Component separation for future CMB B-mode satellites

Next-generation CMB satellite concepts (LiteBIRD, CORE, PIXIE, PICO) are being proposed to detect the primordial CMB B-mode polarization at large angular scales in the sky for tensor-to-scalar ratio values of ${r \lesssim 10^{-3}}$. Yet undetected, primordial CMB B-modes will provide the unique signature of the primordial gravitational waves of quantum origin predicted by inflation. We present recent forecasts on the detection of the primordial CMB B-modes in the presence of astrophysical foregrounds and gravitational lensing effects, in the context of the proposed CMB space mission CORE. We also discuss the problem of foregrounds and component separation for the search for primordial B-modes, and highlight specific challenges in this context: frequency range, spectral degeneracies, foreground modelling, spectral averaging effects.