V2.756 - Framework-Allowed Gravitational Wave Window at LISA
V2.756: Framework-Allowed Gravitational Wave Window at LISA
Summary
The entanglement framework constrains the particle spectrum through Omega_Lambda = |delta|/(6 alpha_s N_eff). This creates a three-way prediction unique to this approach: particle physics <-> dark energy <-> gravitational waves.
No other dark energy framework constrains LISA observations. In LCDM, Lambda is a free parameter that says nothing about BSM physics or gravitational waves.
Key Result: The Allowed GW Window
Previous claim (V2.611): “no EW gravitational waves from LISA.”
This is incomplete. The framework allows scalar extensions of the SM that can produce a first-order electroweak phase transition (FOPT), generating GW in the LISA band. But it excludes gauge-driven FOPT, which produces the strongest signals.
The framework predicts a specific allowed window for LISA:
| Property | Allowed (scalar FOPT) | Forbidden (gauge FOPT) |
|---|---|---|
| Omega_GW h^2 | <= 4 x 10^-9 | 10^-7 to 10^-6 |
| Transition strength alpha | < 0.5 | 0.1 to 20 |
| Signal character | Weak, marginal SNR | Strong, unambiguous |
| Source | Singlet/doublet scalar | Dark photon/SU(N) |
The gap is a factor ~100 in amplitude. LISA can distinguish these.
BSM Model Catalog
| Model | Omega_Lambda | sigma | Allowed | FOPT | Peak GW h^2 | LISA SNR |
|---|---|---|---|---|---|---|
| SM + graviton | 0.6877 | +0.4 | YES | No (crossover) | --- | --- |
| xSM (+1 scalar) | 0.6830 | -0.2 | YES | Yes | 4.1e-9 | 18 |
| Complex singlet (+2 scalars) | 0.6784 | -0.9 | YES | Yes | 5.1e-10 | 19 |
| Triplet scalar (+3 scalars) | 0.6738 | -1.5 | YES | Yes | 1.1e-11 | 28 |
| 2HDM (+4 scalars) | 0.6693 | -2.1 | marginal | Yes | 2.0e-10 | 50 |
| +1 Majorana sterile nu | 0.6805 | -0.6 | YES | No | --- | --- |
| Dirac neutrinos (+3 Weyl) | 0.6667 | -2.5 | NO | No | --- | --- |
| Dark U(1) (+1 vector +1 scalar) | 0.7099 | +3.4 | NO | Yes | 2.4e-7 | 293 |
| Dark SU(2) (+3 vectors +4 scalars) | 0.7464 | +8.4 | NO | Yes | 5.6e-7 | 154 |
| Dark SU(3) (+8 vectors +1 scalar) | 0.8771 | +26.4 | NO | Yes | 2.0e-6 | 67 |
| MSSM | 0.4673 | -29.8 | NO | Yes | 2.8e-12 | 5 |
| 4th generation (+15 Weyl) | 0.5983 | -11.8 | NO | Yes | 4.4e-14 | 0 |
GW amplitudes are best-case (maximum alpha, minimum beta/H from literature parameter scans).
The Physics: Why This Works
1. Field content determines Omega_Lambda
Delta (trace anomaly) is exact for each spin:
- Scalar: -1/90 (small)
- Weyl fermion: -11/180 (moderate)
- Vector: -31/45 (large — dominates)
- Graviton: -61/45
Adding a vector boson shifts Omega_Lambda upward by +3.75 sigma per field — because |delta_vector|/n_comp = (31/45)/2 = 0.344 is much larger than the average |delta|/n_comp ~ 0.097 for the SM. Vectors contribute disproportionately to delta relative to their alpha contribution.
2. Vector extensions drive strong FOPT
Dark gauge sectors (dark photon, dark SU(2), dark SU(3)) naturally produce strong first-order phase transitions via gauge symmetry breaking. These transitions are characterized by:
- Large latent heat (alpha > 0.1)
- Slow nucleation (beta/H < 200)
- Strong GW signals (Omega_GW h^2 ~ 10^-7 to 10^-6)
3. The framework excludes exactly these models
The framework kills every model with extra gauge bosons:
- Dark U(1): +3.4 sigma (excluded)
- Dark SU(2): +8.4 sigma (excluded)
- Dark SU(3): +26 sigma (killed)
This eliminates the strongest GW sources from the EW era.
