The Ghost Complete Model: All Six ΛCDM Parameters Derived from One Constant and One Measurement

Description: The standard model of cosmology (ΛCDM) depends on six fitted parameters to describe a universe that is 95% unknown substances. This paper presents the Ghost Complete Model, which derives all six parameters from a single mathematical constant — the Feigenbaum spatial scaling constant α = 2.502907875, proved rigorously universal by Lanford (1982).

The dark matter density Ωch² = Ωbh²(α² − 1) = 0.1178, derived entirely from α and the Big Bang Nucleosynthesis baryon density, reproduces the CMB power spectrum across all six acoustic peaks at sub-1% precision. The critical first-to-second peak height ratio matches at 0.08%. The dark energy density ΩΛ = 1 − α²×Ωb = 0.691 is the geometric complement of the Feigenbaum matter density in a flat universe, matching ΛCDM's fitted 0.686 at 0.7%. The cosmological constant problem — the 10¹²⁰ discrepancy between quantum field theory and observation — dissolves because the question was malformed: ΩΛ is not vacuum energy but the complement of α²×Ωb.

Version 1.1 added the Cascade CAMB result: the CAMB Boltzmann solver's Fortran expansion engine was modified to use the Feigenbaum time emergence function τ(z) with steepness β = ln(δ) and NO cosmological constant in the code. This modified engine independently reproduces all six CMB peaks to within 0.5% position and 1.0% height, confirming that the expansion mechanics are replaced, not merely reparameterized. The transition redshift z_t = 0.50 is measured — not fitted — because the foundational theorem of nonlinear dynamics proves that transition points in cascade systems cannot be calculated from within the framework.

Version 1.2 completes the parameter set. The reionization optical depth is derived from the cascade geometric series: z_reion = δα/(α−1) = 7.776, where δα/(α−1) = δ × Σₙ₌₀^∞ α⁻ⁿ is the integrated cascade weight across all hierarchical levels (Hubble → clusters → galaxies → stars). Each level n contributes δ/αⁿ to the cumulative structure formation; the geometric sum converges to 7.776, matching the Planck 2018 midpoint z_reion = 7.7 at +0.99% and within 1σ. The standard optical depth integral with Ghost expansion history then gives τ_reion = 0.0572 (Planck: 0.054 ± 0.007, deviation +0.46σ). The scalar amplitude Aₛ = 2.113 × 10⁻⁹ follows from the CMB degeneracy constraint Aₛe⁻²τ, consistent with ΛCDM at +0.70%. Sensitivity analysis confirms the derivation is stable: ±1% in α shifts τ by 0.077σ; ±1% in δ shifts τ by 0.116σ. All six ΛCDM parameters are now cascade-derived.

The Ghost Complete Model matches ΛCDM to sub-1% across every major cosmological observable: the full CMB power spectrum (mean deviation 0.93%), the BAO sound horizon (147.68 vs 147.09 Mpc, 0.40%), the cosmic age (13.717 Gyr, 0.58%), and 1,580 Pantheon+ supernovae (χ²/dof = 0.461 vs 0.434). The open universe alternative (Ωk = 0.693, ΩΛ = 0) was tested against the CMB and ruled out (ℓ₁ = 404 vs 220). The universe is flat.

The model operates at two independently confirmed levels. Level 1: the ΛCDM parameter values are derived from α and confirmed through standard CAMB (sub-1%). Level 2: the cosmological constant is eliminated from the Friedmann equation and replaced by the Feigenbaum τ(z), confirmed through Cascade CAMB with modified Fortran (sub-1%). Together they constitute a complete replacement of ΛCDM.

Dark matter, dark energy, inflation, and the Hubble tension are identified as four projection artifacts of one error: interpreting a Feigenbaum cascade universe with a model that ignores the cascade. Six parameters. Zero fits. One constant. One measurement. α = 2.503. Proved in 1982. Applied in 2026.

KEYWORDS:

Feigenbaum constants, Ghost Complete Model, ΛCDM replacement, dark matter, dark energy, cosmological constant, cosmological constant problem, projection artifact, CMB power spectrum, acoustic peaks, BAO, Pantheon+, Hubble tension, Hubble constant, cascade age, Universal Cascade Law, fractal geometry, Navier-Stokes, zero fitted parameters, Planck 2018, SH0ES, JWST, too old galaxies, spectral index, reionization, optical depth, tau reionization, z_reion, scalar amplitude, primordial perturbations, CMB degeneracy, geometric series, cascade hierarchy, six parameters