Two-point anisotropies in WMAP and the cosmic quadrupole

Abstract

Large-scale modes in the temperature anisotropy power spectrum Cl measured by the Wilkinson Microwave Anisotropy Probe (WMAP) seem to have lower amplitudes (C2, C3 and C4) than that expected in the so-called concordance Λ-cold dark matter (ΛCDM) model. In particular, the quadrupole C2 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 two-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 are in good agreement (≃30 per cent probability) with a ΛCDM model when the WMAP data are considered as a particular realization drawn from a set of realistic ΛCDM simulations with the corresponding covariance. This is also true for the higher-order moments, shown here up to sixth 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-fitting model for the low-order multipoles based on the two-point correlation with different assumptions for the covariance. Assuming that the observations are a fair sample of the true model, we find C2= 123 ± 233, C3= 217 ± 241 and C4= 212 ± 162 (in μK2). The errors increase by about a factor of 5 if we assume the ΛCDM model. If we exclude the Galactic plane ∼b∼ < 30 from our analysis, we recover very similar values within the errors (i.e. C2= 172, C3= 89, C4= 129). This indicates that the Galactic plane is not responsible for the lack of large-scale power in the WMAP data.