de Sitter swampland conjecture and the Higgs potential

Abstract

According to a conjecture recently put forward in [1], the scalar potential V of any consistent theory of quantum gravity satisfies a bound |∇V |/V ≥ 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. arXiv:1807.06581v2 [hep-th]

De Sitter vs Quintessence in String Theory

“…We then use a more phenomenological approach to assess to which extent quintessence is a viable alternative to dS from observations. In particular, we found (as recently shown also in []), that if the quintessence picture is valid, and there is no other scalar field around other than the Higgs, in order to satisfy the swampland conjecture , the Higgs field has to couple directly to the quintessence field. This would be particularly challenging in any string theory/supergravity scenario, as a quintessence field that couples directly to the Higgs would also couple to the SM fermions, violating fifth‐force constraints.…”

“…As already pointed out in [], the swampland conjecture is in tension with basic features of the Higgs potential. In fact if h is the standard Higgs field and χ the quintessence field, the total scalar potential can be written as: The swampland conjecture at the maximum of the Higgs potential for then implies: However the quintessence potential today has to scale as .…”

“…However the unreasonable value of k and C show that this is more a curious observation rather than a real solution. – A direct Higgs‐quintessence coupling : Ref. [] modified the initial potential via the introduction of a coupling between χ and h of the form: In this case the swampland conjecture is satisfied since the ratio in at where takes the form: However, even if the Higgs‐quintessence coupling in is not ruled out by fifth‐force constraints, one would need to explain why the SM fermions are instead decoupled from the quintessence field since a direct coupling between them and χ would not be allowed by fifth‐force bounds. Given that in 4D string models a direct coupling between χ and h would generically also imply a direct coupling between the quintessence field and SM fermions, we interpret this tension as a phenomenological hint against the validity of the swampland conjecture. Adding more fields : Another solution involves the introduction of a third field ϕ which is heavy in the electroweak vacuum but makes a non‐trivial contribution to the criterion at the symmetric point of the Higgs potential.…”

“…See [] for an earlier discussion on some challenges for quintessence in the context of supergravity. Our treatment is more general.…”

On uplifts by warped anti‐D3‐branes

“…As stated, the conjecture would even forbid any de Sitter critical point. This is hard to justify both from a stringy perspective as well as from the bottom‐up . However, it is possible that a statement could hold that is similar in spirit, allows for de Sitter critical points but not minima (see e.g.…”