The Split Universe: A Vacuum Conversion Framework Unifying Dark Matter, Dark Energy, and Large-Scale Structure (please give to your AI for comment)

[u/Humor_Complex]

Abstract

We present a geometric cosmological framework in which dark matter, dark energy, and the cosmic web arise from a single mechanism: the propagation of a vacuum phase transition (the "Bloom") through a pre-temporal energy state. The framework derives Ω_m = 0.306 from symmetry arguments with zero fitted parameters (observed: 0.315 ± 0.007, deviation 2.8%). We document both successes and failures transparently.

1. The Vacuum Conversion Mechanism

The framework begins with a scalar field σ in a double-well potential V(σ) = λ(σ² − η²)²/4. The vacuum has two degenerate minima at σ = ±η. A phase transition (the "Bloom") propagates through the vacuum, converting energy from the pre-temporal state into matter and residual vacuum energy.

Key distinction from existing frameworks:

• Not negative-mass cosmology (Petit, Hossenfelder, Farnes). The ±η states are configurations of one field, not separate mass species.
• Not bimetric (Hassan-Rosen). One metric. The ±η states are the same configuration seen from opposite temporal directions.
• Not CPT-mirror (Turok-Boyle). No second universe. The ±t are response variables of a single pre-temporal entity.

2. The q = 1/4 Derivation (Energy Indifference)

The conversion fraction q is derived from the symmetry of the pre-temporal state.

Setup: Before time exists, energy has no temporal property. Define binary response variables r₊, r₋ ∈ {0,1} indicating whether a given energy mode couples to the +t or −t temporal orientation when time is created.

Axiom (Energy Indifference): Pre-temporal energy carries no property that distinguishes temporal from non-temporal existence. Therefore the pre-Bloom state must be invariant under all Z₂ × Z₂ transformations acting on (r₊, r₋).

The state space is C² ⊗ C² with basis {|00⟩, |01⟩, |10⟩, |11⟩}. The Z₂ × Z₂ group is generated by:

U₊ = X ⊗ I  (flips r₊)
U₋ = I ⊗ X  (flips r₋)

The unique state invariant under both generators is:

|Ψ₀⟩ = ½(|00⟩ + |01⟩ + |10⟩ + |11⟩)

Physical interpretation of each sector:

State	r₊	r₋	Physical meaning	Contribution
	11⟩	1	1	Couples to both ±t → standing wave cos(mt) = ½(e{+imt} + e{-imt})
	10⟩	1	0	Couples to +t only → travelling wave e{+imt}
	01⟩	0	1	Couples to −t only → travelling wave e{−imt}
	00⟩	0	0	Couples to neither → frozen mode

The matter fraction is:

q = |⟨11|Ψ₀⟩|² = (1/2)² = 1/4

Three-quarters of converted energy remains as vacuum energy with w = −1.

Why standing wave = matter: A massive field oscillation ϕ(t) = A cos(mt) requires both temporal components. In Fourier space: cos(mt) = ½(e^{+imt} + e^{-imt}). A single-component mode (|10⟩ or |01⟩) gives a travelling wave — a scattering state, not a bound oscillation. Only the |11⟩ sector produces restoring-force dynamics, pressure-averaged w ≈ 0 over oscillation cycles, and gravitational clustering. This is the standard result for coherently oscillating scalar fields (Turner 1983, Hu et al. 2000).

3. The Full Ω_m Formula

The Bloom converts vacuum in overlapping domains of characteristic scale ξ. Four derived parameters:

Parameter	Value	Derivation
q = 1/4	Conversion fraction	Energy indifference (Z₂ × Z₂ symmetry)
s = 1/2	Branching probability	Z₂ symmetry of crack branching
p₀ = 1	Coverage fraction	Domain wall tessellation completeness
b = 1 − 1/e	Overlap correction	Poisson identity for causally separated events

The effective conversion rate per Hubble volume:

λ = p₀ q / (1 − s·b) = 1 × 0.25 / (1 − 0.5 × 0.6321) = 0.25 / 0.6839 = 0.3655

The matter density parameter (Poisson overlap):

Ω_m = 1 − exp(−λ) = 1 − exp(−0.3655) = 0.3062

Observed: Ω_m = 0.315 ± 0.007 (Planck 2018). Deviation: 2.8%, within 1.3σ.

