Effective Field Theory of the Standard Model, Einstein Gravity and a Unified Scalar Field (MMA-DMF)

We construct a comprehensive Effective Field Theory (EFT) for the Standard Model (SM) coupled to Einstein gravity and a single light scalar field ϕ which, at the level of cosmological phenomenology, replaces both cold dark matter and dark energy. This framework, specifically the MMA-DMF, operates on a “Gravity Hypothesis” rather than a matter hypothesis. The scalar couples to the trace of the energy–momentum tensor and to curvature invariants, implementing a density- and curvature-dependent screening mechanism. We organise the EFT in a phenomenological basis of operators up to dimension six, incorporating a geometric flavor sector where Yukawa matrices are field-dependent. We identify the parameter ranges for which the theory is perturbatively stable up to a multi-TeV cutoff Λ. Furthermore, we demonstrate that for the parameter choices used in MMA-DMF cosmological studies, the model resolves the Hubble tension (H0 ≈ 72.0 km/s/Mpc) via an “Early-X” mechanism and the S8 tension (S8 ≈ 0.772) via force saturation, while remaining compatible with fifth-force experiments, tests of General Relativity, and early-universe constraints from Big Bang Nucleosynthesis (BBN). We summarise the full set of consistency checks in a compact UV–IR validation table.