V2.468 - GW Standard Siren Forecast
V2.468: GW Standard Siren Forecast
Question
The framework predicts H₀ = 67.7 km/s/Mpc. SH0ES gives 73.0 ± 1.0. Gravitational wave standard sirens — binary mergers where GW gives absolute distance and EM gives redshift — provide a COMPLETELY INDEPENDENT measurement. No Cepheids, no SN calibration, no CMB model.
When will standard sirens resolve the Hubble tension?
Method
Fisher matrix forecast for H₀ and w₀ precision from standard siren catalogs, using projected event rates and distance measurement accuracies for:
- LIGO/Virgo O4–O5 (current/near-term)
- LIGO A+ and Voyager upgrades (2028–2034)
- Einstein Telescope and Cosmic Explorer (2035+)
For each detector era, we compute σ(H₀) and the discrimination significance between the framework (67.7) and SH0ES (73.0).
Key Results
Luminosity distance predictions
| z | d_L (Framework) | d_L (SH0ES) | Fractional difference |
|---|---|---|---|
| 0.01 | 44.6 Mpc | 41.4 Mpc | +7.3% |
| 0.05 | 229.8 Mpc | 213.3 Mpc | +7.2% |
| 0.10 | 475.6 Mpc | 442.2 Mpc | +7.0% |
| 1.00 | 6785 Mpc | 6457 Mpc | +4.8% |
The framework predicts 5–7% larger distances at all redshifts — directly measurable with accumulating GW events.
Per-detector H₀ forecast
| Detector | N_events | σ(H₀) km/s/Mpc | FW vs SH0ES |
|---|---|---|---|
| LIGO O4 | 6 | 4.14 | 1.3σ |
| LIGO/KAGRA O5 | 25 | 1.62 | 2.8σ |
| LIGO A+ | 120 | 0.62 | 4.4σ |
| LIGO Voyager | 300 | 0.31 | 4.9σ |
| Einstein Tel. | 5000 | 0.05 | 5.1σ |
| ET + CE | 30000 | 0.01 | 5.2σ |
Discrimination timeline
| Milestone | Year | Detector era |
|---|---|---|
| 3σ | 2029 | LIGO A+ (120 events) |
| 5σ | 2035 | Einstein Telescope |
The discrimination saturates at ~5.2σ because the combined error is dominated by SH0ES’s own σ = 1.04. The “siren-only” significance is much higher (H₀/σ_siren = 67.7/0.05 → 1354σ at ET precision).
Dark energy equation of state
| Detector | σ(w₀) | Comparison |
|---|---|---|
| LIGO O5 | 2.48 | Not competitive |
| LIGO A+ | 0.43 | Marginal |
| Einstein Tel. | 0.015 | DESI-competitive |
| ET + CE | 0.003 | Definitive measurement |
ET will measure w₀ to ±0.015 from GW alone — comparable to DESI+CMB. This tests the framework’s w = -1 theorem independently of supernovae.
Why This Is the Decisive Test
Standard sirens have zero systematic overlap with the distance ladder:
Distance ladder: Cepheids → SN Ia calibration → H₀
CMB: θ_* + ΛCDM model fitting → H₀
Standard sirens: GW amplitude → d_L(z) → H₀ (pure GR)The framework DERIVES GR from entanglement thermodynamics. Standard sirens TEST GR at cosmological distances. If the GW-measured H₀ matches 67.7, both the framework and its foundation (GR at horizon scales) are confirmed.
Current status
GW170817: H₀ = 70 +12/-8 (consistent with both sides). O3 combined: H₀ = 68 +8/-6 (trending toward Planck/framework).
Interpretation
The framework makes two specific, falsifiable predictions for standard sirens:
- H₀ = 67.7 ± 0.4 km/s/Mpc — will be tested at 5σ by 2035
- w₀ = -1.000 — will be tested at σ(w₀) = 0.015 by ET
If both are confirmed:
- Framework receives the strongest possible independent confirmation
- The H₀ tension is identified as a distance ladder systematic
- The DESI w₀wₐ tension is identified as a SN systematic
- Λ from entanglement entropy becomes the leading explanation
If either fails:
- Framework is falsified by the cleanest possible probe
- No systematic excuse is available — GW distances are absolute
Connection to V2.465
V2.465 showed that no BSM physics can resolve the H₀ tension within the framework. This experiment shows WHEN this prediction will be tested independently. Together they form a complete falsification program:
- V2.465: If H₀ ≠ 67.7, no escape via BSM physics
- V2.468: Standard sirens will measure H₀ to ±0.3 by 2032
Files
src/siren_forecast.py: Core physics and Fisher forecaststests/test_siren.py: Validation tests (all passing)run_experiment.py: Full analysis with timelineresults.json: Machine-readable results