BeyondPlanck XII. Cosmological parameter constraints with end-to-end error propagation

Abstract

We present cosmological parameter constraints as estimated using the Bayesian BeyondPlanck analysis framework. This method supports seamless end-to-end error propagation from raw time-ordered data to final cosmological parameters. As a first demonstration of the method, we analyze time-ordered Planck LFI observations, combined with selected external data (WMAP 33-61 GHz, Planck HFI DR4 353 and 857 GHz, and Haslam 408 MHz) in the form of pixelized maps which are used to break critical astrophysical degeneracies. Overall, all results are generally in good agreement with previously reported values from Planck 2018 and WMAP, with the largest relative difference for any parameter of about 1 σ when considering only temperature multipoles between 30 ≤ ≤ 600. In cases where there are differences, we note that the BeyondPlanck results are generally slightly closer to the high-HFI-dominated Planck 2018 results than previous analyses, suggesting slightly less tension between low and high multipoles. Using low-polarization information from LFI and WMAP, we find a best-fit value of τ = 0.066±0.013, which is higher than the low value of τ = 0.051±0.006 derived from Planck 2018 and slightly lower than the value of 0.069 ± 0.011 derived from joint analysis of official LFI and WMAP products. Most importantly, however, we find that the uncertainty derived in the BeyondPlanck processing is about 30 % larger than when analyzing the official products, after taking into account the different sky coverage. We argue that this is due to marginalizing over a more complete model of instrumental and astrophysical parameters, and this results in both more reliable and more rigorously defined uncertainties. We find that about 2000 Monte Carlo samples are required to achieve robust convergence for a low-resolution CMB covariance matrix with 225 independent modes, and producing these samples takes about eight weeks on a modest computing cluster with 256 cores.

Beyondplanck

“…This methodology allows us to characterize degeneracies between instrumental and astrophysical parameters in a statistically welldefined framework, with uncertainties propagating consistently through all stages of the pipeline. It also seamlessly connects low-level instrumental quantities like gain (Gjerløw et al 2022) and correlated noise (Ihle et al 2022), bandpasses (Svalheim et al 2022a), and far sidelobes (Galloway et al 2022b) via Galactic parameters such as the synchrotron amplitude and spectral index (current paper and Svalheim et al 2022b), to the angular CMB power spectrum and cosmological parameters (Colombo et al 2022;Paradiso et al 2022). In this section, we provide a brief review of the BeyondPlanck sky model, data selection, and sampling scheme; we refer to the various companion papers for more details on the model.…”

Beyondplanck

“…In practice, this means that any application of the BeyondPlanck covariance matrices must be accompanied with a convergence analysis that shows that the number of Monte Carlo samples is sufficient to reach robust results for the final statistic in question. How many this is will depend on the statistic in question; for an example of this as applied to estimation of the optical depth of reionization, see Paradiso et al (2022). Second, and even more importantly, we also see that the BeyondPlanck matrices are far more feature rich than the Planck 2018 matrices, and this is precisely because they account for a full stochastic data model, and not just 1/ f correlated noise.…”

“…The final BP10 results consist of four independent Markov chains, each with a total of 1000 Gibbs samples. We conservatively removed 200 samples from each chain as burn-in (Paradiso et al 2022), but it is important to note that we have not seen statistically compelling evidence for significant chain nonstationarity after the first few tens of samples. A total of 3200 samples has been retained for full analysis.…”

“…For several important applications, including low-ℓ CMB likelihood evaluation (e.g., Page et al 2007;Planck Collaboration V 2020;Paradiso et al 2022), it is important to have access to full pixel-pixel covariance matrices. Since the memory required to store these scale as O(N 4 side ), and the CPU time required to invert them scale as O(N 6 side ) (Sherman & Morrison 1950), these are typically only evaluated at very low angular resolution; Planck used N side = 16 (Planck Collaboration V 2020), while Beyond-Planck uses N side = 8 (Paradiso et al 2022).…”

Beyondplanck

“…The BeyondPlanck project is an attempt to build up an end-toend data analysis pipeline for CMB experiments going all the way from raw time-ordered data to cosmological parameters in a consistent Bayesian framework. This allows us to characterize degeneracies between instrumental and astrophysical parameters in a statistically well-defined framework, from low-level instrumental quantities such as gain (Gjerløw et al 2022), bandpasses (Svalheim et al 2022a), far sidelobes (Galloway et al 2022b), and correlated noise via Galactic parameters that include the synchrotron amplitude or spectral index (Andersen et al 2022;Svalheim et al 2022b), and up to the angular CMB power spectrum and cosmological parameters (Colombo et al 2022;Paradiso et al 2022).…”