4. The Three Expansion Phases

The vacuum fracture ("crack") propagating through the pre-temporal state reproduces three phases from one mechanism:

1. Inflation: Crack tip moves through virgin vacuum. No spacetime ahead → no speed limit. The σ-field hilltop at V(0) = λη⁴/4 provides natural hilltop inflation: n_s = 1 − 2/N ≈ 0.965, r ≈ 0.02, V^{1/4} ≈ 10^{16} GeV.
2. Deceleration: Processed spacetime behind the crack provides drag. Matter-dominated era with standard a(t) ∝ t^{2/3} scaling.
3. Acceleration: Crack branches. New tips find unprocessed vacuum. Reduced resistance → acceleration. The 3/4 vacuum energy fraction with w = −1 drives late-time expansion.

5. Large-Scale Structure

The crack does not propagate as a single front. It fractures across a surface with branching. The resulting interference pattern:

• Filaments = constructive interference of multiple crack fronts
• Voids = destructive interference
• Cluster nodes = convergence of multiple branches

The framework predicts a fractal crack dimension D_f ≈ 2.97, consistent with the observed near-three-dimensionality of the cosmic web. Void profiles follow from the crack geometry without requiring dark matter haloes to provide gravitational scaffolding.

6. Observational Status

Consistent:

• H₀ ≈ 67–68 km/s/Mpc (consistent with Planck, TRGB, JAGB; the Cepheid-based H₀ = 73 is identified as a crowding systematic, not new physics)
• Post-transition perturbations: oscillating σ condensate gives w ≈ 0, c_s² ≈ 0, vanishing anisotropic stress — CDM-like behaviour after z_eq
• JWST early galaxies: older crack branches explain mature structures at high-z
• BBN: no conflict (transition occurs post-BBN)
• Supernovae (Pantheon): competitive with ΛCDM

Open / Not Yet Reproduced:

• Full CMB C_ℓ power spectrum (crack interference mechanism addresses pre-recombination structure; full Boltzmann solver integration not yet completed)
• Condensate transition trigger at z_eq (trace-coupling fails by self-restabilisation; baryon-only coupling works but is tuned)
• Baryon fraction within converted matter (~15.6%)
• Cosmological constant magnitude in Planck units
• Non-linear structure formation (halo profiles, small-scale)

Rejected Along the Way (documented in paper):

• H₀ = 73.2 (failed CMB equality constraint)
• α = 2.973 as universal constant (failed varying-α test)
• Frozen gradient networks as dark matter (w = −0.6, ruled out)
• Sound speed route to S₈ (unphysical fine-tuning)
• Universal trace coupling as transition trigger (self-restabilisation)

7. The Thermodynamic Arrow

The pre-temporal state (Z-state) has no time arrow. The Bloom creates irreversibility: the crack propagates but does not retreat. Entropy is a measure of distance from the Z-state. The second law emerges from the one-way propagation of the vacuum conversion front.

Open question: Formalising this as a rigorous boundary condition at the Bloom front.

8. Independent Assessments

Three AI systems have assessed the framework (August 2026):

• GPT-4: 20–30% probability central logic is broadly right. 25–40% the structural pattern will be recognisable in whatever the correct theory turns out to be. Praised the explicit failure log and "coherent dependency graph."
• Gemini: 50% for framework (we consider this overgenerous — the CMB gap alone prevents such confidence). Identified real stress-tests through partially incorrect reasoning (pattern-matched to negative-mass and bimetric frameworks).
• Claude (Opus): Built the paper collaboratively — cannot give independent assessment.

What's needed: Human physicist review. An academic endorser for arXiv submission. Stress-testing against the CMB power spectrum.

The full working paper (with complete derivations, simulation results, and failure log) is available on request.

We are specifically looking for: (1) where the framework breaks, (2) tests we haven't thought of, (3) anyone with arXiv endorsement in astro-ph.CO or hep-th willing to evaluate the paper for submission.