Robust paths to primordial $B$ modes in the presence of polarised point source contamination
A detection of primordial $B$ modes in the Cosmic Microwave Background (CMB) polarisation relies on a robust control and removal of contamination from astrophysical polarised foreground emission. We examine how much polarised extragalactic point sources may contaminate the cosmological signal in ground-based CMB experiments, propagating their impact through component separation to the final parameter constraints. We discuss masking and modelling strategies to ensure that the resulting constraints remain both accurate and precise under this source of contamination. We produce synthetic data containing polarised emission from extragalactic radio sources (ERSs) and dusty star-forming galaxies (DSFGs) following state-of-the-art models for both samples. We find that, while the DSFG contribution is likely too small to cause any significant bias to the cosmological or foreground parameters, the ERS contribution instead, if left unmasked, leads to a bias in the parameters describing the Galactic synchrotron and lensing $B$-mode components. For experiments targeting noise levels of order $σ_P\simeq 1\,μK\,{\rm arcmin}$, we find that masking all ERSs with fluxes above $\sim$0.1 Jy, coupled with a relatively simple model to marginalise over residual point-source contamination, achieves a suitable balance that allows for the robust recovery of unbiased cosmological and foreground parameters at a negligible cost in parameter uncertainties.