The Ghost of α: Dark Matter Density as a Feigenbaum Projection Artifact at 0.99% Precision

Description: The ratio of total matter density to baryonic matter density in the ΛCDM concordance model satisfies √(Ωm/Ωb) = 2.528, matching the Feigenbaum spatial scaling constant α = 2.503 at 0.99% precision. The total matter density is α² times the baryon density. This paper demonstrates it is a consequence of fitting a non-cascade model (ΛCDM) to a cascade universe: the dark matter density is a projection artifact whose magnitude is determined by the Feigenbaum spatial scaling constant.

Version 1.1 extends the original density ratio result with three major confirmations. First, the value Ωch²_eff = Ωb(α² − 1) = 0.1169 — derived from the Feigenbaum constant, not fitted to CMB data — reproduces the CMB power spectrum across all six acoustic peaks at sub-1.3% precision. The first-to-second peak height ratio, the primary evidence for dark matter at cosmological scales, matches at 0.13%. This is the eighth independent domain in which α appears at sub-2% precision.

Second, Model E — using α²×Ωb for matter, τ(z) with β = ln(δ) for acceleration, and one measured transition redshift — passes five independent cosmological tests simultaneously: 1,580 Pantheon+ supernovae (χ²/dof = 0.461 vs ΛCDM 0.434), six CMB peak heights (sub-1.3%), BAO sound horizon (147.92 vs 147.09 Mpc, 0.57% deviation), cosmic age (13.899 Gyr), and mean CMB spectral deviation (1.73% across ℓ = 30–2500). The transition redshift z_t = 1.430 converges to within 1.3% of Paper 9's independent determination, confirming internal consistency.

Third, the cosmic age of 13.899 Gyr — derived from the cascade expansion history without ΛCDM input — breaks the circularity that prevented a first-principles Hubble constant. H₀ = ln(α)/t_age = 64.5 km/s/Mpc falls below both Planck (67.4) and SH0ES (73.0), identifying the Hubble tension as a fourth projection artifact alongside dark matter, dark energy, and inflation. All four arise from interpreting a Feigenbaum cascade universe with a model that ignores the cascade.

Dark matter is not a substance. It is the ghost of α — the residual of fitting a non-cascade model to a cascade universe. The ghost is now confirmed across the density ratio (0.99%), the CMB power spectrum (six peaks at sub-1.3%), the BAO scale (0.57%), and the cosmic age (0.8%).

Keywords: Feigenbaum constants, dark matter, projection artifact, ΛCDM, cosmological parameters, JWST, galaxy formation, Hubble tension, Universal Cascade Law, fractal geometry, baryon density, spatial scaling, too old galaxies, expansion history