Detecting Primordial $B$-Modes after Planck

We update the forecasts for the measurement of the tensor-to-scalar ratio $r$ for various ground-based experiments (AdvACT, CLASS, Keck/BICEP3, Simons Array, SPT-3G), balloons (EBEX 10k and Spider) and satellites (CMBPol, COrE and LiteBIRD), taking into account the recent Planck data on polarized dust and using a component separation method. The forecasts do not change significantly with respect to previous estimates when at least three frequencies are available, provided foregrounds can be accurately described by few parameters. We argue that a theoretically motivated goal for future experiments is $r\sim2\times10^{-3}$, and that this is achievable if the noise is reduced to $\sim1\,\mu$K-arcmin and lensing is reduced to $10\%$ in power. We study the constraints experiments will be able to put on the frequency and $\ell$-dependence of the tensor signal as a check of its primordial origin. Futuristic ground-based and balloon experiments can have good constraints on these parameters, even for $r\sim2\times10^{-3}$. For the same value of $r$, satellites will marginally be able to detect the presence of the recombination bump, the most distinctive feature of the primordial signal.