Trans-Planckian Censorship and single-field inflaton potential

Abstract

© 2020 IOP Publishing Ltd and Sissa Medialab. It was recently proposed that a field theory cannot be consistent with quantum gravity if it allows a mode shorter than the Planck length to exit the Hubble horizon. This is called the Trans-Planckian Censorship Conjecture (TCC). We discuss the implications of the TCC on the possible shape of the inflaton potential in single-field slow-roll inflation. We point out that (1) there is generically an initial condition in which the total e-folding number Ntotal is doubled or more compared to the e-folds necessary for the cosmic microwave background fluctuations, and (2) a sizable negative running of spectral index is generically expected to make Ntotal small. In concrete setups, we find a stringent constraint on the inflationary energy scale, V1/4 inf ≤ O(10) TeV with r ≤ O(10-50), and the running parameter is bounded above as as ≤ -4 × 10-