V2.423 - Lambda Through Cosmic Phase Transitions
V2.423: Lambda Through Cosmic Phase Transitions
Date: 2026-03-11 Group: 7-cosmological-prediction Status: COMPLETE — unique prediction derived and verified
Objective
Derive and verify the framework’s most distinctive prediction about the cosmological constant problem: Λ is exactly unchanged through every phase transition in cosmic history. This prediction is:
- (a) Unique: No other approach makes it. ΛCDM requires 10^55 fine-tuning, quintessence predicts varying w(z), string landscape gives no specific Λ.
- (b) Testable: w(z) = -1 exactly at all redshifts (DESI DR3, Euclid 2027).
- (c) Surprising: Resolves the cosmological constant problem structurally — vacuum energy simply does not source Λ.
Core Argument
The framework gives Λ = |δ|/(2αL²_H), where:
- δ = trace anomaly (a₂ Seeley-DeWitt coefficient): topological, mass-independent, protected by Adler-Bardeen non-renormalization
- α = area-law coefficient = N_eff × α_s: UV quantity, mass-independent
Phase transitions change masses and vacuum condensates. They do not change the UV field content that determines δ and α. Therefore ΔΛ = 0 exactly.
Results
1. Goldstone Equivalence for Trace Anomaly
The EW phase transition converts 3 massless scalars (Goldstone bosons) into the longitudinal modes of W±, Z. The trace anomaly must be preserved:
| Quantity | Value | Status |
|---|---|---|
| δ(massless vector) + δ(scalar) | -31/45 + (-1/90) = -7/10 | |
| δ(massive vector) | -7/10 | EXACT MATCH ✓ |
| EW sector δ before (4s + 12v) | -374/45 | |
| EW sector δ after (1s + 9v + 3V) | -374/45 | EXACT MATCH ✓ |
2. N_eff Conservation
| Phase | Breakdown | N_eff |
|---|---|---|
| Before EW | 4×1(scalars) + 12×2(vectors) | 28 |
| After EW | 1×1(Higgs) + 9×2(massless) + 3×3(massive) | 28 |
N_eff is conserved because each eaten scalar (1 DOF) becomes a longitudinal polarization (1 DOF), and each massive vector has 3 polarizations = 2 transverse + 1 longitudinal.
3. Constancy Across All Cosmic Epochs
| Epoch | T range | N_eff | δ_total | R |
|---|---|---|---|---|
| Unbroken EW | T >> 100 GeV | 128 | -149/12 | 0.6877 |
| Broken EW | 1–100 GeV | 128 | -149/12 | 0.6877 |
| Post-QCD | 1 MeV – 200 MeV | 128 | -149/12 | 0.6877 |
| Post-ν decoupling | 0.3 eV – 1 MeV | 128 | -149/12 | 0.6877 |
| Today | 2.725 K | 128 | -149/12 | 0.6877 |
R = 0.6877 at ALL epochs, constant to machine precision. Tension with Ω_Λ,obs = 0.6847 ± 0.0073: +0.4σ (excellent agreement).
4. Vacuum Energy Shifts in Standard QFT (That We Don’t Need)
| Transition | ΔV (GeV⁴) | ΔV/Λ_obs | Framework |
|---|---|---|---|
| Electroweak | 2.4 × 10⁸ | 10^55 | ΔΛ = 0 |
| QCD confinement | 1.6 × 10⁻³ | 10^44 | ΔΛ = 0 |
| Neutrino mass | 6.3 × 10⁻⁴² | 10^5 | ΔΛ = 0 |
5. Fine-Tuning Eliminated
| Contribution | ΔV/Λ_obs | Standard QFT | Framework |
|---|---|---|---|
| Planck-scale gravity | 10^120 | 1 in 10^120 | NONE |
| EW Higgs condensate | 10^55 | 1 in 10^55 | NONE |
| Top quark loop | 10^53 | 1 in 10^53 | NONE |
| QCD condensate | 10^44 | 1 in 10^44 | NONE |
Standard QFT worst-case: 1 part in 10^120. Framework: ZERO.
The Unique Prediction
ΔΛ = 0 through all cosmic phase transitions.
This is not “w = -1” (which ΛCDM also gets via fine-tuning). This is a structural prediction: Λ depends on trace anomaly and area-law coefficient, both UV quantities that are invariant under symmetry breaking and confinement. The enormous vacuum energy shifts (10^55 × Λ_obs at EW, 10^44 at QCD) predicted by standard QFT simply do not appear in the formula Λ = |δ|/(2αL²_H).
How to Test
-
w(z) = -1 exactly at all z — DESI DR3 (2027), Euclid (2028)
- Quintessence predicts w varies: orthogonal test
- DESI DR1 shows 2.5σ tension (supernova-driven, not BAO-driven)
-
Ω_Λ(z) = const across epochs — CMB + BAO + SNe cross-correlation
- Any epoch-dependent Ω_Λ would falsify
-
No dark-energy scalar field — DESI, LSST, future 21cm
What Would Falsify
- w ≠ -1 confirmed at > 5σ with consistent supernova samples
- Ω_Λ varying with cosmic epoch
- Discovery of a light vector boson (dark photon, > 4σ per V2.422)
Contrast with Other Approaches
| Approach | Λ formula | Phase transition behavior | Fine-tuning |
|---|---|---|---|
| This framework | δ | /(2αL²_H) | |
| ΛCDM | Λ_bare + Σ ΔV_i | Requires cancellation | 10^120 |
| Quintessence | V(φ) | w varies, ΔΛ ≠ 0 | moderate |
| String landscape | 10^500 vacua | no prediction | anthropic |
| LQG | no Λ formula | N/A | N/A |
Honest Assessment
Strengths:
- The Goldstone equivalence for trace anomaly is exact and verifiable (Fraction arithmetic)
- N_eff conservation through EW breaking is a clean algebraic identity
- Eliminates 10^120 fine-tuning problem structurally, not by adjustment
- Prediction w = -1 at all z is maximally falsifiable
Weaknesses:
- The argument that “QCD confinement doesn’t change δ” relies on UV-completeness of the trace anomaly. Strictly, δ is the a₂ heat kernel coefficient computed in the UV theory (quarks + gluons), not the IR effective theory (pions). This is standard in QFT but deserves a more rigorous treatment showing that the entanglement entropy at the cosmological horizon sees the UV fields even at low T.
- The claim “vacuum energy doesn’t source Λ” is the framework’s most radical assertion. It is self-consistent (Λ_bare = 0 derived in V2.250, V2.256) but not independently confirmed experimentally.
- DESI DR1 tension (2.5σ with w₀w_a parametrization) remains a live threat.
What this experiment adds:
- First explicit verification that Goldstone equivalence preserves δ through EW breaking
- Quantitative fine-tuning comparison (10^120 vs 0)
- Clear falsification criteria connecting to near-future experiments
Files
src/phase_transitions.py— Core module: epoch builder, Goldstone verification, vacuum energy shiftstests/test_phase_transitions.py— 11 tests, all passingrun_experiment.py— Full 8-part analysis pipelineresults.json— Machine-readable output