One-Metric Quantum Gravity: Unifying SR, GR, and QM with a Shared Causal Cone

This record presents a one-metric framework in which a single deterministic scalar field fixes a universal causal cone and thereby an effective spacetime metric shared by all sectors. In the geometric-optics limit, local special-relativistic kinematics is encoded by this single cone. Integrating out a diffeomorphism-covariant environmental sector on that background induces an Einstein–Hilbert term with positive Planck mass and suppressed higher-curvature corrections. A diffeomorphism Noether identity then makes the scalar’s equation redundant on the general-relativistic branch (“Closure”), so the low-energy field equations reduce to Einstein’s equations with covariant corrections.

The work quantises spin-2 fluctuations of the same metric using BRST–BV techniques with ghost-free entire form factors that preserve the principal wave operator. Curved-space reflection positivity and Schwinger–Keldysh cutting yield positive spectral densities and consistent optical-theorem cuts; the graviton two-point function contains only the massless spin-2 pole, and retarded realisations preserve causal microcausality. Operator-theoretic foundations for nonlocal functions of the wave operator and their retarded or Stieltjes representations give all-loop ultraviolet softness with counterterms closed on the same manifold of actions, and well-posedness via Volterra-structured retarded kernels, including energy inequalities and small-data stability on cosmological and black-hole backgrounds.

Phenomenologically, exact Friedmann–Robertson–Walker and Schwarzschild geometries arise from healthy disformal data, and Kerr is realised exactly by a two-gradient Kerr–Schild completion aligned with its principal null congruences. The framework reproduces standard general-relativistic limits (post-Newtonian parameters matching observations, two tensor gravitational-wave polarisations with light-speed propagation, no scalar dipole or species-dependent cones) and predicts achromatic wavefronts with a controlled envelope-level dispersion that maps to a parametrised post-Einsteinian phase with exponent b = +3. Vacuum energy appears as an integration constant in a unimodular or four-form language, with smallness realised through a multi–four-form discretuum and boundary selection. Quantum fields minimally coupled to the metric admit a functional Schrödinger description whose polar decomposition yields a covariant continuity equation and Born-rule equivariance without a typicality postulate, and any anomaly-free gauge or matter theory (including the Standard Model) can be embedded on this background while preserving the single cone, Closure, and unitarity.