BEYONDPLANCK

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

¹ Dipartimento di Fisica, Università degli Studi di Milano, Via Celoria, 16, Milano, Italy
e-mail: loris.colombo@unimi.it
² Institute of Theoretical Astrophysics, University of Oslo, Blindern, Oslo, Norway
³ INFN, Sezione di Milano, Via Celoria 16, Milano, Italy
⁴ INAF-IASF Milano, Via E. Bassini 15, Milano, Italy
⁵ INAF – Osservatorio Astronomico di Trieste, Via G. B. Tiepolo 11, Trieste, Italy
⁶ Planetek Hellas, Leoforos Kifisias 44, Marousi, 151 25 Greece
⁷ Department of Astrophysical Sciences, Princeton University, Princeton, NJ, 08544 USA
⁸ Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA, USA
⁹ Department of Physics, University of Helsinki, Gustaf Hällströmin katu 2, Helsinki, Finland
¹⁰ Helsinki Institute of Physics, University of Helsinki, Gustaf Hällströmin katu 2, Helsinki, Finland
¹¹ Computational Cosmology Center, Lawrence Berkeley National Laboratory, Berkeley, CA, USA
¹² Haverford College Astronomy Department, 370 Lancaster Avenue, Haverford, PA, USA
¹³ Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Str. 1, 85741 Garching, Germany
¹⁴ Dipartimento di Fisica, Università degli Studi di Trieste, Via A. Valerio 2, Trieste, Italy

Received: 28 July 2022
Accepted: 17 January 2023

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 used these samples to study correlations between CMB, foreground, and instrumental parameters. We identified a particularly strong degeneracy between CMB temperature fluctuations and free-free emission on intermediate angular scales (400 ≲ ℓ ≲ 600), mitigated through model reduction, masking, and resampling. We compared our posterior-based CMB results with previous Planck products and found a generally good agreement, however, with notably higher noise due to our exclusion of Planck HFI data. We found a best-fit CMB dipole amplitude of 3362.7 ± 1.4 μK, which is 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 ${\sigma }_2^{TT}=229\pm 97\mathrm{\mu }{\text{K}}^2$, which is in good agreement with previous results in terms of the amplitude, but the uncertainty is one order of magnitude greater than the naive diagonal Fisher uncertainty. Concurrently, we find less evidence of a possible alignment between the quadrupole and octopole than previously reported, due to a much larger scatter in the individual quadrupole coefficients that is caused both by marginalizing over a more complete set of systematic effects – as well as by requiring a more conservative analysis mask 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 that the sample-based, asymptotically exact Blackwell-Rao estimator has been successfully established for multipoles up to ℓ ≤ 600. 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.