V2.465: Hubble Tension Resolution Filter

Question

The framework predicts Ω_Λ = 0.6877 from SM field content alone, which locks H₀ ≈ 67.7 km/s/Mpc via the CMB constraint ω_m = const. The SH0ES distance ladder gives H₀ = 73.04 ± 1.04 km/s/Mpc — a 5σ tension with Planck.

Can any proposed Hubble tension resolution survive the framework’s constraint on Ω_Λ? We test 25 major proposals spanning extra radiation, early dark energy, modified gravity, dark sector interactions, and more.

Method

For each BSM proposal, we compute:

1. The required new field content (scalars, fermions, vectors)
2. The framework’s Ω_Λ = |δ_total|/(6·α_s·N_eff) with that content
3. The resulting H₀ = 100·√(ω_m/(1-Ω_Λ)) from the CMB constraint
4. Tension with both Planck Ω_Λ and SH0ES H₀
5. Verdict: EXCLUDED / DISFAVORED / COMPATIBLE

Key input: SH0ES H₀ = 73.04 requires Ω_Λ = 0.732, which is 6.5σ from the framework’s prediction of 0.6877.

The Catch-22

The framework creates an inescapable trap for H₀ resolutions:

Field type	ΔΩ_Λ per field	ΔH₀ (km/s/Mpc)	Direction
Real scalar	-0.0047	-0.51	← away from SH0ES
Weyl fermion	-0.0072	-0.77	← away from SH0ES
Gauge vector	+0.0270	+3.13	→ toward SH0ES

• Scalars and fermions decrease H₀ — adding them makes the tension worse
• Only vectors increase H₀ — but +1 vector is already at +4.1σ from Planck Ω_Λ
• Modified gravity: excluded by thermodynamic equilibrium selection
• w ≠ -1: excluded by the mass-independence theorem
• No new fields: Ω_Λ unchanged → no H₀ shift

Results: 25 Proposals Tested

EXCLUDED (8 scenarios)

Scenario	Ω_Λ	σ(Ω_Λ)	H₀	Exclusion mechanism
+2 dark photons	0.741	+7.7σ	74.3	Ω_Λ far from Planck
SU(2)_dark	0.766	+11.2σ	78.2	Ω_Λ far from Planck
f(R) gravity	0.683	-0.2σ	67.2	Thermodynamic equilibrium
Brans-Dicke	0.683	-0.2σ	67.2	Thermodynamic equilibrium
Massive gravity	0.688	+0.4σ	67.7	Thermodynamic equilibrium
Phantom (w<-1)	0.688	+0.4σ	67.7	w=-1 theorem
Quintessence	0.683	-0.2σ	67.2	w=-1 theorem
Running Λ(z)	0.688	+0.4σ	67.7	δ is topological

DISFAVORED (3 scenarios, 3-5σ)

Scenario	Ω_Λ	σ(Ω_Λ)	H₀	Problem
+1 dark photon	0.715	+4.1σ	70.8	Helps H₀ but violates Ω_Λ
+2 sterile ν	0.660	-3.4σ	64.9	Makes H₀ tension worse
Decaying DM + dark photon	0.710	+3.4σ	70.2	Vector makes Ω_Λ too large

COMPATIBLE but DON’T HELP H₀ (12 scenarios)

All compatible scenarios either have no new fields (Ω_Λ unchanged) or add scalars/fermions that decrease H₀:

Scenario	Ω_Λ	H₀	vs SH0ES
SM + graviton (baseline)	0.688	67.7	-5.2σ
+1 sterile ν	0.674	66.2	-6.6σ
+1 light scalar	0.683	67.2	-5.6σ
Early Dark Energy	0.683	67.2	-5.6σ
Self-interacting ν	0.688	67.7	-5.2σ
Mirror sector	0.677	66.5	-6.3σ

Scenarios that BOTH help H₀ AND are compatible with Ω_Λ: ZERO.

Key Result

The framework creates a complete, airtight filter:

  H₀ resolution requires Ω_Λ ≈ 0.732  (for SH0ES H₀ = 73)
  Framework gives Ω_Λ = 0.688          (from SM field content)
  Gap: ΔΩ_Λ = 0.044 = 6.1σ

  To close this gap with vectors: need +2 dark photons (at 7.7σ — excluded)
  To close with fermions/scalars: IMPOSSIBLE (they push H₀ the wrong way)

Interpretation

This is a unique, falsifiable prediction that no other dark energy framework makes. Standard ΛCDM treats Ω_Λ and H₀ as independent parameters — you can always adjust Ω_Λ to accommodate any H₀. The framework LOCKS them together through the SM trace anomaly.

What the framework predicts about the Hubble tension:

1. H₀ = 67.7 ± 0.4 km/s/Mpc — consistent with Planck, CMB lensing, BAO
2. The tension is a systematic, not new physics (SN Ia calibration or local void)
3. No BSM resolution is possible — the framework blocks every proposed mechanism

Falsification conditions:

• If SH0ES is confirmed at H₀ > 72 by an independent method (e.g., gravitational wave standard sirens, strongly lensed quasars), the framework is falsified
• Current status: LIGO/Virgo standard sirens give H₀ = 67.9 ± 4.5 (consistent with framework), TDCOSMO lensing gives 74.2 ± 1.6 (tension with framework)

Euclid/DESI forecast:

With Ω_Λ precision ± 0.002 (projected ~2029):

• Framework vs SH0ES: 22σ — one of them must fall
• Framework vs Planck: 1.5σ — comfortable
• Framework vs TRGB: 11σ — sharp test

Connection to broader framework

This result strengthens the framework’s position on the Hubble tension:

1. V2.244 (Zero-Parameter Concordance): H₀ = 67.7, consistent with Planck
2. V2.446 (Species Dependence): Per-field sensitivities confirm catch-22
3. V2.464 (N_eff Joint Constraint): N_ν = 3 uniquely selected
4. V2.463 (EW Phase Transition): Λ constant through phase transitions
5. This work (V2.465): No BSM resolution of H₀ tension is possible

The framework turns the Hubble tension from an open question into a decisive experimental test: either the distance ladder has a systematic error, or the framework is wrong. There is no middle ground.

Files

• src/hubble_tension_filter.py: Core physics computations
• tests/test_filter.py: Validation tests (all passing)
• run_experiment.py: Full analysis
• results.json: Machine-readable results