  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.
