V2.331 - Dark Matter Constraints from the Cosmological Constant
V2.331: Dark Matter Constraints from the Cosmological Constant
The Novel Idea
No other framework derives dark matter constraints from the cosmological constant. In this framework, Ω_Λ = R = |δ_total|/(6·α_total), where δ and α depend on the field content. Any dark matter particle that contributes to entanglement entropy at the cosmological horizon shifts R. Since Ω_Λ is measured to ~1% (Planck), this constrains what DM can and cannot be.
This connects two of the biggest open problems in physics — the cosmological constant problem and the dark matter problem — through a single mechanism.
Method
Starting from the SM+graviton(n=10) baseline (R = 0.6877, +0.4σ), compute R for 22 dark matter candidates spanning scalars, fermions, vectors, and composites. Determine per-field sensitivities, maximum allowed fields, and hidden sector windows.
Key Results
Per-field sensitivity (from SM+grav baseline)
| Field type | δR per field | Planck σ/field | Euclid σ/field |
|---|---|---|---|
| Scalar | −0.0047 | −0.65σ | −2.4σ |
| Weyl | −0.0073 | −1.0σ | −3.6σ |
| Vector | +0.0270 | +3.7σ | +13.5σ |
Maximum allowed light fields (within 2σ)
| Field type | Planck | Euclid |
|---|---|---|
| Scalar | 3 | 1 |
| Weyl | 2 | 0 |
| Vector | 0 | 0 |
DM candidate exclusion summary
At Planck precision (σ = 0.0073):
- Allowed: 12/22 candidates
- Marginal (2-3σ): 2 (Wino, inert doublet)
- Excluded (>3σ): 8 (all vectors, Higgsino, fermion quintuplet, string axiverse ≥10)
At Euclid precision (σ = 0.002):
- Allowed: 6/22 candidates
- Marginal (2-3σ): 2
- Excluded (>3σ): 14
Strongest predictions
-
Dark photon DM: EXCLUDED at +4.1σ (Planck). A single dark vector boson overshoots Ω_Λ. If dark photon DM is discovered, the framework is falsified.
-
String axiverse: >3 ALPs excluded at 2σ (Planck), >1 at Euclid. This constrains string compactifications that predict many light axions.
-
Wino/Higgsino DM: marginal → excluded at Euclid. If Euclid confirms Ω_Λ to 0.002 AND direct detection finds Wino or Higgsino DM, the framework is in strong tension.
-
PBH DM: fully consistent. Primordial black holes add no new fields, leaving R unchanged. PBH is the framework’s “preferred” DM candidate.
-
Scalar singlet DM: allowed. The simplest DM model (1 real scalar) shifts R by only −0.2σ. This is the framework’s “minimal dark matter.”
Mass Independence
From V2.330: δ is mass-independent (Adler-Bardeen theorem). α is mass-dependent, but ALL DM candidates have m ≪ M_Pl (even “superheavy” DM at 10^16 eV has m/M_Pl ~ 10^{-13}). The constraint applies equally across 40+ orders of magnitude in DM mass, from fuzzy DM (10^{-22} eV) to superheavy DM (10^{16} eV).
Hidden Sector Windows
Scanning over (n_s, n_f, n_v) ∈ [0,30]×[0,20]×[0,10], we find 1254 hidden sector configurations within 3σ of Ω_Λ. Most are small (≤15 total fields). Pure scalar sectors can have up to ~25 fields; any sector with vectors is tightly constrained.
Comparison with Traditional DM Constraints
| Constraint | What it constrains | Mass range |
|---|---|---|
| Direct detection (LZ) | σ_SI (coupling) | ~1 GeV – 10 TeV |
| Collider (LHC) | Mass | > ~100 GeV |
| Indirect (Fermi) | ⟨σv⟩ (annihilation) | ~10 GeV – 100 TeV |
| Relic density (Planck) | m × coupling | Model-dependent |
| This framework (Ω_Λ) | Field content (spin × number) | ALL masses |
The Λ constraint is orthogonal to all traditional constraints. It is the only one that works for ALL DM masses and constrains field type/number rather than couplings.
Honest Assessment
Strengths:
- Genuinely novel: no other framework derives DM constraints from Λ
- Mass-independent: applies to all DM candidates from 10^{-22} to 10^{16} eV
- Falsifiable: dark photon discovery would falsify; PBH detection consistent
- Tightens with Euclid (3.5× improvement in σ)
Weaknesses:
- Assumes ALL light fields contribute fully to horizon entanglement entropy
- The “contributes/doesn’t contribute” boundary at m ~ M_Pl is a crude estimate; the actual transition is smooth (V2.330 showed α decreases gradually with mass)
- For DM candidates that might decouple from the thermal bath (sterile neutrinos, axions), whether they contribute to the cosmological horizon EE is debatable
- These constraints assume the SM+graviton(n=10) baseline is correct; the baseline itself has a theoretical uncertainty (V2.328: n_grav = 10.6 ± 1.4)
Key question: Do non-thermal relics (axions, sterile neutrinos) contribute to horizon entanglement entropy? The entanglement entropy is a UV property of the vacuum state, not a thermal property, so the answer should be yes — but this deserves a dedicated analysis.
Impact
This experiment establishes a new class of constraints: dark matter from the cosmological constant. The strongest prediction — exclusion of dark vector bosons at >4σ — is immediately testable (dark photon searches are ongoing). The string axiverse constraint (≤3 light ALPs) is relevant to string phenomenology. Euclid (2028) will sharpen all constraints by ~3.5×, excluding Wino and Higgsino DM if Ω_Λ is confirmed at current central value.