CMB LIKELIHOOD AND COSMOLOGICAL PARAMETERS ESTIMATION IN A BAYESIAN END-TO-END FRAMEWORK

The cosmic microwave background (CMB) constitutes one of the most powerful probes of cosmology available today, as the statistical properties of the pattern of small vari- ations in the intensity and polarisation of this radiation impose strong constraints on cosmological structure formation processes in the early universe. The first discovery of these fluctuations was made by Smoot et al. (1992), and during the last three decades massive efforts have been spent on producing detailed maps with steadily increasing sensitivity and precision (e.g., Bennett et al. 2013; de Bernardis et al. 2000; Louis et al. 2017; Sievers et al. 2013; Ogburn et al. 2010; Planck Collaboration I 2020, and references therein). State-of-the-art full-sky CMB measurements from the Planck satellite, complemented by ground and balloon observations and data from non-CMB cosmological probes have led to a spectacularly successful cosmological concordance model called ΛCDM that posits that the Universe was created during a hot Big Bang about 13.8 billion years ago; that it was seeded by Gaussian random density fluctuations during a brief period of exponential expansion called inflation; and that it consists of about 5 % baryonic matter, 25 % dark matter, and 70 % dark energy. This model is able to describe a host of cosmological observables with exquisite precision (see e.g. Planck Collaboration VI 2020), although it leaves much to be desired in terms of theoretical understanding. Indeed, some of the biggest questions in modern cosmology revolves around understanding the physical nature of inflation, dark matter and dark energy, and billions of dollars and euros are spent on these questions. CMB observations play a key role in all these studies. The next major scientific endeavour for the CMB community is the search for primordial gravitational waves created during the inflationary epoch (e.g., Kamionkowski & Kovetz 2016). Current theories predict that such gravitational waves should imprint large-scale B-mode polarisation in the CMB anisotropies, with a map-domain amplitude no larger than a few tens of nK on degree angular scales. Detecting such a faint signal requires at least one or two orders of magnitude higher sensitivity than Planck, and correspondingly more stringent systematics suppression and uncertainty assessment. Indeed, Planck marked the transition from noise dominated CMB measurements, at least for temperature anisotropies, to instrumental and foregrounds systematics dominated measurements, necessitating a change of approach in CMB data analysis. Perhaps the single most important lesson learned in this respect is an understanding of the tight relationship between instrument characterisation and astrophysical component separa- tion. Because any current and planned CMB experiment in practice must be calibrated with in-flight observations of astrophysical sources, the calibration is in practice limited by our knowledge by the astrophysical sources in question—which also typically must be derived from the same data set. Instrument calibration and component separation must therefore be performed jointly, and a significant fraction of the full uncertainty budget arise from degeneracies between the two. This project addresses this challenge by constructing a complete end-to-end analysis pipeline for CMB observation into one integrated framework that does not require intermediate human intervention. This is the first complete approach to support seamless end-to-end error propagation for CMB applications, including full marginalisation over both instrumental and astrophysical uncertainties and their internal degeneracies; see BeyondPlanck Collaboration (2021); Colombo et al. (2021) for further discussion. For pragmatic reasons, the current pipeline has so far only been applied to the Planck LFI observations, which have significantly lower computational requirements and signal- to-noise ratio than the Planck HFI observations. The cosmological parameter constraints derived in the following are therefore not competitive in terms of absolute uncertain- ties as compared with already published Planck constraints. Rather, the present analysis focuses primarily on general algorithmic aspects, and serves as a first real-world demonstration of the end-to-end Bayesian framework, serving as a platform for further development and data integration (Gerakakis et al. 2021). Within BP, my activity focused on the scientific analysis of CMB products, at map, power spectrum and cosmological parameters level. More specifically, noting the sen- sitivity of systematics on large-scale polarisation reconstruction, I used the reionisation optical depth τ to assess the stability and performance of the BEYONDPLANCK frame- work, estimating P (τ | d) from Planck LFI and WMAP observations. I also constrained a basic 6-parameter ΛCDM model, combining the BEYONDPLANCK low-l likelihood with a high-l Blackwell-Rao CMB temperature likelihood that for the first time covers the two first acoustic peaks, or l ≤ 600. Due to LFI angular resolution and sensitivity, I complemented this with the Planck high-l likelihood to extend the multipole range to the full Planck resolution, as well as selected external non-CMB data sets. I also studied different model independent parameterisations to constrain the reionisatio history of the Universe.