Bayesian analysis of an anisotropic universe model: systematics and polarization

TL;DR

This paper extends the ACW anisotropic inflation framework to include CMB polarization and a broader set of systematics within an exact Bayesian Gibbs-sampling approach. It implements a polarization-capable, sparse covariance formulation and validates it with simulations, then reanalyzes the 5-year WMAP temperature data with the corrected (-i)^{l-l'} term. The results show a strong ACW-like signal in WMAP data that shifts toward the ecliptic poles, strongly suggesting a solar-system or instrument–systematic origin rather than cosmology, after testing several potential systematics. Planck polarization forecasts indicate that forthcoming data will decisively test the anisotropy hypothesis, thanks to improved sensitivity and the inclusion of E- and B-mode information in the covariance structure.

Abstract

We revisit the anisotropic universe model previously developed by Ackerman, Carroll and Wise (ACW), and generalize both the theoretical and computational framework to include polarization and various forms of systematic effects. We apply our new tools to simulated WMAP data in order to understand the potential impact of asymmetric beams, noise mis-estimation and potential Zodiacal light emission. We find that neither has any significant impact on the results. We next show that the previously reported ACW signal is also present in the 1-year WMAP temperature sky map presented by Liu & Li, where data cuts are more aggressive. Finally, we reanalyze the 5-year WMAP data taking into account a previously neglected (-i)^{l-l'}-term in the signal covariance matrix. We still find a strong detection of a preferred direction in the temperature map. Including multipoles up to l=400, the anisotropy amplitude for the W-band is found to be g = 0.29 +- 0.031, nonzero at 9 sigma. However, the corresponding preferred direction is also shifted very close to the ecliptic poles at (l,b)= (96,30), in agreement with the analysis of Hanson & Lewis, indicating that the signal is aligned along the plane of the solar system. This strongly suggests that the signal is not of cosmological origin, but most likely is a product of an unknown systematic effect. Determining the nature of the systematic effect is of vital importance, as it might affect other cosmological conclusions from the WMAP experiment. Finally, we provide a forecast for the Planck experiment including polarization.

Figures (7)

• Figure 1: W and V-band posteriors for the temperature analysis, using $\ell_{\textrm{cutoff}}=400$ and the KQ85 mask. The north and south ecliptic poles are marked with a red circle. Note how the posterior peaks correspond with the ecliptic poles. The yellow circles indicate the direction from the previous analysis by groeneboom:2008b.
• Figure 2: Various systematic effects compared with the ACW signal (upper left). Asymmetric beams (upper right), noise maps (bottom left) and the Zodiacal light template (lower right) are similar in shape to the ACW signal, and could therefore be thought to contribute to the ACW signal in the WMAP data.
• Figure 3: An analysis of the same isotropic map convolved with symmetric (black) and asymmetric (red) beams. Note how both results are consistent with $g_*=0$
• Figure 4: $g_*$ posteriors for several analysis of noiseless simulated $\ell_{\textrm{max}}=64$ map, using both MCMC and brute-force calculations. Note how the polarization data narrows the distribution.
• Figure 5: Posterior from a simulated set with $g_*=1.0$. The original temperature ACW-signal in the input map can be seen in the background. Note how the estimated direction corresponds well with the posterior.