4. Scalar extensions survive but produce weak signals
Scalar extensions (xSM, complex singlet, triplet) shift Omega_Lambda downward (improving the prediction) and can produce FOPT, but:
- Scalar-driven FOPT is generically weaker (alpha < 0.5)
- Nucleation is faster (beta/H > 10)
- GW amplitude is 100x lower than gauge-driven FOPT
Vacuum Energy Decoupling
The framework dissolves the cosmological constant fine-tuning problem at each SM phase transition:
| Transition | Vacuum energy shift | Fine-tuning (LCDM) | Framework |
|---|---|---|---|
| Electroweak (T ~ 160 GeV) | (88 GeV)^4 = 6.0e43 eV^4 | 54 digits | 0 digits |
| QCD (T ~ 150 MeV) | (235 MeV)^4 = 3.1e33 eV^4 | 44 digits | 0 digits |
| Chiral symmetry | (90 MeV)^4 = 6.6e31 eV^4 | 42 digits | 0 digits |
| Total | 140 digits | 0 digits |
The trace anomaly delta is topological (Wess-Zumino protected). It does not change with mass or temperature. Omega_Lambda = 0.6877 at the Planck epoch, through EW, through QCD, through BBN, through CMB, to today — identically.
Correction to V2.611
V2.611 stated: “LISA prediction: NO gravitational waves from the EW-era phase transition. BSM models that produce detectable GWs (2HDM, MSSM) are independently excluded by the Lambda constraint.”
This is incorrect on two counts:
- The xSM (+1 singlet scalar, sigma = -0.2) is firmly ALLOWED and CAN produce FOPT with Omega_GW h^2 ~ 10^-9, detectable by LISA at SNR ~ 18.
- The 2HDM (+4 scalars, sigma = -2.1) is only marginally excluded. At 3-sigma threshold it would be allowed.
The correct prediction is not “no GW” but “only weak, scalar-driven GW.” A strong gauge-driven signal is the smoking gun for falsification.
Falsification Criteria for LISA (2035+)
| LISA observation | Framework verdict |
|---|---|
| No EW-era GW signal | CONSISTENT (SM crossover baseline) |
| Weak signal (Omega_GW h^2 ~ 10^-13 to 10^-9) | CONSISTENT (scalar extension) |
| Strong signal (Omega_GW h^2 > 10^-8) | FALSIFIED (requires gauge extension) |
| Signal spectrum matches MSSM | FALSIFIED (SUSY killed at >30 sigma) |
| Signal consistent with dark SU(N) confinement | FALSIFIED (gauge sector excluded) |
What Makes This Unique
-
No other dark energy framework constrains LISA. In LCDM, Lambda is free; it says nothing about particle physics or GW. In quintessence, the scalar potential is unrelated to GW. In the string landscape, Lambda is random.
-
Three-way connection. This experiment links:
- Particle physics (field content) via delta counting
- Dark energy (Omega_Lambda) via the framework formula
- Gravitational waves (LISA) via EW phase transition dynamics
A single number (the trace anomaly) connects all three observatories.
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The prediction is sharp. The allowed GW window spans ~10^-13 to ~10^-9. The forbidden region starts at ~10^-7. The factor-100 gap is resolvable by LISA.
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Both outcomes are informative:
- No signal: SM field content confirmed (consistent, not distinctive)
- Weak signal: scalar BSM confirmed, framework survives
- Strong signal: framework falsified, AND we learn about dark gauge sectors
Caveats
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The GW spectrum calculation uses simplified formulas (Caprini et al. 2020). Full lattice simulations for each BSM model would shift amplitudes by O(1) factors but not change the order-of-magnitude prediction.
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The 2HDM is at -2.1 sigma — just outside the 2-sigma threshold. Using a 3-sigma threshold, 2HDM enters the allowed window (its GW is similar to complex singlet, so the maximum allowed amplitude stays at ~10^-9).
-
The LISA sensitivity curve is approximate. The actual power-law integrated sensitivity depends on astrophysical foregrounds (WD binaries), which could raise the effective threshold in the mHz band.
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Phase transition parameters (alpha, beta/H) are literature benchmarks. Specific BSM coupling values within each model class can give a wide range of GW amplitudes. The “best case” numbers are optimistic but physically achievable.
Tests
29/29 tests pass:
- Framework predictions: SM baseline, xSM allowed, dark photon excluded, MSSM killed
- GW spectrum: positivity, peak location, scaling with alpha and beta/H
- LISA sensitivity: in-band finite, out-of-band infinite, correct order
- Vacuum energy: EW fine-tuning ~54 digits, framework zero
- Temperature independence: R constant across all cosmic epochs
- Catalog consistency: all models analyzable, allowed window exists
Bottom Line
The entanglement framework predicts that if LISA detects gravitational waves from the electroweak era, the signal must be weak (Omega_GW h^2 < 4 x 10^-9) and sourced by a scalar extension of the SM. A strong, gauge-driven signal — the kind most GW theorists are hoping for — would falsify the framework.
This is a concrete, testable prediction connecting dark energy physics to gravitational wave astronomy. No other approach makes it.