The Trans-Planckian Censorship Conjecture in different frameworks of viable inflation

Abstract

We review the recently proposed Trans-Planckian Censorship Conjecture that stems from the Trans-Planckian problem of cosmological perturbations. We analyze the implications and constraints that TCC introduces in different frameworks of viable inflation. We revisit the case of slow-roll scalar field inflation and we investigate the cases of slow-roll $f(R)$ and $f(R,\phi)$-gravity. Finally, we consider the conjecture in the context of constant-roll scalar field inflation.