A Pre-Structural Substrate Framework for Cosmology and Boltzmann Verification

Abstract

Timestamp: Saturday, August 22, 2026 — 20:02:41 (UTC+2) Abstract: Persistent cosmological anomalies, including early mature massive galaxies revealed by the James Webb Space Telescope (JWST) at z > 10, the persistent 5σ Hubble expansion tension (H₀), and four decades of null direct-detection results in particle dark matter searches, suggest foundational limitations in standard ΛCDM cosmology. We develop a comprehensive cosmological framework based on a pre-structural Layer 0 substrate (Primal Energy, PE) that is non-particulate and devoid of structural mass, electric charge, frequency, or quantum spin. The substrate acts as a pre-manifest scalar Hamiltonian density (E²_substrate) undergoing non-kinematic density compounding until reaching a critical mass-energy equivalence threshold (ρ_critical ≈ mc² / V). At criticality, the system undergoes a constructive phase transition (Midnight Phase Transition) that projects substrate tension into the relativistic 4-momentum dispersion relation, bifurcating via Monadic Inversion into discrete invariant rest mass (mc²)² and spatial momentum/radiation (pc)². We embed this mechanism in a 5D warped geometry with long-range metric tendrils, deriving the complete variational action, 5D field equations, Israel junction boundary conditions at the 4D hypersurface, explicit Kaluza-Klein dimensional reduction, Goldberger-Wise radion stabilization, and the full system of linear cosmological perturbation equations across conformal Newtonian and synchronous gauges. We prove covariant energy-momentum conservation (∇^μ T_μν = 0), absence of Ostrogradsky ghosts, subluminal sound speed (0 ≤ c_s² ≤ 1), Null Energy Condition (NEC) satisfaction, and strict BBN concordance (ΔN_eff = 0). Implementing the derived Bessel Green's transfer kernel into a live multiprocessing CLASS Boltzmann engine with parallel Bayesian Markov Chain Monte Carlo (MCMC) sampling against empirical Planck 2018 PR3 data resolves the Cosmic Microwave Background (CMB) low-ℓ quadrupole deficit (A_PE = 0.3673 ± 0.0445, ℓ_decay = 14.20 ± 2.27) and provides a +33.3% early matter power boost at z = 10 (A_FFD = 0.2760 ± 0.0394) via the Formed-Flew-Dragged (FFD) mechanism verified via 256³ particle-mesh halo simulations while preserving exact acoustic peak concordance (ℓ ≥ 500), cosmic shear stability (S₈ = 0.8347), and distance concordance across Pantheon+ Supernovae and DESI 2024 BAO (r_d = 147.41 Mpc). Accounting for off-diagonal geometric mode-coupling and cosmic variance (f_sky = 0.58), the full covariance matrix fit yields Δχ²_cov = −11.77, ΔAIC = −7.77, and ΔBIC = −6.97, decisively demonstrating empirical preference over standard ΛCDM. Multimessenger observational signatures, including a prompt gravitational wave burst and synchronized neutrino light-curve step in core-collapse supernovae, are formulated as empirical tests.