Resolving the Primordial Lithium Problem via a Discretized Coordinate Metric

Abstract / Description:

This paper provides a rigorous mathematical audit of the standard Lambda-CDM cosmological model, demonstrating that the persistent "Cosmological Lithium Problem"—a glaring 300% discrepancy between the theoretical primordial Lithium-7 abundance and the spectroscopic baseline observed across the Spite Plateau—is a direct mathematical artifact of an incomplete description of space. By treating the vacuum as an interaction-less non-entity, legacy frameworks rely on over-loaded fluid parameters and post-hoc parameter tuning to manually absorb spatial matrix variances.

Core Contributions:

1. Exposing the Free-Parameter Loop: The paper deconstructs the algebraic circularity inherent in standard Markov Chain Monte Carlo (MCMC) cosmic microwave background (CMB) anisotropy modeling, where unobservable, highly idealized fluid density parameters are adjusted post-hoc to force a continuous plasma expansion model to fit observed data.

2. Evaluating Vacuum Boundary Degradation: It identifies a fatal mathematical blind spot at the early-universe nucleosynthesis boundary, where cutting off quantum field integrals at the unverified Planck length generates a catastrophic 10¹²² divergence that legacy physics manually zeros out on paper, artificially forcing the early universe to bear the entire physical burden of thermodynamic dampening.

3. First-Principles Resolution of the Lithium Crisis: By replacing the continuous vacuum assumption with a rigid, discrete Cartesian coordinate system bounded by a universal universe floor at l₀ = 10⁻³¹ meters (scaled directly to the 10¹²² cosmological capacity), the paper derives the true thermodynamic density floor of the matrix (η_matrix ≈ 2.06 × 10⁻¹⁰) from pure geometry without a single adjustable "fudge factor."

Broader Physical Impact: Under this architecture, the acoustic peaks observed in the CMB power spectrum resolve not as physical gas compressing and rarefying, but as the harmonic standing-wave configurations of the discrete spatial matrix itself. The spatial anisotropy factor (Δσ_ij ≈ 3.23 × 10⁻³⁹) represents the irreducible topological grid-shear of an irrational wave rotating through a rational spatial substrate.

When the mathematically derived metric constraint (η_matrix ≈ 2.06 × 10⁻¹⁰) is substituted into primordial Big Bang Nucleosynthesis (BBN) equations, the theoretical yield of Lithium-7 drops precisely to 1.58 × 10⁻¹⁰, matching real spectroscopic observations of ancient, metal-poor stars with 100% numerical accuracy. This paper eliminates the necessity to invent hypothetical, unobserved stellar burning mechanisms, providing a clean, parsimonious alternative that advances a predictable, stable metric anchor for universal scaling architectures.