The Uncorrelated Universe: Statistical Anisotropy and the Vanishing Angular Correlation Function in WMAP Years 1-3

TL;DR

This study reanalyzes the WMAP three-year data to test statistical isotropy at large angular scales using multipole vectors and the angular two-point function ${\cal C}(\theta)$. Despite identifying solar-system–aligned systematics in the 3-year data, the quadrupole and octopole continue to exhibit strong internal alignment and correlations with the ecliptic and related directions, and ${\cal C}(\theta)$ remains near zero for $\theta>60^\circ$ outside the galactic mask, more inconsistent with $\Lambda$CDM than in the first year. The authors emphasize that standard interpretations based on the angular power spectrum ${\tilde{C}}_\ell$ or full-sky reconstructions can be misleading when statistical isotropy is violated, and they explore several non-cosmological explanations involving systematics and foregrounds. Overall, the work challenges the conventional inflationary picture at the largest scales and motivates cautious, systematic investigations of residual systematics, foregrounds, or new physics that could produce the observed large-angle anomalies.

Abstract

The large-angle (low-ell) correlations of the Cosmic Microwave Background (CMB) as reported by the Wilkinson Microwave Anisotropy Probe (WMAP) after their first year of observations exhibited statistically significant anomalies compared to the predictions of the standard inflationary big-bang model. We suggested then that these implied the presence of a solar system foreground, a systematic correlated with solar system geometry, or both. We re-examine these anomalies for the data from the first three years of WMAP's operation. We show that, despite the identification by the WMAP team of a systematic correlated with the equinoxes and the ecliptic, the anomalies in the first-year Internal Linear Combination (ILC) map persist in the three-year ILC map, in all-but-one case at similar statistical significance. The three-year ILC quadrupole and octopole therefore remain inconsistent with statistical isotropy -- they are correlated with each other (99.6% C.L.), and there are statistically significant correlations with local geometry, especially that of the solar system. The angular two-point correlation function at scales >60 degrees in the regions outside the (kp0) galactic cut, where it is most reliably determined, is approximately zero in all wavebands and is even more discrepant with the best fit LambdaCDM inflationary model than in the first-year data - 99.97% C.L. for the new ILC map. The full-sky ILC map, on the other hand, has a non-vanishing angular two-point correlation function, apparently driven by the region inside the cut, but which does not agree better with LambdaCDM. The role of the newly identified low-ell systematics is more puzzling than reassuring.

Figures (5)

• Figure 1: The $\ell=2$ (top panel) and $\ell=3$ (bottom panel) multipoles from the ILC123 cleaned map, presented in Galactic coordinates, after correcting for the kinetic quadrupole. The solid line is the ecliptic plane and the dashed line is the supergalactic plane. The directions of the equinoxes (EQX), dipole due to our motion through the Universe, north and south ecliptic poles (NEP and SEP) and north and south supergalactic poles (NSGP and SSGP) are shown. The multipole vectors are plotted as the solid red symbols for $\ell=2$ and solid magenta for $\ell=3$ (dark and medium gray in gray scale versions) for each map, ILC1 (circles), ILC123 (triangles), TOH1 (diamonds) and LILC1 (squares). The open symbols of the same shapes are for the normal vectors for each map. The dotted lines are the great circles connecting each pair of multipole vectors for the ILC123 map. For $\ell=3$ (bottom panel), the solid magenta (again medium gray in the gray scale version) star is the direction of the maximum angular momentum dispersion axis for the ILC123 octopole.
• Figure 2: The quadrupole vectors (filled triangles) and normals (open triangles) of the yr1-yr123 difference maps for the V band (white), W band (black) and the ILC (grey). The background shows the ILC123 quadrupole in the same coordinates as in Figs. \ref{['fig:map:ilc123:2and3']} and \ref{['fig:map:ilc123:2+3']}.
• Figure 3: The $\ell=2+3$ multipoles from the ILC123 cleaned map, presented in Galactic coordinates. This is a combination of the two panels of Fig. \ref{['fig:map:ilc123:2and3']} with only the multipole vectors for the ILC123 map shown for clarity. The solid line is the ecliptic plane and the dashed line is the supergalactic plane. The directions of the equinoxes (EQX), dipole due to our motion through the Universe, north and south ecliptic poles (NEP and SEP) and north and south supergalactic poles (NSGP and SSGP) are shown. The $\ell=2$ multipole vectors are plotted as the solid red (dark gray in gray scale version) triangle and their normal is the open red (dark gray in the gray scale version) triangle. The $\ell=3$ multipole vectors are the solid magenta (medium gray in gray scale version) triangles and their three normals are the open magenta (medium gray in the gray scale version) triangles. The dotted lines are the great circles connecting the multipole vectors for this map (one for the quadrupole vectors and three for the octopole vectors). The solid magenta (again medium gray in the gray scale version) star is the direction to the maximum angular momentum dispersion for the octopole.
• Figure 4: Histogram of the $S^{(4, 4)}({\hat{d}}|\{\vec{w}\})$ statistics applied to the ILC123 map quadrupole and octopole area vectors and a fixed direction or plane on the sky, compared to $10^5$ random directions. Vertical lines show the $S$ statistics of the actual area vectors applied to the ecliptic plane, NGP, supergalactic plane, dipole and equinox directions (Table \ref{['tab:given23']} shows the actual product percentile ranks among the random rotations for ILC1, ILC123 and TOH1). This Figure and Table \ref{['tab:given23']} show that, given the relative location of the quadrupole-octopole area vectors (i.e. their mutual alignment), the dipole and equinox alignments remain unlikely at about $95\%$ C.L., whereas the ecliptic alignment, significant at 98.3-99.8% C.L. in year 1, is only significant at the 90% C.L. in year 123. The galactic plane and supergalactic plane alignments remain not significant.
• Figure 5: Two point angular correlation function, ${\cal C}(\theta) \equiv {\overline{ T({\hat{e}}_1)T({\hat{e}}_2)}}_\theta$ computed in pixel space, for three different bands masked with the kp0 mask. Also shown is the correlation function for the ILC map with and without the mask, and the value expected for a statistically isotropic sky with best-fit $\Lambda$CDM cosmology together with 68% error bars. Left panel: year 1 results. Right panel: year 123 results. Even by eye, it is apparent that masked year 123 maps have $C(\theta)$ that is consistent with zero at $\theta\gtrsim 60$ deg, even more so than in year 1 maps. We also show the $C(\theta)$ computed from the "official" published $C_\ell$, which (at $\ell<10$) are the pseudo-$C_\ell$ in year 1, the and MLE $C_\ell$ in year 123. Clearly, the MLE-based $C_\ell$, as well as ${\cal C}(\theta)$ computed from the full-sky ILC maps, are in significant disagreement with the angular correlation function computed from cut-sky maps.