The Ultimate Black Hole as a Fractal Cosmological Model: A Proof of Concept with Supernova Data

We present the Ultimate Black Hole (UBH) cosmology as a fractal and entropic alternative to the ΛCDM paradigm. In this scenario, the Universe originates from the fragmentation of an Ultimate Black Hole, producing a self-similar distribution of smaller black holes and scale-dependent entropy growth. The resulting expansion law modifies the Hubble function in a testable way. Using the Pantheon Type Ia supernova dataset, we directly fit the UBH expansion model to the luminosity–distance relationship. For the high-redshift range (z = 500–1089.92), the modified Hubble function is calibrated against the ΛCDM prediction but using the same Hubble constant, H0 = 73 km s−1 Mpc−1. This unified value successfully reproduces both the local supernova observations and the CMB-derived expansion rate, thereby resolving the long-standing Hubble tension. For the 1048 supernovae, the UBH model achieves a lower χ2 and RMS scatter than ΛCDM, with reduced χ2 values close to unity. Standard robustness checks (clipping, jackknife, bootstrap, and MCMC calibration) confirm that the improvement is not due to outliers or calibration bias. Information criteria further favour UBH despite its larger parameter set, indicating genuine descriptive power. Our results establish UBH as a statistically competitive and physically motivated alternative to ΛCDM. By linking fractal entropy growth, Buchert’s backreaction, the Fractal Early Energy term, and the curvature window, the model offers a natural resolution of the entropy paradox in cyclic cosmology and a coherent reconciliation of early- and late-universe expansion. These findings motivate further tests with upcoming multi-probe datasets.