Universal Upper Bound on the Inflationary Energy Scale from the Trans-Planckian Censorship Conjecture

Abstract

We study the constraint on the inflationary energy scale from the recently proposed Trans-Planckian Censorship Conjecture (TCC). We find a universal upper bound on the inflationary Hubble expansion rate $H_\text{inf}$ which is solely determined by the reheating temperature $T_\text{rh}$: $H_\text{inf}/M_\text{Pl}\lesssim T_0/T_\text{rh}$, where $T_0$ is the photon temperature today. The upper limit can be saturated by a post-inflationary oscillatory stage with the critical equation-of-state parameter $w\approx-1/3$, or by an inflation model with multiple stages. In the lowest reheating temperature required for big bang nucleosynthesis, the upper bound on the tensor-to-scalar ratio $r$ at the CMB scales is $r\lesssim10^{-8}$, which can be realized in many string-inspired inflation models.