Cosmic Gradient Energy Model (CGEM): A Testable Scalar–Tensor Extension of Inhomogeneous Cosmology

We present the Cosmic Gradient Energy Model (CGEM), a minimal extension of inhomogeneous cosmology in which large-scale density contrasts source an effective scalar field that modifies the locally inferred expansion rate. The model operates within a constrained scalar–tensor framework and introduces a finite interaction scale λ to ensure locality of the effect, replacing the unbounded Poisson equation with a screened (Yukawa-type) field equation.

For a spherical underdense region (void) with density contrast δ ≈ −0.3, the central scalar field value yields a fractional Hubble deviation of order ΔH/H ∼ β²|δ|, arising from the scalar-tensor modification of the effective gravitational coupling G_eff = G(1 + 2β²). For coupling strength β ~ 0.1, this predicts a contribution of order ΔH/H ~ 0.3%, representing a partial structural contribution to local expansion variance rather than a complete resolution of the Hubble tension.

CGEM predicts that underdense regions exhibit enhanced local expansion rates while overdense regions suppress expansion, providing a direct structural contribution to Hubble variance. These effects are testable through void expansion measurements, peculiar velocity fields, and weak lensing constraints on effective gravitational coupling (DESI, Euclid, LSST). The model introduces no violations of general relativity and remains fully constrained by existing observational bounds β ∈ [0, 0.3].