Trans-Planckian Censorship and $k$-inflation

TL;DR

This paper extends the Trans-Planckian Censorship Conjecture to models with varying sound speed, revealing stronger constraints on inflation models with $c_S<1$ and applying these to string-inspired Dirac-Born-Infeld inflation.

Contribution

It introduces a generalized TCC applicable to $k$-inflation models with variable sound speed, providing new bounds on inflationary parameters and analyzing string theory motivated models.

Findings

Models with $c_S<1$ face tighter constraints from TCC.

Upper bounds on tensor/scalar ratio are reduced significantly for low sound speeds.

Some models satisfying the TCC violate the non-classicality condition for trans-Planckian modes.

Abstract

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.