Improved limits on the tensor-to-scalar ratio using BICEP and Planck data

We present constraints on the tensor-to-scalar ratio $r$ using a combination of BICEP/Keck 2018 (BK18) and Planck PR4 data allowing us to fit for $r$ consistently with the six parameters of the $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ model. We discuss the sensitivity of constraints on $r$ to uncertainties in the $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ parameters as defined by the Planck data. In particular, we are able to derive a constraint on the reionization optical depth $\ensuremath{\tau}$ and thus propagate its uncertainty into the posterior distribution for $r$. While Planck sensitivity to $r$ is slightly lower than the current ground-based measurements, the combination of Planck with BK18 and baryon-acoustic-oscillation data yields results consistent with $r=0$ and tightens the constraint to $r<0.032$ at 95% confidence.