A Maximum Likelihood Analysis of the Low CMB Multipoles from WMAP

TL;DR

This paper reanalyzes the low quadrupole and octopole amplitudes in WMAP data using a quadratic maximum likelihood estimator, finding these amplitudes are higher than previously reported and less inconsistent with the standard cosmological model.

Contribution

It introduces a quadratic maximum likelihood estimator for low multipole analysis and demonstrates its stability across different Galactic cuts, providing more accurate amplitude estimates.

Findings

Low multipole amplitudes are higher than WMAP estimates.

Results show the discrepancy with Lambda CDM is only a few percent.

Analysis confirms the robustness of low multipole measurements.

Abstract

The amplitudes of the quadrupole and octopole measured from the Wilkinson Microwave Anisotropy Probe (WMAP) appear to be lower than expected according to the concordance Lambda CDM cosmology. However, the pseudo-Cl estimator used by the WMAP team is non-optimal. In this paper, we discuss the effects of Galactic cuts on pseudo-Cl and quadratic maximum likelihood estimators. An application of a quadratic maximum likelihood estimator to Galaxy subtracted maps produced by the WMAP team and Tegmark, de Oliveira-Costa and Hamilton (2003) shows that the amplitudes of the low multipoles are stable to different Galactic cuts. In particular, the quadrupole and octopole amplitudes are found to lie in the ranges 176 - 250 (micro K)**2 794 - 1183 (micro K)**2 (and more likely to be at the upper ends of these ranges) rather than the values of 123 (micro K)**2 and 611 (micro K)**2 found by the WMAP team. These results indicate that the discrepancy with the concordance Lambda CDM model at low multipoles is not particularly significant and is in the region of a few percent. This conclusion is consistent with an analysis of the low amplitude of the angular correlation function computed from quadratic maximum likelihood power spectrum estimates.