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 $N_{\text{total}}$ 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 $N_{\text{total}}$ small. In concrete setups, we find a stringent constraint on the inflationary energy scale, $V_{\text{inf}}^{1\mathrm{/}4}<\mathcal{O}(10)\text{TeV}$ with $r < $\mathcal{O}$(10^{-50})$,andtherunningparameterisboundedaboveas$\alpha_$\text{s}$ \lesssim - 4 \times 10^{-3}$.