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 gravitational response of heavy-particle vacuum energies is strongly suppressed. 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 and although none suffices on its own, taken together they can dramatically suppress the net vacuum-energy density. The dilaton's vev τ determines the weak scale M W ∼ M p/√τ. We compute the potential for τ and find it can be stabilized in a local de Sitter minimum at sufficiently large field values to explain the size of the electroweak hierarchy, doing so using input parameters no larger than O(60) because the relevant part of the scalar potential arises as a rational function of lnτ. The de Sitter vacuum energy at the minimum is order c M 8 W α 1/τ 4, with a coefficient c ≪ 𝒪(M W -4). We discuss ways to achieve c ∼ 1/M p 4 as required by observations. 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 can evade fifth-force bounds through the novel screening mechanism described in arXiv:2110.10352. Cosmological axio-dilaton evolution predicts 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 inflationary implications and some remaining challenges, including the unusual supersymmetry breaking regime used and the potential for UV completions of our approach.

RG-induced modulus stabilization: perturbative de Sitter vacua and improved D3-$$ \overline{\mathrm{D}3} $$ 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 higher-dimensional 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.…”

Naturalness: A Snowmass White Paper

“…Although the added ingredients in both proposals are somewhat exotic, they pave the way towards potentially viable relaxation of the cosmological constant. A relaxation mechanism without NEC violation has recently been proposed [89], involving a very supersymmetric gravity sector coupled to a matter sector with non-linearly realized supersymmetry and an accidental approximate scale invariance. A related "crunching" mechanism for solving the cosmological constant problem was proposed in [90], wherein regions of space with a large cosmological constant crunch shortly after inflation, whereas regions with a small cosmological constant are metastable and survive to late times.…”

Snowmass2021 Theory Frontier White Paper: Data-Driven Cosmology

“…Refs. [366,367]). Another possibility is modify the helium abundance near the epoch of recombination, which would affect the free-electron fraction in the cosmic plasma and thus change the photon diffusion length.…”