Unified Scalar Field Theory of Gravity: Classical, Quantum, and Phenomenological Perspectives

We present the Unified Scalar Field Theory (USFT) of gravity, built on a single foundational axiom: time is governed by a discrete scalar field ΦT that evolves in minimum steps δτ∼tP (the Planck time). From this axiom, two limits emerge without additional postulates. In the continuum limit δτ →0, the Schwarzschild metric to first post-Newtonian order, Newton’s constant G0 = β/(4π), and the Friedmann equation at leading order are recovered as infrared approximations of the USFT scalar field equations. We emphasise that recovering GR phenomenology at 1PN order is a necessary but not sufficient condition for a full GR equivalent: the tensorial Einstein equations and propagating spin-2 modes are not derived; USFT contains only scalar propagating degrees of freedom. In the discrete limit δτ∼tP, the Schroedinger equation, the Born rule, and the particle guidance equation emerge from the tick algebra without wavefunction postulates or measurement axioms. All physical singularities are absent by theorem: the Big Bang is replaced by a bounce and black holes have a finite-density Planck core, both consequences of Axiom 1 alone. The anomalous perihelion precession of Mercury (43′′/cy) is derived from a finite-speed Tick-Lag retardation of the temporal scalar field ΦT: the e2ΦT time-dilation factor for a fast-moving body produces a 1/r3 deceleration term that yields the observed precession rate without invoking curved spacetime or the Schwarzschild geodesic. The cosmological sector predicts thawing dark energy with w0 ≈−0.91 and wa ≈−0.26, consistent with the DESI DR2 preference for w0 >−1 at 4.2σ. Enhanced early gravity Geff(z = 8.6) ≈1.09–1.11 G0 resolves the JWST tension on massive black hole formation within 558–566 Myr. Photon lensing is derived from the scalar–photon coupling ΦGFµνFµν/4Λ, giving a measurable shadow deviation ∆θsh ∼5 µas for M87* at the EHT resolution limit. The discrete tick structure reproduces galactic flat rotation curves and the baryonic Tully–Fisher relation from baryons alone, without a dark matter particle, through a 1decoherence-derived acceleration scale a0 ≈1.2×10−10 m s−2 that matches the Milgrom scale. The same field ΦT that guides quantum particle trajectories via the guidance equation also drives cosmic dark energy via the Clock equation. This structural unity constitutes the unification. Going beyond gravity, USFT mechanises the fine structure constant (α≈1/137) and electric charge as topological torsion defects of the discrete Loom medium: charge quantization (q= ne) follows as a topological necessity of the 2π-winding condition on the discrete lattice, and α emerges as a geometric ratio of the Planck-scale lattice grain to the electromagnetic defect loop circumference, derived without any free parameters. Together with the identification of inertial mass as m ≡Esoliton/c2 (the energy of a localised ΦG tension loop), this constitutes the first simultaneous mechanisation of m, q, and α from a single underlying medium quantities that remain external inputs in General Relativity, the Standard Model, and String Theory. Two open tensions are identified and discussed: the benchmark coupling λGT = 0.05 versus the Cassini PPN bound, and the status of scalar-only gravitational wave polarization versus current LIGO/Virgo observations.