B-modes and the sound speed of primordial fluctuations

It was recently shown that a large value of the tensor to scalar ratio $r$ implies a constraint on the minimum value of the sound speed $c_s$ of primordial curvature perturbations during inflation that is stronger than current bounds coming from non-Gaussianity measurements. Here we consider additional aspects related to the measurement of B-modes that may provide additional leverage to constrain the sound speed parametrizing non-canonical models of inflation. We find that a confirmation of the consistency relation $r = -8 n_t$ between the tensor to scalar ratio $r$ and the tensor spectral index $n_t$ is not enough to rule out non-canonical models of inflation with a sound speed $c_s$ different from unity. To determine whether inflation was canonical or not, one requires knowledge of additional parameters, such as the running of the spectral index of scalar perturbations $\alpha$. We also study how other parameters related to the ultra violet completion of inflation modify the dependence of $r$ on $c_s$. For instance, we find that heavy degrees of freedom interacting with curvature fluctuations generically tend to make the constraint on the sound speed stronger. Our results, combined with future observations of primordial B-modes, may help to constrain the background evolution of non-canonical models of inflation.