Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Are There Cosmic Microwave Background Anomalies?

TL;DR

The paper analyzes seven-year WMAP data to test for deviations from the standard $\Lambda$CDM model by examining $C_\ell$ statistics, Gaussianity, isotropy, and possible anomalies. It employs Gibbs sampling for low-$l$ power, optimal quadratic estimators for dipole and quadrupole modulations, and the bipolar power spectrum formalism to characterize potential anisotropies. Across cold spots, the low quadrupole, large-scale power, multipole alignments, and hemispherical/dipole asymmetries, the data are largely consistent with LCDM, with any apparent anomalies attributable to posterior choices, foregrounds, or instrument systematics (notably beam asymmetry in the quadrupolar signal). The study concludes that there is no compelling cosmological anomaly in the seven-year data and provides a framework for anomaly assessment applicable to current and future CMB experiments.

Abstract

(Abridged) A simple six-parameter LCDM model provides a successful fit to WMAP data, both when the data are analyzed alone and in combination with other cosmological data. Even so, it is appropriate to search for any hints of deviations from the now standard model of cosmology, which includes inflation, dark energy, dark matter, baryons, and neutrinos. The cosmological community has subjected the WMAP data to extensive and varied analyses. While there is widespread agreement as to the overall success of the six-parameter LCDM model, various "anomalies" have been reported relative to that model. In this paper we examine potential anomalies and present analyses and assessments of their significance. In most cases we find that claimed anomalies depend on posterior selection of some aspect or subset of the data. Compared with sky simulations based on the best fit model, one can select for low probability features of the WMAP data. Low probability features are expected, but it is not usually straightforward to determine whether any particular low probability feature is the result of the a posteriori selection or of non-standard cosmology. We examine in detail the properties of the power spectrum with respect to the LCDM model. We examine several potential or previously claimed anomalies in the sky maps and power spectra, including cold spots, low quadrupole power, quadropole-octupole alignment, hemispherical or dipole power asymmetry, and quadrupole power asymmetry. We conclude that there is no compelling evidence for deviations from the LCDM model, which is generally an acceptable statistical fit to WMAP and other cosmological data.

Figures (17)

• Figure 1: Top: A large colder-than-average region, highlighted by the white curve, appears prominently on the raw V-band temperature map. The full-sky map is shown with the Galactic plane horizontal across the center of the map with the Galactic center at the center of the displayed projection. Bottom: With the foreground signals strongly suppressed by the ILC technique, the highlighted cold spot is seen to be at least as prominent. It is offset from the Galactic center in both latitude and longitude. This fact, combined with the fact that the clearly effective ILC foreground reduction does not diminish this feature, establishes that this is a CMB fluctuation and not a foreground effect. This feature is not anomalous in that simulated realizations of $\Lambda$CDM model skies routinely produce features like this.
• Figure 2: Visual inspection of the ILC map reveals four elongated valleys of cooler temperature that stretch from about the Galactic equator to nearly the south Galactic pole. Ridges of warmer-than-average temperature lie between the cooler fingers. These features are a consequence of large-scale power in the southern sky. It is more difficult to discern as much large-scale power in the northern sky. Cold Spot I is located near the northernmost part of one of the fingers, while Cold Spot II (within the red curve) is near the southernmost part of another finger.
• Figure 3: Curve is a Blackwell-Rao estimate of the relative likelihood of the quadrupole power $l(l+1)C_2/2\pi$ in $\mu$K$^2$ from WMAP . The WMAP ILC data were smoothed to $5^\circ$ and the KQ85y7 mask was used, both degraded to res 5. The Gibbs sampling produced a likelihood that has been marginalized over all other multipoles. The highly non-Gaussian likelihood distribution is characteristic of the lowest-$l$ multipoles. For $l > 32$ the curves become nearly Gaussian. The vertical line with the label "$\Lambda$CDM" is the expected quadrupole from the full power spectrum $\Lambda$CDM model best fit to the WMAP data. The maximum likelihood of the WMAP -measured $l=2$ quadrupole is at the vertical dotted line. These two values are consistent to well within the 95% confidence region. The WMAP quadrupole is not anomalously low.
• Figure 4: Cumulative distribution function of the quadrupoles from the Gibbs sampling based on 300,000 points. The vertical line is the predicted $\Lambda$CDM model quadrupole value. The cumulative probability is 0.824 where the vertical line crosses the cumulative distribution function . Since the expected quadrupole from the $\Lambda$CDM model is well within the 95% confidence range of the measured quadrupole, accounting for noise and cosmic variance, we conclude that the measured quadrupole is not anomalously low.
• Figure 5: Angular correlation function of the full-sky WMAP ILC map is shown (heavy black curve). For comparison, the angular correlation function for the best-fit $\Lambda$CDM model is also shown (thin black curve), along with the associated 68% and 95% confidence ranges, as determined by Monte Carlo simulations. The angular correlation function of the full-sky map is seen to be within the 95% confidence range of the best-fit $\Lambda$CDM model. This angular correlation function was computed from the $C_l$ power spectrum, but is nearly indistinguishable from a pixel pair computation. Either way, there is no evidence of a lack of large-scale power.