find the claims by the WMAP team to be premature as they have not taken into account the consistency of the estimated direction. Comparing with 1000 isotropic simulations we find that less than 1% of them exhibit a similar consistency with estimated direction across l_mod