BEYONDPLANCK XI. Bayesian CMB analysis with sample-based end-to-end error propagation

Abstract

We present posterior sample-based cosmic microwave background (CMB) constraints from Planck LFI and WMAP observations as derived through global end-to-end Bayesian processing within the BeyondPlanck framework. We first use these samples to study correlations between CMB, foreground, and instrumental parameters, and we identify a particularly strong degeneracy between CMB temperature fluctuations and free-free emission on intermediate angular scales (400 ≲ ℓ ≲ 600), which is mitigated through model reduction, masking, and resampling. We compare our posterior-based CMB results with previous Planck products, and find generally good agreement, although with notably higher noise due to our exclusion of HFI data. We find a best-fit CMB dipole amplitude of 3362.7 ± 1.4 µK, in excellent agreement with previous Planck results. The quoted dipole uncertainty is derived directly from the sampled posterior distribution, and does not involve any ad hoc contributions for Planck instrumental systematic effects. Similarly, we find a temperature quadrupole amplitude of ${σ}_{2}^{TT}$ = 229 ± 97 µK 2 , which is in good agreement with previous results in terms of the amplitude, but the uncertainty is an order of magnitude larger than the naive diagonal Fisher uncertainty. Relatedly, we find lower evidence for a possible alignment between the quadrupole and octopole than previously reported due to a much larger scatter in the individual quadrupole coefficients, caused both by marginalizing over a more complete set of systematic effects, but also by our more conservative analysis mask required to mitigate the free-free degeneracy. For higher multipoles, we find that the angular temperature power spectrum is generally in good agreement with both Planck and WMAP. At the same time, we note that this is the first time the sample-based asymptotically exact Blackwell-Rao estimator has been successfully established for multipoles up to ℓ ≤ 600, and it now accounts for the majority of the cosmologically important information. Overall, this analysis demonstrates the unique capabilities of the Bayesian approach with respect to end-to-end systematic uncertainty propagation, and we believe it can and should play an important role in the analysis of future CMB experiments. Cosmological parameter constraints are presented in a companion paper.