(GC) Finite-Response Coupled Field Dynamics (FRCFD): A Minimalist Field-Theoretic Framework for Non-Pathological Gravity
A Self-Consistent Finite-Response Field Theory of Gravitation: Finite-Response Coupled Field Dynamics
Author: Derek Flegg
Date: March 21, 2026
“This work establishes internal consistency and testable structure; full cosmological fitting is a subsequent program.”
Abstract
Finite-Response Coupled Field Dynamics (FRCFD) is formulated as a 3+1-dimensional field theory in which the vacuum is modeled as a finite-response substrate with a maximum stress capacity S_max. This replaces the implicit infinite-capacity assumption of General Relativity with a saturating response function that constrains field growth in high-stress regimes. Gravitational dynamics emerge from a scalar substrate field S whose local state determines an effective propagation metric through the update-rate function:
f(S) = exp(−S / S_eff(σ))
where S_eff(σ) is a scale-dependent effective capacity defined in terms of the invariant:
σ = |∇S|^2
The framework reproduces standard post-Newtonian behavior in the infrared limit S_eff → 1, yielding agreement with Solar System constraints, including perihelion precession and Parametrized Post-Newtonian (PPN) bounds. In higher-stress regimes, the effective capacity runs toward a finite saturation value, producing controlled deviations from General Relativity. The theory introduces a self-regulating feedback mechanism: as substrate stress increases, the effective response softens and the update-rate slows, preventing the formation of divergent field configurations. Cosmological implications are explored through a path-dependent substrate response in which redshift arises from cumulative interaction with the finite-response medium. This sector is treated as a provisional extension pending derivation from the field equations. FRCFD therefore shifts the theoretical focus from resolving divergences to preventing their formation, providing a finite-response alternative in which gravitational behavior emerges from bounded field dynamics without introducing additional geometric or matter-sector assumptions.
I. Substrate Field Definition
The substrate is defined as a fundamental scalar field S whose local state determines the effective spacetime structure. The field does not reside within spacetime; rather, its configuration defines the propagation properties associated with geometry.
A finite maximum stress S_max imposes a natural regulator on field growth, preventing divergent behavior in high-density regimes.
II. Field Equations
Substrate Field:
∂²S/∂t² − c²∇²S + β S³ = J[Ψ]
The nonlinear term β S³ enforces saturation and encodes the finite-capacity response of the substrate.
Matter Field:
∂²Ψ/∂t² − v²∇²Ψ + μΨ + λ|Ψ|²Ψ = κ S Ψ
The coupling term κ S Ψ links matter dynamics to the local substrate state.
III. Effective Metric and Update Rate
ds² = f(S)^2 dt² − f(S)^(-2) dr² − r² dΩ²
f(S,σ) = exp( − S / S_eff(σ) )
This metric is not fundamental but provides an effective description of signal propagation in the substrate.
IV. Running Capacity and Invariant Scale
σ = |∇S|^2
For a static central source:
S(r) ≈ GM / r σ = G²M² / r⁴
The running capacity S_eff(σ) introduces scale dependence while preserving locality.
V. Weak-Field Limit and PPN Structure
Expanding the metric:
g_tt ≈ 1 − 2GM / (r S_eff) g_rr ≈ −(1 + 2GM / (r S_eff))
Matching to the PPN formalism yields:
γ(σ) = 1 / S_eff(σ) β(σ) = 1 / S_eff(σ)^2
Solar System constraints require:
|S_eff − 1| < 10^-5
This enforces an infrared fixed point in which FRCFD reproduces General Relativity to high precision.
VI. Strong-Field Behavior
At high σ, the effective capacity runs toward a lower saturation value:
S_eff → S_UV ≈ 0.3 – 0.5
This produces controlled deviations from GR without divergence.
VII. Cosmological Sector (Provisional)
A candidate description introduces a path-dependent substrate profile:
S(χ) = γχ (ansatz)
Redshift arises from cumulative interaction:
1 + z = 1 / f(S_emit)
This reproduces observational scaling at a phenomenological level but is not yet derived from the field equations and remains under development.
VIII. Conclusion: Finite-Response Gravity
FRCFD replaces the assumption of infinite gravitational response with a finite, self-limiting substrate. This introduces a built-in feedback mechanism in which increasing stress reduces the effective response, preventing pathological divergences. Rather than resolving singularities after they arise, the framework precludes their formation through bounded dynamics. General Relativity emerges as the infrared limit of this finite-response structure, while deviations appear only in regimes where the substrate approaches its capacity.
