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

TLDR: In this article, the authors study the TCC constraint on the inflationary energy scale from the recently proposed trans-Planckian censorship conjecture and find a universal upper bound on inflationary Hubble expansion rate which is solely determined by the reheating temperature.

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 ${H}_{\mathrm{inf}}$ which is solely determined by the reheating temperature ${T}_{\mathrm{rh}}$: ${H}_{\mathrm{inf}}/{M}_{\mathrm{Pl}}\ensuremath{\lesssim}{T}_{0}/{T}_{\mathrm{rh}}$, where ${T}_{0}$ is the photon temperature today. The upper limit can be saturated by a postinflationary oscillatory stage with the critical equation-of-state parameter $w\ensuremath{\approx}\ensuremath{-}1/3$, 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 $r\ensuremath{\lesssim}{10}^{\ensuremath{-}8}$, which can be realized in many string-inspired inflation models.