Bayesian analysis of sparse anisotropic universe models and application to the five-year WMAP data

Abstract

We extend the previously described cosmic microwave background Gibbs sampling framework to allow for exact Bayesian analysis of anisotropic universe models, and apply this method to the five-year Wilkinson Microwave Anisotropy Probe (WMAP) temperature observations. This involves adding support for nondiagonal signal covariance matrices, and implementing a general spectral parameter Monte Carlo Markov chain sampler. As a working example, we apply these techniques to the model recently introduced by Ackerman et al., describing, for instance, violations of rotational invariance during the inflationary epoch. After verifying the code with simulated data, we analyze the foreground-reduced five-year WMAP temperature sky maps. For ℓ ≤ 400 and the W-band data, we find tentative evidence for a preferred direction pointing toward (l, b) = (110°, 10°) with an anisotropy amplitude of g * = 0.15 ± 0.039. Similar results are obtained from the V-band data (g * = 0.11 ± 0.039; (l, b) = (130°, 20°)). Further, the preferred direction is stable with respect to multipole range, seen independently in both ℓ = [2, 100] and [100, 400], although at lower statistical significance. We have not yet been able to establish a fully satisfactory explanation for the observations in terms of known systematics, such as noncosmological foregrounds, correlated noise, or asymmetric beams, but stress that further study of all these issues is warranted before a cosmological interpretation can be supported. © 2009. The American Astronomical Society. All rights reserved.