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

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, (ii) a very supersymmetric gravity sector coupled to matter for 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 {\it vev}~$\tau$ determines the weak scale $M_W \sim M_p/\sqrt\tau$. We compute the potential for $\tau$ and find it can be stabilized in a local de Sitter minimum at sufficiently large field values to explain the electroweak hierarchy, doing so using input parameters no larger than $O(60)$ because the relevant potential arises as a rational function of $\ln\tau$. The de Sitter vacuum energy at the minimum is order $c\, M_W^8 \propto 1/\tau^4$, with $c \ll O(M_W^{-4})$. We discuss how to achieve $c \sim 1/M_p^4$ as required by observations. Scale invariance implies the dilaton couples to matter like a Brans-Dicke scalar with dangerously large coupling yet because it comes paired with an axion it can evade bounds through the novel screening mechanism described in {\tt ArXiV:2110.10352}. Cosmological axio-dilaton evolution predicts a natural quintessence model for Dark Energy, whose evolution can 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.