Renormalizable Flat-Background Scalar Gravity Coupled to the Standard Model version 6 Revised December 14, 2025

Abstract We present Inertial Gravity Theory (IGT), a flat-background scalar formulation of gravity that couples consistently to the Standard Model while avoiding curved spacetime. In IGT, gravity is generated not by metric deformation but by changes in local inertial density described by a scalar field ρᵢ. Gravitational dynamics arise from an energy-partition mechanism in which field energy increases inertia and induces the physical scalings γg(r) that govern time, length, and energy in the field. These scalings reproduce all classical weak-field and strong-field tests of General Relativity, including light-bending, Shapiro delay, perihelion advance, and the tensorial quadrupole strain pattern observed by LIGO.IGT introduces a Planck-normalized dimensionless coupling αp = MQ/MP, where MQ c² is the energy of the quantized excitation of the inertial-density field (“inertion”). Although the mediator is a spin-0 scalar, tensorial gravitational-wave strain arises from second spatial derivatives of the scalar field under anisotropic radial scaling.All operators in the IGT Lagrangian are dimension-4, and explicit counterterm analysis demonstrates one-loop perturbative renormalizability. This yields a gauge-invariant, flat-background formulation of gravity without geometric structures that underlie GR and modern quantum gravity frameworks.