Abstract We present a renormalizable scalar formulation of gravity, the Inertial Gravity Theory (IGT) that couples consistently to the Standard Model within a flat background. The theory replaces geometric curvature with a scalar inertial field that modifies local inertial density rather than spacetime itself. IGT is novel because it reformulates gravitational interaction as a classical energy‑partition process in which the time and distance scalings in the field emerge from increase in inertia as field energy is applied to rest mass. The resulting field law replicates all classical weak-field and strong field tests of General Relativity (GR) 1-3 , including tensorial gravitational waves in a purely vector‑scalar framework. We introduce dimensionless coupling αₚ = GMQ / ℓP c2 = MQ / MP, where MP = √(ℏ c / G) and MQ = mass of the single quantized excitation of the inertial field (e.g., particle or quantum). This is motivated by evaluating the geometric form α(r) = 2GM / (r c²) at the Planck length r = ℓP, with ℓP = √(ℏ G / c³). This establishes IGT as a self‑consistent, self‑renormalizing alternative to both metric gravity and quantum‑gravity extensions 7,18,19 . All operators in the Lagrangian are dimension-4, ensuring perturbative renormalizability at one loop. Explicit counterterm analysis shows that divergences close on the original operator basis, without requiring higher-dimensional corrections or tensor structures. The framework preserves gauge invariance and canonical kinetic normalization, yielding a well-defined set of beta functions for both gravitational and gauge couplings . This provides a minimal, flat-background alternative to general relativity and scalar-tensor models, compatible with established quantum-field-theoretic methods and standard renormalization procedures.
Batra, Rajeev (2025) studied this question.