Trans-Planckian censorship and single-field inflaton potential

摘要: It was recently proposed that a field theory cannot be consistent with quantum gravity if it allows mode shorter than the Planck length to exit Hubble horizon. This is called Trans-Planckian Censorship Conjecture (TCC). We discuss implications of TCC on possible shape inflaton potential in single-field slow-roll inflation. point out (1) there generically an initial condition which total e-folding number $N_\text{total}$ doubled or more compared e-folds necessary for cosmic microwave background fluctuations, and (2) sizable negative running spectral index expected make small. In concrete setups, we find stringent constraint inflationary energy scale, $V_\text{inf}^{1/4} < \mathcal{O}(10) \, \text{TeV}$ $r \mathcal{O}(10^{-50})$, parameter bounded above as $\alpha_\text{s} \lesssim - 4 \times 10^{-3}$.