The dS swampland conjecture and the Higgs potential

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 $|\nabla V|/V\ge \mathcal{O}(1)$. 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.

Comments: 10 pages, v2: edited for clarity, references added