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 contains tremendous amount of undiscovered, complementary information, about the Universe’s first moments as well as the formation and evolution of large scale structures. Among others, unveiling such signals would constrain the energy scale and uncover dynamics of the so-called inflationary mechanism, thought to be responsible for the universe as we see today, and enable testing 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 interest, 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 that due to 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 in certain circumstances, which in turn define sufficient and necessary characteristics of the data set, which the forthcoming experiments have to collect to ensure successful outcome of the entire effort. This is even more complex in the presence of instrumental effects, which have to be accurately modeled and potentially mitigated. Many of them depend on observational frequency in a non-trivial manner confusing and limiting accuracy of the component separation procedures.

The proposed PhD thesis will consist in:

(1) developing novel component separation techniques suitable for the B-mode science and taking into account the presence of instrumental effects (as motivated by the LiteBIRD mission); 

(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 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;

(5) validating on and applying them to the optimization and design of the satellite project, 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 directly to design and optimization of the LiteBIRD instrument ensuring that the mission will be capable of reaching its ambitious science goals. Using the formalism developed here we will set up requirements for the precision of calibration of different elements of the detection chain.

The thesis will be performed in the context of the French involvement in the LiteBIRD mission and will strengthen contributions of the APC team, who has been playing very visible roles in the LiteBIRD collaboration on the European and global mission levels, including the LiteBIRD performance team (led by J. Errard (APC) one of the proposers of this project) and the foreground (Errard, Stompor (APC), the proposers) and systematic Joint Study Groups (co-led by G. Patanchon (APC) collaborator on this project, and Stompor (APC), one of the proposers).