Trans-Planckian Censorship and $k$-inflation

We propose a more general version of the Trans-Planckian Censorship Conjecture (TCC) which can apply to models of inflation with varying speed of sound. We find that inflation models with $c_S<1$ are in general more strongly constrained by censorship of trans-Planckian modes than canonical inflation models, with the upper bound on the tensor/scalar ratio reduced by as much as three orders of magnitude for sound speeds consistent with bounds from data. In particular, models which satisfy the TCC, and therefore the de Sitter Swampland Conjecture, can still violate the more general condition for non-classicality of trans-Planckian modes. As a concrete example, we apply the constraint to Dirac-Born-Infeld inflation models motivated by string theory.