What question did this study set out to answer?

The aim is to propose a scalar-tensor effective theory that accounts for density-dependent kinetic screening impacting gravity.

April 20, 2026Open Access

Universal Force Relations: Density-Driven Kinetic Screening and Hierarchical Balance Collapse

Key Points

The aim is to propose a scalar-tensor effective theory that accounts for density-dependent kinetic screening impacting gravity.
Developed an effective theory with a pseudo-Goldstone mode based on density variations.
Derived a modified gravitational constant G_eff as a function of density.
Confirmed critical values and functional forms using geometric phase dynamics and a companion study.
Established a universal critical value I* = 0.071 through spatial structure analysis.
G_eff functional form was geometrically validated from z-axis phase dynamics.
Observed void peculiar velocity excess of +17.8%, relevant to future observational targets.

Abstract

Universal Force Relations: Density-Driven Kinetic Screening and Hierarchical Balance Collapse Abstract This paper proposes a scalar-tensor effective theory with density-dependent kinetic screening. The scalar degree of freedom is interpreted as a pseudo-Goldstone mode. The critical density ρ* ≈ 0. 026 ρcrit induces an environment-dependent modified gravity: Gₑff (ρ) = G 1 + α / (1 + ρ/ρ*) v3. 5 core addition: The functional form of Gₑff and the critical value I* = 0. 071 are geometrically derived from z-axis phase difference dynamics of space pixels. I* = 7. 1% is established as a necessary consequence of spatial structure — The Universal Critical Ratio (UCR). This value is independently confirmed in a companion paper (UCR Paper v1. 0, DOI: 10. 5281/zenodo. 19140461) via the 1/14 face partition of the Truncated Octahedron lattice with formal Lemma-Theorem structure and LSM simulation confirmation. Key Results - Gₑff functional form geometrically derived from pixel z-axis phase dynamics - I* = UCR = 0. 071 established as universal critical value - fσ₈ = 0. 440 (within observational range 0. 40–0. 45) - Void peculiar velocity excess +17. 8% (Euclid verification target) - All solar system and GW constraints satisfied Note Version: v3. 5 Author: Sonkichul (Son Kichul), Independent Researcher AI Research Assistance: Gemini, Claude (calculation verification) Contact: shionup@gmail. com -- v3. 6 (March 2026) - §3. 4 added: Relation to Horndeski and Extended Scalar-Tensor (EST) theories — EMWC formally positioned within EST framework - §3. 4. 1 added: UCR as kinetic screening threshold within EST framework - Energy, information, and pressure established as identical critical structure — all expressions of TO lattice geometry (UCR Paper v1. 1) - UCR Paper v1. 1 reference updated (DOI: 10. 5281/zenodo. 19158694) - References added: Horndeski (1974), Deffayet (2009), Kobayashi (2011), Zumalacárregui EMWC applies I* as a cosmological input via single-direction reference. 3. Parameter consistency audit All parameter values cross-checked across versions. Retired values (β₀=4. 1, β₀=3. 9, λ*=0. 111) documented with explicit retirement notices and replacement derivations. Version-by-version change history consolidated in §1. 2. 4. Appendix consolidation Intermediate appendices scattered mid-document in v3. 5–v4. 0 are unified at document end as App. A–G. The Management Section is retired from the main body as its content has been incorporated into the relevant sections. 5. Open Problems register (App. G) All open problems from v3. 5–v4. 1 consolidated with current status (✓ / SKETCH / OPEN) and missing piece identification. No new physics results in v4. 1. All theoretical content is preserved from v4. 0. --- v4. 2 (April 2026) Changes from v4. 