Classical and Stochastic Trans-Planckian Censorship
Abstract
The trans-Planckian censorship conjecture (TCC) limits inflation to a deadline of NTCC=ln(MPl/Hend) e-folds. We formulate it in stochastic inflation as a bound at confidence 1−δ on the probability that a history outlasts the deadline, with three readings: one worldline, the region grown from one Hubble patch, and the reheated volume. Each reading becomes a closed-form condition, rigorous for a linear roll in leading-order stochastic inflation (for the region, in a branching model) and sharp at leading order in NTCC: a linear roll whose classical history lasts Ncl e-folds respects the TCC if 1−Ncl/NTCC≥{2𝒫ζ[w+ln(1/δ)/NTCC]}1/2, with w=0 for a worldline and w=3 for a region. On a linear slope without vacuum decay, the worldline and region readings are never weaker than the classical TCC, and on the CMB-normalized attractor all readings agree closely with it, so the bounds on the scale of inflation stand. A classical phase that ends in a flat quantum well, which the overdamped classical TCC excludes, is allowed with a margin of a few e-folds per worldline. Near the onset of eternal inflation, the readings differ. On a linear slope, a region must leave the fraction √(6𝒫ζ) of the deadline unused at leading order: eternal inflation is excluded for every classical history that uses a finite fraction of the deadline, as is a band of non-eternal slopes, and the slope bound becomes |V'|>V3/2/[√2 π(1−Ncl/NTCC)]. Per worldline, every slope is allowed, given a margin of a few standard deviations. A false vacuum must decay at about the eternal threshold Γ=9H4/(4π) or faster for a region or the volume, but only faster than 3H4ln(1/δ)/(4πNTCC) per worldline. Whether the TCC forbids eternal inflation depends on the reading.
Related
- The trans-Planckian problem and gravitational interactions
- Planckian dissipation from classical hydrodynamics
- Wasserstein-2 gradient flows and the geometry of entropy production in classical and quantum stochastic thermodynamics
- Universal Scaling of Conditional Mutual Information in Classical Stochastic Dynamics
- Advanced computational methods for simulating the classical hydrogen atom in stochastic electrodynamics
BibTeX
@misc{guleryuz2026classical,
title = {{Classical and Stochastic Trans-Planckian Censorship}},
author = {Omer Guleryuz},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.27319},
eprint = {2610.27319},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.27319},
}
RIS
TY - UNPB
TI - Classical and Stochastic Trans-Planckian Censorship
AU - Omer Guleryuz
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2610.27319
UR - https://arxiv.org/abs/2610.27319
AB - The trans-Planckian censorship conjecture (TCC) limits inflation to a deadline of N_TCC=ln(M_Pl/H_end) e-folds. We formulate it in stochastic inflation as a bound at confidence 1−δ on the probability that a history outlasts the deadline, with three readings: one worldline, the region grown from one Hubble patch, and the reheated volume. Each reading becomes a closed-form condition, rigorous for a linear roll in leading-order stochastic inflation (for the region, in a branching model) and sharp at leading order in N_TCC: a linear roll whose classical history lasts N_cl e-folds respects the TCC if 1−N_cl/N_TCC≥{2𝒫_ζ[w+ln(1/δ)/N_TCC]}^1/2, with w=0 for a worldline and w=3 for a region. On a linear slope without vacuum decay, the worldline and region readings are never weaker than the classical TCC, and on the CMB-normalized attractor all readings agree closely with it, so the bounds on the scale of inflation stand. A classical phase that ends in a flat quantum well, which the overdamped classical TCC excludes, is allowed with a margin of a few e-folds per worldline. Near the onset of eternal inflation, the readings differ. On a linear slope, a region must leave the fraction √(6𝒫_ζ) of the deadline unused at leading order: eternal inflation is excluded for every classical history that uses a finite fraction of the deadline, as is a band of non-eternal slopes, and the slope bound becomes |V'|>V^3/2/[√2 π(1−N_cl/N_TCC)]. Per worldline, every slope is allowed, given a margin of a few standard deviations. A false vacuum must decay at about the eternal threshold Γ=9H^4/(4π) or faster for a region or the volume, but only faster than 3H^4ln(1/δ)/(4πN_TCC) per worldline. Whether the TCC forbids eternal inflation depends on the reading.
ER -