Inflation with 0 ≤ c s ≤ 1

We investigate a novel single field inflationary scenario which allows a transition between a slow-roll k-inflation with c _s of order unity and a ghost inflation with c _s ≃ 0, where c _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 _s ≃ 0 regime. The model achieves the whole range of 0 ≤ c _s ≤ 1 avoiding strong coupling and gradient instability, and allows us to access the c _s ≃ 0 regime in a self-consistent manner. We also discuss implications to the formation of primordial black holes.