2-point anisotropies in WMAP and the Cosmic Quadrupole

TL;DR

The paper reexamines the WMAP large-scale anomalies by analyzing the two-point angular correlation function $w_2(\theta)$ and its higher-order moments, instead of relying on spherical-harmonic power spectra. Using realistic LCDM simulations with full covariance and sky masks, it shows that the WMAP sky is consistent with LCDM at about 30% probability when treated as a random realization, while higher-order moments remain Gaussian within pixel noise. The analysis also demonstrates that the mask and estimator choice significantly influence perceived tensions with LCDM, and excluding the Galactic plane does not eliminate the large-scale power deficit. Overall, the work argues that the low quadrupole may be a statistical fluctuation within LCDM rather than evidence for new physics, though interpretations depend on the error model and masking strategy.

Abstract

Large-scale modes in the temperature anisotropy power spectrum C_l measured by the Wilkinson Microwave Anisotropy Probe (WMAP), seem to have lower amplitudes (C_2, C_3 and C_4) than that expected in the so called concordance LCDM model. In particular, the quadrupole C_2 is reported to have a smaller value than allowed by cosmic variance. This has been interpreted as a possible indication of new physics. In this paper we re-analyse the WMAP data using the 2-point angular correlation and its higher-order moments. This method, which requires a full covariance analysis, is more direct and provides better sampling of the largest modes than the standard harmonic decomposition. We show that the WMAP data is in good agreement (~ 30% probability) with a LCDM model when the WMAP data is considered as a particular realization drawn from a set of realistic LCDM simulations with the corresponding covariance. This is also true for the higher-order moments, shown here up to 6th order, which are consistent with the Gaussian hypothesis. The sky mask plays a major role in assessing the significance of these agreements. We recover the best fit model for the low-order multipoles based on the 2-point correlation with different assumptions for the covariance. Assuming that the observations are a fair sample of the true model, we find C_2 = 123 +/- 233, C_3= 217 +/- 241 and C_4 = 212 +/- 162 (in mu K^2). The errors increase by about a factor of 5 if we assume the \lcdm model. If we exclude the Galactic plane |b|<30 from our analysis, we recover very similar values within the errors (ie C_2=172, C_3= 89, C_4=129). This indicates that the Galactic plane is not responsible for the lack of large-scale power in the WMAP data.

Figures (16)

• Figure 1: Power spectrum $C_l$ for the $\Lambda$CDM model (continuous line). Open squares show the first multipoles by Bennett et al. (2003). Closed triangles with errors correspond to Eq.[\ref{['eq:wmapcls']}]. Unlike the conventional way of plotting this curve, each amplitude here shows the contribution of each multipole to the sky anisotropies in Eq. [\ref{['eq:w2cl']}]. Dashed line shows the low-Q model in Eq. [\ref{['eq:low-Q']}].
• Figure 2: Theoretical prediction of the 2-point angular correlation $w_2$ in the $\Lambda$CDM model with all multipoles (continuous line), without the quadrupole (long dashed line) and without quadrupole and octopole (short dashed line).
• Figure 3: The 2-pt function $w_2(\theta)$ from simulations (continuous line) with 1-sigma confidence region (shaded region) compared to $w_2(\theta)$ from the input $C_l$ spectrum (dashed line). Top left: $\Lambda$CDM model with kp0-mask. Top right: $\Lambda$CDM model with kp0-mask and $|b|>30$ Galactic cut. Bottom left: low-Q model with kp0-mask. Bottom right: low-Q model with kp0-mask and $|b|>30$ Galactic cut.
• Figure 4: Short, long-dashed and dotted lines show the absolute errors (or dispersion) in $w_2$ from the low-Q simulations, the first 40 and the first 1000 $\Lambda$CDM simulations respectively. The continuous lines corresponds to estimated jackknife errors with N=8 and N=32 subsamples within the WMAP data, while the shaded region shows the dispersion in jackknife errors from each of the low-Q realizations.
• Figure 5: Normalised covariance (or correlation) matrices between different angular bins in $w_2(\theta)$ . Grey scale goes from -1 (black) to +1 (white). Left: $\Lambda$CDM model. Middle: low-Q model. Right: jackknife samples in low-Q model.