Constraining the Inchrononym Fractal Emergence Model (IFEM) with H(z) Observations

This work investigates the “Inchrononym Fractal Emergence Model” (IFEM) as an alternative cosmological framework that incorporates large-scale fractal corrections into the cosmic expansion history. By deriving the Hubble parameter H(z) from IFEM’s modified dynamics, we compare its predictions to those of the standard ΛCDM model and to a suite of current observational datasets, including Type Ia Supernovae (SNe Ia), Baryon Acoustic Oscillations (BAO), and cosmic chronometers. A statistical χ2 analysis is performed to constrain the single free parameter, ε, which quantifies the magnitude of the fractal correction. Our results indicate that the IFEM is consistent with current observational bounds. We show that the model smoothly reduces to the ΛCDM scenario in the limit where ε → 0, and that ε can be interpreted in terms of an effective fractal dimension, Df . We conclude that IFEM offers a testable and minimal extension to the standard cosmological model with a rich phenomenology.