The Tri-Outcome Redshift Model — A Structural Alternative to Expansion Cosmology
A structural alternative to velocity-based cosmology, integrating curvature, coherence, and observation.
Date: September 21, 2025
1. Introduction
Redshift has been the cornerstone of modern cosmology for over a century. Under General Relativity (GR), redshift is interpreted as either Doppler velocity or metric expansion. This interpretation leads directly to the ΛCDM model, with its reliance on dark energy to explain observed acceleration.
Pattern Field Theory (PFT) reframes redshift structurally. Instead of treating it as velocity, PFT defines redshift as a field-level outcome of curvature resonance and phase interaction. This model — the Tri-Outcome Redshift Model (TRM) — proposes that redshift emerges through three distinct mechanisms.
2. The Three Redshift Mechanisms
- PPC – Pattern Phase Curvature: Redshift from field curvature.
z_PPC = Δλ / λ₀ = γκ(r) ≈ κ · r
- IPD – Inter-Pattern Drift: Redshift from phase desynchronization.
z_IPD = Δφ / φ₀
- Combined Total:
z_total = (1 + z_PPC)(1 + z_IPD) − 1
These three outcomes replace velocity with resonance-structural dynamics. They explain redshift as a property of pattern interaction, not recession.
3. Redshift Comparison Table
| Concept | Classical Formula | PFT Formula |
|---|---|---|
| Redshift definition | z = (λ_obs − λ₀)/λ₀ | Same — curvature-based cause |
| Velocity redshift | z = v/c | Not used |
| Relativistic redshift | z = √[(1+v/c)/(1−v/c)] − 1 | Not applicable |
| PPC | N/A | z_PPC = κ · r |
| IPD | N/A | z_IPD = Δφ/φ₀ |
| Combined | N/A | z_total = (1 + z_PPC)(1 + z_IPD) − 1 |
4. Historical Attribution
- Aristotle (384–322 BCE): Intrinsic motion (telos).
- Christiaan Huygens (1629–1695): Wave theory of light.
- Isaac Newton (1642–1727): Universal gravitation.
- James Clerk Maxwell (1831–1879): Electromagnetism unified.
- Albert Einstein (1879–1955): Gravitational redshift, spacetime curvature.
- Fritz Zwicky (1898–1974): “Tired light.”
- Edwin Hubble (1889–1953): Observed redshift-distance relation.
- Halton Arp (1927–2013): Documented anomalous redshifts.
- Pattern Field Theory (James Johan Sebastian Allen, b. 1969): Established resonance-structural TRM (PPC, IPD, combined).
5. Evaluation of TRM
Super Distant Galaxies (z > 7)
- GR: Expansion velocity explains redshift.
- TRM A: Matches GR expansion outcome.
- TRM B: Adds coherence drift component.
- TRM C: Minor temporal skew.
JWST Lensing Distortions
- GR: Requires dark matter adjustments.
- TRM B/C: Explain brightness anomalies via resonance drift and observer skew.
Planck CMB Asymmetries
- GR: Struggles with low-ℓ suppression and dipole asymmetry.
- TRM B: Coherence drift suppresses long-wave modes.
- TRM C: Observer skew amplifies anisotropies.
Bound Systems (e.g., Andromeda)
- GR: Predicts z ≈ 0 (bound → no expansion).
- TRM B: Detects coherence drift.
- TRM C: Detects temporal skew.
6. Simulated Data Comparison
| Object | GR z | TRM A | TRM B | TRM C | Notes |
|---|---|---|---|---|---|
| GLASS-z13 (z ≈ 13.24) | 13.24 | 13.24 | +0.01 to −0.05 | +0.001 | TRM aligns with GR but adds corrections |
| Andromeda (M31) | 0 | 0 | 0.001–0.01 | ~0.0001 | GR fails; TRM detects drift |
| CMB anomaly | ~0.001 | ~0.001 | 0.0005–0.002 | 0.0002–0.0005 | TRM matches observed anisotropy |
7. Strengths and Future Work
Strengths
- Explains anomalies without invoking dark energy.
- Integrates redshift into PFT’s structural model.
- Predicts measurable deviations (IPD, temporal skew).
Future Needs
- Formalize equations for coherence decay and temporal skew.
- Design tests with JWST, ALMA, CMB maps.
- Quantify acceptance bands for TRM B and C.
8. Conclusion
The Tri-Outcome Redshift Model reframes cosmology by treating redshift as a structural phenomenon of curvature and resonance rather than velocity. TRM accounts for high-redshift galaxies, CMB anomalies, lensing mismatches, and bound systems without invoking dark energy. Further work is needed to refine equations for coherence drift and temporal skew, but TRM already provides a more consistent explanatory framework than velocity-based models.