The dS swampland conjecture and the Higgs potential

TL;DR

The paper tests the de Sitter swampland conjecture, which requires $|\nabla V|/V \ge c$ with $c \sim {\cal O}(1)$, in the context of the Standard Model plus a quintessence field. Analyzing a minimal, decoupled SM+quintessence setup shows a dramatic violation $|\nabla V|/V \sim 10^{-55}$ today, challenging the conjecture; a highly specific coupling of the quintessence field to the Higgs could, in principle, restore $c \sim {\cal O}(1)$ but appears extremely fine-tuned from a 4d EFT perspective. The authors discuss loop-induced couplings to nucleons that remain below observational bounds and explore a Higgs-coupled form $V(\phi,H)=e^{-{\lambda}\phi}(V_H(H)+\Lambda)$ that generates a $\phi h^2$ interaction, highlighting the tension between naturalness and the conjecture. They also consider implications for QCD and possible modifications to the conjecture and call for explicit string theory realizations of SM+quintessence to determine whether such setups can be realized without excessive tuning. The work raises the possibility either that the conjecture is too strong or that new, testable predictions (e.g., long-range scalar forces) could emerge, depending on future theoretical and observational progress.

Abstract

According to a conjecture recently put forward in arXiv:1806.08362, the scalar potential $V$ of any consistent theory of quantum gravity satisfies a bound $|\nabla V|/V \geq {\cal O}(1)$. This forbids dS solutions and supports quintessence models of cosmic acceleration. Here we point out that in the simplest models incorporating the Standard Model in addition to quintessence, with the two sectors decoupled as suggested by observations, the proposed bound is violated by 50 orders of magnitude. However, a very specific coupling between quintessence and just the Higgs sector may still be allowed and consistent with the conjecture.