The Tri-Outcome Redshift Model — A Structural Alternative to Expansion Cosmology
A structural alternative to velocity-based cosmology, integrating curvature, coherence, and observation.
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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 observed redshift decomposes into two primary structural contributions and their interaction.
2. The Three Redshift Mechanisms
-
PPC — Pattern Phase Curvature (curvature-driven):
\( z_{\mathrm{PPC}} \;\equiv\; \frac{\Delta\lambda}{\lambda_0} \;=\; \gamma\,\kappa(r) \;\approx\; \kappa\,r \)
with curvature density \( \kappa \), pathscale \( r \), and calibration factor \( \gamma \) (absorbing geometry/selection).
-
IPD — Inter-Pattern Drift (phase desynchronization):
\( z_{\mathrm{IPD}} \;=\; \frac{\Delta\phi}{\phi_0} \)
-
Combined Total (interaction in measurement):
\( z_{\mathrm{total}} \;=\; (1+z_{\mathrm{PPC}})(1+z_{\mathrm{IPD}}) - 1 \)
In TRM, recession kinematics are replaced by resonance-structural dynamics. The same observed $z$ can arise from curvature and drift without requiring metric expansion.
3. Redshift Comparison Table
| Concept | Classical Formula | PFT / TRM Formula |
|---|---|---|
| Redshift definition | \( z = (\lambda_{\mathrm{obs}}-\lambda_0)/\lambda_0 \) | Same — different cause (curvature & drift) |
| Velocity redshift | \( z \approx v/c \) | Not used |
| Relativistic redshift | \( z = \sqrt{\frac{1+v/c}{1-v/c}} - 1 \) | Not applicable |
| PPC | N/A | \( z_{\mathrm{PPC}} \approx \kappa\,r \) |
| IPD | N/A | \( z_{\mathrm{IPD}} = \Delta\phi/\phi_0 \) |
| Combined | N/A | \( z_{\mathrm{total}} = (1+z_{\mathrm{PPC}})(1+z_{\mathrm{IPD}})-1 \) |
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 & curvature.
- Fritz Zwicky (1898–1974): “Tired light.”
- Edwin Hubble (1889–1953): Redshift–distance relation.
- Halton Arp (1927–2013): Anomalous redshifts.
- Pattern Field Theory (James Johan Sebastian Allen): Resonance-structural TRM (PPC, IPD, combined).
5. Evaluation of TRM
Super-distant galaxies (z > 7)
- GR: Expansion velocity explains redshift.
- TRM A: Matches GR outcome via PPC-dominated pathscale.
- TRM B: Adds IPD (coherence drift) component.
- TRM C: Minor observer-frame skew (timing / calibration).
JWST lensing distortions
- GR: Often tuned via dark-matter maps.
- TRM B/C: Brightness anomalies as resonance drift & observer skew.
Planck CMB asymmetries
- GR: Tension with low-$\ell$ suppression / hemispherical asymmetry.
- TRM B: Coherence drift suppresses long-wave modes.
- TRM C: Observer skew amplifies residual anisotropies.
Bound systems (e.g., Andromeda)
- GR: $z \approx 0$ for bound systems (no expansion).
- TRM B: Small coherence drift detectable.
- TRM C: Tiny temporal skew possible.
6. Simulated Data Comparison
Note: Values below are simulated placeholders illustrating how TRM variants could be tabulated against GR; they are not fits to real datasets.
| 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 | Bound system drift/skew terms only |
| CMB anomaly | ~0.001 | ~0.001 | 0.0005–0.002 | 0.0002–0.0005 | Long-wave suppression / asymmetry handling |
7. Strengths and Future Work
Strengths
- Explains anomalies without invoking dark energy.
- Integrates redshift into PFT’s structural model (Φλ / π-axes).
- Predicts measurable deviations (IPD, observer-skew bands).
Future Needs
- Formalize equations for coherence decay and temporal skew with priors.
- Design blinded tests with JWST, ALMA, and CMB maps (consistent masks/beams).
- Quantify acceptance bands for TRM B and C vs. ΛCDM posteriors.
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-$z$ objects, CMB anomalies, lensing mismatches, and bound systems within a single coherence-based framework. Further work will refine the PPC/IPD interaction and deliver head-to-head fits alongside ΛCDM.