Trans-Planckian Censorship and single-field inflaton potential

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 N-total 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 N-total small. In concrete setups, we find a stringent constraint on the inflationary energy scale, V-inf(1/4) < O(10) TeV with r < O(10(-50)), and the running parameter is bounded above as alpha(s) <= x 10(-3).