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.
