Yoga Dark Energy: Natural Relaxation and Other Dark Implications of a Supersymmetric Gravity Sector

Abstract

We construct a class of 4D 'yoga' (naturally relaxed) models for which the vacuum energies of heavy particles do not gravitate. The models contain three ingredients: (i) a relaxation mechanism driven by a scalar field (the 'relaxon'), (ii) a very supersymmetric gravity sector coupled to the Standard Model in which supersymmetry is non-linearly realised, and (iii) an accidental approximate scale invariance expressed through the presence of a low-energy dilaton supermultiplet. All three are common in higher-dimensional and string constructions. Although none suffices on its own, taken together they predict a current Dark Energy density that is of order (M 2 W /M p ) 4 and a gravitino mass of order M 3 W /M 2 p , with M W , M p the weak and Planck scales respectively. The dilaton's vev τ determines the weak scale M W ∼ M p / √ τ and because the relevant part of the scalar potential arises as a function of ln τ it stabilizes τ in a local de Sitter minimum with exponentially large fields obtained using input parameters no larger than O(60), thereby explaining both the size of the electroweak hierarchy and the cosmological constant. Scale invariance implies the dilaton couples to matter like a Brans-Dicke scalar with coupling large enough to be naively ruled out by solar-system tests of gravity. Yet because it comes paired with an axion it escapes fifth-force bounds through the novel screening mechanism described in ArXiV:2110.10352. Cosmological axio-dilaton evolution provides a natural quintessence model for Dark Energy, whose evolution might realize recent proposals to resolve the Hubble tension, and whose axion contributes to Dark Matter. We summarize some of the remaining challenges, comment on implications for inflation and sketch possible UV completions of our approach.

RG-Induced Modulus Stabilization: Perturbative de Sitter Vacua and Improved $\hbox{D3}$-$\overline{\hbox{D3}}$ Inflation

“…Our proposal differs substantially from both of them by being purely based on perturbative corrections within the corresponding effective field theory (EFT), but doing so in a way consistent with the Dine-Seiberg problem. Our scenario adapts a proposal made for higherdimensional theories in [10] (and further elaborated for 4D supergravity in [11]).…”

“…An attentive reader might be struck by the similarity between this list of ingredients and those used in ref. [11], for which the only difference is that there the field φ instead enters as a 'relaxation' field whose presence dynamically helps suppress the size of the scalar potential at its minimum.…”

“…The appearance of φ in [11] is at first sight a bit jarring, since it appears to arise in a bespoke way with nothing to do with any other physics. We argue here that one way to understand the presence of φ is as an inflaton: its very definition requires it to interpolate between a potential that is dominated by a large positive vacuum energy and one where the potential energy is small.…”

“…We argue here that one way to understand the presence of φ is as an inflaton: its very definition requires it to interpolate between a potential that is dominated by a large positive vacuum energy and one where the potential energy is small. (The only surprise in [11] is in just how small the potential at this minimum turns out to be.) All that is needed to make early-universe evolution of φ into an inflationary mechanism is a reason why this transition should happen slowly (and showing how this occurs is the baton we take up here).…”

Quintessence and the Swampland: The numerically controlled regime of moduli space

“…This contribution would raise the scale of the potential well beyond the dark energy scale. A loophole is to consider a new contribution to the scalar potential that would cancel supersymmetry breaking effects with some fine-tuning, as in [72], where the additional effect is assumed to come from the backreaction of non-supersymmetric visible sector branes (see also [99] for recent developments of quintessence models in scenarios with non-linearly realised supersymmetry).…”