Large-angle correlations in the cosmic microwave background

It has been argued recently by Copi et al. 2009 that the lack of large angular correlations of the CMB temperature field provides strong evidence against the standard, statistically isotropic, inflationary Lambda cold dark matter (Lambda CDM) cosmology. We compare various estimators of the temperature correlation function showing how they depend on assumptions of statistical isotropy and how they perform on the Wilkinson Microwave Anisotropy Probe (WMAP) 5-yr Internal Linear Combination (ILC) maps with and without a sky cut. We show that the low multipole harmonics that determine the large-scale features of the temperature correlation function can be reconstructed accurately from the data that lie outside the sky cuts. The reconstructions are only weakly dependent on the assumed statistical properties of the temperature field. The temperature correlation functions computed from these reconstructions are in good agreement with those computed from the ILC map over the whole sky. We conclude that the large-scale angular correlation function for our realization of the sky is well determined. A Bayesian analysis of the large-scale correlations is presented, which shows that the data cannot exclude the standard Lambda CDM model. We discuss the differences between our results and those of Copi et al. Either there exists a violation of statistical isotropy as claimed by Copi et al., or these authors have overestimated the significance of the discrepancy because of a posteriori choices of estimator, statistic and sky cut.