The Evolution of the Hubble Parameter in EBIKK-β Cosmology: From a Regularized Big Bang to Late-Time Acceleration

We present a comprehensive analysis of the Hubble parameter H within the EBIKK-β framework, a quantum-corrected cosmologicalmodel that resolves the initial singularity through β-regularization.The model predicts:• A maximum finite value Hmax ∼ β−1/2 at the Big Bang (β ∼10−56 m4), avoiding Planck-scale divergences• Inflationary dynamics driven by entropic terms Tent ln det G,with H decaying as H(t) ≈ H0(1 − t/β1/2)• Late-time agreement with ΛCDM (H0 ≈ 67.4 km/s/Mpc),but with testable deviations in the CMB (low-ℓ power suppression) and primordial gravitational waves (spectral dip at f ∼β−1/8)The theory offers a unified description of cosmic expansion froma non-singular beginning to the present epoch, with signatures detectable by CMB-S4 and LISA.