Inference of the optical depth to reionization from low multipole temperature and polarisation Planck data

Understand

This paper explores methods for constructing low multipole temperature and polarisation likelihoods from maps of the cosmic microwave background anisotropies that have complex noise properties and partial sky coverage.

• We use Planck 2018 High Frequency Instrument (HFI) and updated SRoll2 temperature and polarisation maps to test our methods.
• We present three likelihood approximations based on quadratic cross spectrum estimators: (i) a variant of the simulation-based likelihood (SimBaL) techniques used in the Planck legacy papers to produce a low multipole EE likelihood; (ii) a semi-analytical likelihood approximation (momento) based on the principle of maximum entropy; (iii) a density-estimation `likelihood-free' scheme (DELFI).
• Approaches (ii) and (iii) can be generalised to produce low multipole joint temperature-polarisation (TTTEEE) likelihoods.