1: 1. Supplementary Derivations companion document filed alongside this record (App. H–N): detailed step-by-step derivations for β₀=52/15, Hubble tension, α hierarchy, μ origin, MOND connection, EWI model, and TO-LSM simulation results. 2. Reference notes added to §10, §13, §14, §15, §16, §17 directing readers to corresponding supplementary appendices. 3. aₘax corrected: c×H★×2. 56 (empirical) → c×H★×12/5 = c×H★×2. 4 (exact geometric result from αₛ=5/7). 4. UCR v1. 9. 3 DOI confirmed and updated throughout: 10. 5281/zenodo. 19368813. No new physics results. All theoretical content preserved from v4. 1. --- v4. 3 (April 2026) — Integrated Edition Main paper: EMWCᵥ4₃complete. pdf (48 pages) = v4. 2 (40p) + New Sections S25-S31 (8p) New Sections: - S25: Nₘax geometric derivation Nₘax = (R/Lₚx) ² x exp (-Z₁2²) = 10⁵9. 6 Holographic surface DOF x phase entropy suppression Sₚhase = Z₁2² = 144 (independent phase modes) - S26: N₁d saturation and Hubble tension N₁d = Nₘax x alphaₒbs OmegaLambda = N₁d / Nₘax = alphaₒbs = 0. 679 New Dark energy = lattice saturation fraction CMB (complete): H₀ = 66. 7 km/s/Mpc Local (partial): H₀ = 70. 2 km/s/Mpc Hubble tension = saturation degree difference - S27: fgeom = F x Z₁0 / pi = 44. 56 Three independent derivations (0. 04% agreement): (1) Geometric: F x Z₁0 / pi (2) Time-scale: (tau₀/Dtₚx) / N₁d (3) Energy-phase: Eₚxₘax / Eₘin = N₁d x fgeom - S28: Omegab precision derivation Omegab = I* x sin (2 thetac) = 0. 049235 Error 0. 018% vs Planck 2018 (improved from 0. 54%) Uses only integers 13, 14, 27 - S29: Complete cosmic composition from alphaₒbs alone OmegaLambda = alphaₒbs = 0. 6786 (0. 9%) Omegab = I* x sin (2 thetac) = 0. 04924 (0. 018%) OmegaDM = (1-alphaₒbs) - Omegab = 0. 2722 (1. 6%) Sum = 1. 000000 (exact) - S30: lambda* = lambda₀ OP Resolved lambda* (elastic critical strain) = lambda₀ (expansion tension) Both = Deltaₑps x Z₁0 / (Z₄ x I*) = 0. 2139 Same physical constant, OP-lambda* closed - S31: Complete parameter chain v4. 3 Companion documents (same record): - UCREMWCSupplementaryᵥ2. pdf App O: Nₘax/N₁d/H₀ derivation chain App P: Cosmic composition from alphaₒbs App Q: fgeom three independent derivations - EMWCH0Derivation. pdf Complete H₀ derivation with all sub-terms - EMWCDESIDR2Comparison. pdf w (z) vs DESI DR2 BAO measurements - EMWCResearchNotes. pdf Working document: GammaF, Lₚx, open problems --- v4. 4 (April 2026) — Equalization Principle Integration Main paper: EMWCᵥ4₄complete. pdf (57 pages) = v4. 3 (48p) + v4. 4 New Sections (9p) Physical Foundation: All EMWC equations are now grounded in the Equalization Principle (UCR v2. 0, DOI 10. 5281/zenodo. 19414658): phiᵢ -> I* = 1/14 Excess -> expansion (H₀) Deficit -> gravity (Gₑff) Boundary -> elasticity (gravitational waves) New Sections (v4. 4): - Introduction addendum: Equalization Principle as physical basis. UCR v2. 0 DOI 10. 5281/zenodo. 19414658 referenced. - S4 update: Gₑff = equalization restoration force Gₑff (rho) physically derived from equalization deficit. alpha = alphaₒbs = present equalization capacity. rho* = equalization direction reversal density. - S10 update: beta correction CONFIRMED OP-6 resolved beta (z=0) = beta₀/ (1-lambda*) = 4. 412 (obs 4. 41, err 0. 05%) Physical: equalization loss compensation. lambda* = 3/14 = equalization cycle loss rate. - S11 update: gamma = 1/2 derived OP-16 direction confirmed etaₑff (rho) = eta₀ x sqrt (rho/rhoc) Physical: equalization geometric mean response. - S16 update: Hubble tension OP-Hubble direction confirmed vₒbs² = vL² x (1 + alphaₛ/Z₄) Physical: equalization capacity distributes across Z₄ directions. Non-equilibrium assumption replaced by equalization decomposition. - S18 update: Cosmic composition = equalization stages OmegaLambda = unused

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