Cosmic Microwave Background without Expansion

Abstract

The cosmic microwave background is often taken as definitive evidence for universal expansion. No static framework has yet reproduced its exact blackbody spectrum under known physical conditions. This study extends the companion paper, Redshift without Expansion , by applying a frequency-independent redshift mechanism within a Liouville formulation. The kinetic redshift operator preserves a perfect Planck spectrum, maintains μ = 0 , and yields T ∝ K − 1 with an identical temperature-redshift relation T ( z ) = T 0 ( 1 + z ) consistent with measurements from COBE and FIRAS. Photon number and energy densities evolve as n ˙ γ = − 3 H eff n γ and ρ ˙ γ = − 4 H eff ρ γ , where H eff = K ˙ / K represents an effective Hubble parameter without metric expansion. The result establishes an observational degeneracy between kinetic redshift and geometric expansion while predicting a measurable secular temperature drift T ˙ / T = − H eff ≈ − 2.3 × 10 − 18 s − 1 . The framework provides a static, falsifiable pathway for examining the cosmic microwave background without reliance on expanding-space assumptions. The redshift kernel emerges from scalar field relaxation dynamics Φ ¨ + Γ ( Φ ˙ − Φ ˙ ∞ ) = 0 , with coupling H eff = g Φ ˙ reproducing the required CMB temperature scaling to illustrative ~0.1% precision for the example parameter set, and predicting H eff ( z = 1100 ) ≈ 281 H 0 , testable via high-redshift measurements.