V2.97 - Scale-Dependent Lambda and w(z) Prediction
V2.97: Scale-Dependent Lambda and w(z) Prediction
Objective
Compute the effective dark energy equation of state w(z) predicted by field decoupling, producing a unique, testable prediction for Euclid/DESI/Rubin.
Background
As redshift increases, H(z) grows and the Hubble horizon shrinks. The mass-radius product mR_H = m/H(z) for each SM species changes. If a field’s mR_H drops below ~1, that field becomes active and contributes to delta_eff and alpha_eff. This would make R(z) = |delta_eff(z)|/(12*alpha_eff(z)) vary with z, producing w(z) != -1.
Results
Field Activation Thresholds
| Species | mass (eV) | mR_H(z=0) | z_activate |
|---|---|---|---|
| Photon | 0 | 0 | always active |
| Neutrinos | 0.05 | 3.3 x 10^31 | 1.5 x 10^21 |
| Electron | 5.1 x 10^5 | 3.4 x 10^38 | 7.2 x 10^25 |
| Up quark | 2.2 x 10^6 | 1.5 x 10^39 | 1.9 x 10^26 |
| W boson | 8.0 x 10^10 | 5.4 x 10^43 | 2.1 x 10^29 |
| Top quark | 1.7 x 10^11 | 1.2 x 10^44 | 3.5 x 10^29 |
No SM field activates below z ~ 10^21. The lightest massive particles (neutrinos) have mR_H ~ 10^31 at z = 0, requiring z ~ 10^21 for H(z) to reach the neutrino mass.
Lambda_eff(z) / Lambda_obs
Lambda_eff / Lambda_obs = 1.759 (constant to 10^{-16} precision across 0 < z < 10).
The field content is exactly constant across all observable redshifts. Only the photon contributes at every epoch.
w(z) Prediction
w_0 = -1.0000 (exact to 10^{-15})
w_a = 0.0000 (exact to 10^{-15})For both power-law and step-function suppression models.
Observational Comparison
| Survey | sigma(w_0) | sigma(w_a) | Detection significance |
|---|---|---|---|
| Euclid (2025-2031) | 0.02 | 0.1 | 0 (w=-1 exactly) |
| DESI Year 5 | 0.03 | 0.15 | 0 |
| Rubin LSST (Y10) | 0.03 | 0.12 | 0 |
| Euclid+DESI combined | 0.01 | 0.05 | 0 |
Robustness
- Neutrino mass: Even with m_nu = 0.3 eV (high), z_activate ~ 5 x 10^21. No effect.
- Omega_Lambda: w = -1 for all Omega_Lambda in [0.678, 0.692].
- Suppression model: Power-law and step function both give w = -1.
Key Finding
The framework predicts w = -1 exactly (a true cosmological constant) at all observable redshifts (z < 3). This is because:
- Only the photon is active at the Hubble scale (V2.93)
- The lightest massive field (neutrinos, m ~ 0.05 eV) has mR_H ~ 10^31
- No field transition occurs below z ~ 10^21
- R(z) = 1.205 = constant across all observable cosmology
Falsifiability
This is a sharp, parameter-free, falsifiable prediction: any detection of w != -1 by Euclid, DESI, or Rubin would rule out this framework. Conversely, continued confirmation of w = -1 is consistent with the framework but does not uniquely confirm it.
The prediction w = -1 is shared with a bare cosmological constant, but the framework additionally predicts the specific value Lambda/Lambda_obs = 1.76 (ratio R = 1.205 vs target Omega_Lambda = 0.685).
Runtime
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