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, $V_\text{inf}^{1/4} < \mathcal{O}(10) \, \text{TeV}$ with $r <
\mathcal{O}(10^{-50})$, and the running parameter is bounded above as
$\alpha_\text{s} \lesssim - 4 \times 10^{-3}$.
