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A Tiered Multiverse Model: Cosmological Evolution, Tier-Dependent Constants, and Kerr Gateways

Publicado
Servidor
Preprints.org
DOI
10.20944/preprints202608.1209.v1

We formulate a covariant effective framework in which a universe’s vacuum occupies discrete stationary states of a scalar meta-field Φ, structurally analogous to atomic energy levels. Each tier n carries a gravitating vacuum energy density and tier-dependent dimensional scales, c_n=c_0 e^(-α(n-30) ) and ℏ_n=ℏ_0 e^(+α(n-30) ), with α≃0.01. Consequently, ℏ_n c_n and, under the stated reference convention, the fine-structure constant remain invariant. The empirically calibrated spectrum ρ_vac^((n) )=10^(64-(111/29)(n-1) ) GeV^4 connects an inflation-compatible scale at n=1 to the observed order of the present vacuum-energy density at n=30. Within a fixed tier, the standard radiation- and matter-dominated background evolution is recovered; global transitions allow energy exchange between a universe and the multiverse while conserving total multiverse energy-momentum. Inflation, reheating, and late-time acceleration are thereby interpreted within the same quantized vacuum structure. We distinguish these global transitions from localized quantum conversion of a particle mode between universe sectors. This process is represented by a two-state Hamiltonian containing a postulated localized Hermitian off-diagonal gateway operator. In Kerr geometry, frame dragging provides the local energy and angular-momentum exchange needed to satisfy the resonance condition. For the benchmark transition U_31→U_32, the adjacent-tier electron energy release is 9.9181 keV. For an a_*=0.998 black hole and inward 1MeV electrons that are flux-isotropic in the local zero-angular-momentum frame, the Kerr resonance condition selects 0.271284% of the incident population. For eligible particles, the exact transition probability is P_(31→32)=sin^2⁡Θ. Under the additional benchmark assumption that the coherent phase is unresolved and uniformly sampled, ⟨P⟩=1/2, giving a conditional phase-averaged transition fraction of 0.135642%. The absolute transition normalization remains dependent on the postulated off-diagonal amplitude Γ(τ). Exact propagation of 4,194,304 photons emitted at r_*=1.30188M, outside the horizon and inside the ergosphere, yields a 4.72% escape fraction for electron-rest-frame isotropic emission. A local 9.9181 keV photon becomes a broad X-ray component with mean observed energy 3.95 keV and central 90% interval 0.88–6.93 keV. For a 10M_⊙ black hole at 8 kpc accreting at 0.1M ̇_Edd, using this phase-averaged benchmark the photon flux is 6.99×10^(-9) B cm^(-2) s^(-1), where B=f_q b_γ T_los. The calculated spectrum and its correlations with black-hole spin, mass, accretion rate, and distance define a falsifiable X-ray test. The framework thus converts a tiered-multiverse hypothesis into a quantitative model with explicit cosmological dynamics, transition probabilities, and observable strong-gravity signatures.

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