Trans-Planckian Censorship and the Swampland (1909.11063v5)

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 $[\phi_1,\phi_2]$ satisfies $V(\phi_2)\leq A\cdot\exp(-2(\phi_2-\phi_1))/\sqrt{(d-1)(d-2)})$ 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.

• The paper introduces the TCC, which restricts effective field theories by ensuring sub-Planckian fluctuations never expand beyond the Hubble horizon.
• The methodology establishes an upper bound on the scalar potential’s slope and constrains the lifetime of de Sitter spaces in inflationary models.
• The analysis aligns TCC with other Swampland conjectures, offering a unified framework to test quantum gravity’s implications in cosmology and string theory.

An Examination of the Trans-Planckian Censorship Conjecture and the Swampland

The paper "Trans-Planckian Censorship and the Swampland" by Alek Bedroya and Cumrun Vafa introduces a novel conjecture, the Trans-Planckian Censorship Conjecture (TCC), within the framework of the Swampland program. This body of work explores the constraints on effective field theories that are consistent with quantum gravity, with particular emphasis on the fate of sub-Planckian fluctuations in cosmological settings. The TCC stipulates that such fluctuations should remain quantum and never expand beyond the Hubble horizon to become classical. This conjecture is posited to offer a more specific benchmark than the dS Swampland conjecture and carries significant implications for the life span of de Sitter (dS) spaces and inflationary models.

Key Contributions and Analysis

The authors propose that the TCC leads to significant constraints on cosmological models driven by scalar fields. Specifically, TCC imposes an upper bound on the asymptotic value of the scalar potential's slope, expressed as $|V'|/V \leq 2/\sqrt{d-2}$, where $d$ denotes the number of spacetime dimensions. Additionally, a monotonically decreasing portion of the scalar potential is restricted by an exponential decay, further bounding the potential's growth. This aligns with a prohibition of long-lived, meta-stable dS spaces while permitting sufficiently short-lived ones, thereby providing a natural resolution to the cosmological constant problem.

The paper explores several consequences of TCC, particularly in relation to inflationary scenarios. It argues against the classical breakdown of field theories due to trans-Planckian fluctuations and emphasizes that any physical theory consistent with quantum gravity should avoid scenarios where sub-Planckian modes "freeze" at scales exceeding the Hubble horizon.

Mathematical and Theoretical Implications

A noteworthy aspect of TCC is its boundary on Hubble parameter $H$ throughout cosmic evolution, ensuring that $H < 1$ in natural Planck units, thereby preserving sub-Planckian behavior over cosmic timescales. The conjecture further bounds the universe's lifetime $T$ as $T \leq H^{-1} \log(M_p/H)$, with $M_p$ being the Planck mass. For scenarios such as long-range positive scalar potentials, TCC extends the de Sitter Swampland conjecture by considering emergent light states at large field values to refine predictions without field-space limitations.

In the paper's examination of examples from string theory, including the KKLT and LVS scenarios, TCC challenges existing models by imposing more intense restrictions, particularly in terms of dS vacuum lifetimes. String constructions, which have proposed stable dS vacua, are shown to conflict with TCC due to excessively long lifespans that TCC constrains.

Convergence with Other Swampland Conjectures

The paper deftly explores the interplay between TCC and other Swampland conjectures, including the distance conjecture and the dS conjecture. It suggests that TCC intrinsically aligns with principles established within these conjectures by providing a unified framework that accounts for both asymptotic field limits and field interior spaces. The authors speculate that TCC offers a compelling explanation for the refined dS conjecture's predictions, acting as a primary principle of physics that transcend current paradigms in early universe cosmology.

Implications for Future Developments

TCC heralds profound implications for future research in cosmology and string theory. Its robust framework provides a stringent yardstick for assessing the potential viability of effective field theories within quantum gravity. Given its alignment with Swampland criteria and compatibility with quantum gravitation principles, TCC may well shape models of dark energy, inflation, and universe expansion. Moreover, as theoretical and observational data converge, the rigorous bounds presented by TCC may inform robust tests to further delineate the scope of viable quantum gravitational theories in the ongoing quest to unravel the fundamental nature of the universe.