Inflation with $0 \leq c_{\rm s} \leq 1$
  We investigate a novel single field inflationary scenario which allows a
transition between a slow-roll k-inflation with $c_{\rm s}$ of order unity and
a ghost inflation with $ c_{\rm s} \simeq 0$, where $ c_{\rm s}$ is the sound
speed for the curvature perturbations. We unify the two phases smoothly by
appropriately taking into account a higher derivative scordatura term, which is
always there from the effective field theory point of view but which becomes
important only in the $c_{\rm s} \simeq 0$ regime. The model achieves the whole
range of $0 \leq c_{\rm s} \leq 1$ avoiding strong coupling and gradient
instability, and allows us to access the $c_{\rm s} \simeq 0$ regime in a
self-consistent manner. We also discuss implications to the formation of
primordial black holes.
