The Phenomenological Holket Theory: A Single-Parameter Cosmological Model Resolving the Hubble and BAO Tensions

This manuscript introduces the Phenomenological Holket Theory (HolketH) — a single-parameter phenomenological modification of the Friedmann equation — and an early-universe extension HolketQ. The model is governed by the dimensionless parameter ε=e/2472≈0.011476. HolketH modifies the late-time expansion through a multiplicative logarithmic correction to H(z), producing a local Hubble constant H0≃72.38 km s−1 Mpc−1 while preserving the CMB acoustic angle under a rescaling of distances. HolketQ is a Gaussian early dark energy (EDE) extension that reduces the sound horizon to satisfy BAO constraints; the EDE amplitude is fixed by the BAO condition to fEDE=0.0621. The combined HolketH+HolketQ framework addresses the Hubble tension, improves BAO fits relative to ΛCDM, and predicts a positive shift in the effective number of relativistic species ΔNeff in the indicative range [0.2, 0.5]. The manuscript presents background and proxy perturbation results (CLASS HolketB2), discusses observational consequences for S8 and growth observables, and lists falsifiable near-term predictions for DESI, Euclid, ELT-HIRES, and CMB-S4.