Temporal Theory of Gravitation: Phenomenological Core with Screening
Year: 2025
Type: article
Abstract: We extend the minimal anchor core (v1.0) of the Temporal Theory of Gravitation (TTG) by introducing a class of nonlinear, even-parity coupling functions A(τ) that implement environmental screening. This preserves strict Solar System constraints while allowing scale-dependent deviations from General Relativity on galactic and cosmological scales. The formalism remains relativistic and falsifiable, with signatures spanning MICROSCOPE, SPARC rotation curves, and gravitational-wave phasing in LISA/ET. Keywords Temporal theory of gravitation, nonlinear coupling, even-parity functions, environmental screening, solar system constraints, general relativity deviations, galactic dynamics, cosmological scales, relativistic formalism, falsifiability, gravitational waves, LISA, EINSTEIN TELESCOPE Table of Contents Abstract Keywords Units & Conventions 1. Introduction: From Anchor to Screening 2. Canonical Coupling Families A(τ) 2.1 Hyperbolic Model (H) 2.2 Gaussian Model (G) 3. Field Equations 3.1 Scalar Field Dynamics 3.2 Matter Coupling and Non-Conservation 4. Screening Mechanism 4.1 Environmental Field τ_env(ρ) 4.2 Screening Transition Criterion 5. Phenomenology: Newtonian & PPN; Rotation Curves 5.1 Yukawa-Corrected Gravitational Potential 5.2 Modified Circular Velocity 5.3 PPN Parameters in Screened Regime 6. Gravitational Waves 6.1 Tensor Mode Propagation 6.2 Scalar Dipole Radiation in Mixed Binaries 7. Falsifiability & Constraints 7.1 Key Observational Tests 7.2 Critical Constraints and Falsification Conditions 8. Comparison to Alternatives 8.1 TTG vs ΛCDM 8.2 TTG vs MOND 8.3 TTG vs Chameleon/Vainshtein Mechanisms 9. Conclusions 10. Outlook: Toward Quantization (TTG-QG) and Thermodynamics References Appendix A: Numerical Implementation and SPARC Fitting A.1 Objective and Galaxy Selection A.1.1 NGC 2403 Properties A.2 Theoretical Framework and Equations A.2.1 Gravitational Acceleration in TTG A.2.2 Screening Equation A.2.3 Hyperbolic Coupling Function A.3 Numerical Implementation A.3.1 Data Preparation from SPARC Database A.3.2 Complete Python Implementation A.4 Results and Analysis A.4.1 Best-Fit Parameters for NGC 2403 A.4.2 Rotation Curve Fit (Figure A1) A.4.3 Screening Mechanism Validation (Figure A2) A.5 χ² Analysis A.5.1 Fit Quality Comparison (Table A1) A.6 Robustness Across Galaxies A.6.1 Parameter Stability Analysis (Table A2) A.7 Discussion and Implications A.7.1 Key Features of TTG v1.2 A.7.2 Physical Interpretation of Results A.8 Conclusion of Numerical Implementation Units & Conventions We work in natural units ħ = c = 1 for the theoretical development (Sections 2-3). In phenomenological, post-Newtonian and gravitational-wave expressions (Sections 4-6), constants c and ħ are reinstated explicitly to maintain SI units. The Newtonian potential Φ carries dimensions [Φ] = m²·s⁻² and its dimensionless PN counterpart is U ≡ Φ/c². The scalar mass m_τ sets a Yukawa range λ_τ ≡ ħ/(m_τ c) (SI), which reduces to λ_τ = 1/m_τ in natural units. Hence [m_τ²] = m⁻² in natural units.
Author: Lemeshko, Andriy
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7083210983
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