Observations of the Cosmic Microwave Background fluctuations provide a unique view onto the early universe and the fundamental laws of physics at the most extreme energies (typically twelve orders of magnitude above what could be achieved at the Large Hadron Collider). The successful European-led space mission Planck provided the ultimate characterization of the CMB fluctuations in total intensity and a robust detection of some of the polarization signal. Yet, this latter signal still contain tremendous amount of undiscovered, complementary informations, about the universe’s first moments as well as the formation and evolution of large scale structures. Among others, unveiling such signals would allow the scientific community to constrain the energy scale and dynamics of the so-called inflationary mechanism, thought to be responsible for the universe as we see today, and help probing fundamental laws of physics as close to the Planck scale as currently imaginable.

Maps of the CMB polarization sky are usually decomposed into E- and B-modes, corresponding to specific patterns of polarization, which are sourced by distinct physical mechanisms in the early universe. The B-modes are of particular interest as they could have been, on the largest angular scales, generated by hypothetical primordial gravitational waves produced by inflation, and on the smallest angular scales by gravitational lensing effects due to large-scale structures emerging in the universe at redshifts of a few. Although the lensing contribution to B-modes has been gradually characterized since 2014, the primordial signal is still undiscovered at the moment. 

Several CMB space missions are currently being designed and studied, with the goal, among others, of characterizing primordial B-modes on the largest angular scales. Yet, all these instruments have to face and deal with galactic foregrounds: our own galaxy, the Milky Way, emits in the microwave frequency bands of interests, namely through synchrotron radiation and dust thermal radiation dominating at low (< 80GHz) and high (>150GHz) frequencies respectively. The foreground B-mode polarization signal is expected to be significantly above the CMB even in the cleanest regions of the sky and the cleanest frequency bands. A robust foreground-cleaning procedure, so-called component separation, is necessary to detect primordial B-modes and to set reliable constraints on inflationary theories. Such procedures can only be efficient if applied to data sets with specific characteristics what sets constraints on instrumental designs of future CMB missions, which need to be fulfilled if the missions are to succeed.

The proposed PhD thesis will consist in (1) developing novel component separation techniques suitable for the B-mode science; (2) implementing these techniques in a form of numerically efficient well-documented codes; (3) demonstrating and validating them on advanced simulated data implementing cutting-edge models of the galactic foregrounds physics (e.g. as delivered by the ANR BxB project in which we are involved) and real data sets coming from ground-based efforts, such as the Simons Array and Simons Observatory; (4) turning these techniques in software tools, permitting efficient optimization and validation of the instrumental designs. These techniques and tools will be general and applicable to any considered mission, however, as part of this thesis we will specifically validate them on and apply them to the currently most advanced satellite project, called LiteBIRD. LiteBIRD is an international project, led by JAXA, which is in Phase A at JAXA and CNES. It is designed to have both a very sensitive focal plane and an exquisite control of instrumental systematic effects. Its launch is planned for 2027, and it will observe the whole sky over 3 years. This thesis will contribute to design and optimization of the LiteBIRD focal plane, ensuring that the mission will be capable of reaching its ambitious science goals.