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 a 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-to-scalar ratio reduced by as much as 3 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 nonclassicality of trans-Planckian modes. As a concrete example, we apply the constraint to Dirac-Born-Infeld inflation models motivated by string theory.