Trans-Planckian Censorship and the Swampland

TL;DR

The paper proposes the Trans-Planckian Censorship Conjecture (TCC), a principled Swampland criterion that forbids sub-Planckian quantum fluctuations from crossing the Hubble horizon in an expanding universe, thereby linking Planck-scale physics to cosmological evolution. It develops both asymptotic and interior implications for scalar potentials, deriving a sharp long-field bound $ (|\nabla V|/V)_\infty \ge 2/\sqrt{(d-1)(d-2)}$ and an exponential interior bound $V(\phi) \le A e^{-2\Delta\phi/\sqrt{(d-1)(d-2)}}$, while also constraining short-range behavior via local inequalities. The framework yields a finite lifetime bound for metastable de Sitter phases and imposes lower bounds on curvature around unstable maxima, with extensive tests in string theory examples (KKLT, LVS, heterotic, and Type II no-go theorems) showing broad compatibility but highlighting tensions for long-lived dS vacua. It further connects to the Distance Conjecture by predicting a lower exponent in the tower mass scale decay with field distance and provides a unified perspective on the dS Swampland conjecture, including logarithmic corrections in the interior. Overall, TCC offers a physically motivated, testable principle that constrains cosmology and string constructions in a way closely aligned with, yet distinct from, existing Swampland conjectures.

Abstract

In this paper, we propose a new Swampland condition, the Trans-Planckian Censorship Conjecture (TCC), based on the idea that in a consistent quantum theory of gravity sub-Planckian quantum fluctuations should remain quantum and never become larger than the Hubble horizon and freeze in an expanding universe. TCC leads to conditions that are similar to the refined dS Swampland conjecture. For example, applied to the case of cosmologies driven only by a scalar field, the TCC imposes an upper bound of $2/\sqrt{d-2}$ on the asymptotic value of $|V'|/V$. Additionally, it implies that a monotonically decreasing potential across $[φ_1,φ_2]$ satisfies $V(φ_2)\leq A\cdot\exp(-2(φ_2-φ_1))/\sqrt{(d-1)(d-2)})$ for some $\mathcal{O}(1)$ constant $A$. Like the dS Swampland conjecture, the TCC forbids long-lived meta-stable dS spaces, but allows sufficiently short-lived ones.

Figures (1)

• Figure 1: The curves $\gamma_\alpha$ are causal curves that initiate in the interior region $\mathcal{M}_I$ and collectively span the asymptotic region $\mathcal{M}_\infty$.