Cosmic strings and domain walls: the impact of CMB $B$-mode data

We analyse CMB constraints on stable networks of cosmic strings and domain walls using for the first time full Planck 2018 data together with BICEP/Keck 2018 $B$-mode measurements. The defect-induced anisotropies are computed using the Unconnected Segment Model for Nambu-Goto and Abelian-Higgs strings, as well as for stable domain walls, and included in a full Markov Chain Monte Carlo analysis jointly varying all $\Lambda$CDM parameters, the tensor-to-scalar ratio, and the string/domain wall tension. No statistically significant evidence for defects is found, although we observe a mild preference for non-zero cosmic string tension. Our results improve previous constraints on the defect power spectrum by up to a factor of two. In the particular case of strings, the improvement is driven by the $B$-mode data, and is especially pronounced for Abelian-Higgs strings. We also present forecasts for the Simons Observatory and the LiteBIRD satellite: the former will improve string tension constraints by about a factor of three, while the latter those on the domain wall tension by about a factor of ten. Finally, we assess the impact of Nambu-Goto string loops on CMB anisotropies in light of both current and future observations.