Redshift Evolution of the Fractal Cosmic Web Correction to the Hubble Constant

ABSTRACT

Nottale and Lehner found that the fractal structure of today's cosmic web produces a macroquantum potential that lifts the local Hubble rate by 7.5% at redshift zero, from the Planck to the SH0ES value. We extend this correction to all redshifts with a formation function tied to supercluster growth. We fit DESI DR1 and DR2 BAO data separately, each with Pantheon+ supernovae and full covariances. With a flat prior on the early‐universe Hubble constant, both releases place the transition redshift inside the expected range of 0.3 to 0.7, and DR2 fits slightly better than . A Planck prior, which clashes with BAO, pushes it toward zero in both releases. Anchoring DR2 to the CMB acoustic scale sharpens the transition redshift to , but the local expansion rate is then 67.7 km/s/Mpc, so the correction alone does not remove the Hubble tension. We also compare exponential and power‐law formation histories, show how the potential acts on matter and derive its perturbation. Growth‐rate data fit every model once is free, and we give predictions for the next DESI release.