Modified Cosmology from Mass-to-Horizon Relation: Observational Bounds

We constrain the class of modified cosmologies derived in Paper I [1] from a generalized mass-to-horizon relation (MHR) that enforces thermodynamic consistency between the Cai-Kim horizon temperature and generalized horizon entropies. The modified Friedmann equations depend on an entropy exponent m, an MHR coupling parameter gamma, and an entanglement-correction amplitude f B, with standard CDM recovered in the appropriate limit. Using Pantheon + /SH0ES Type Ia supernovae, cosmic chronometers, DESI DR2 baryon acoustic oscillations, and Planck 2018 CMB distance priors, we constrain eight physically motivated sub-cases via Markov chain Monte Carlo and compare models through the Bayesian log-evidence. The entropy exponent is tightly bounded, m-1 O(10-4) when the MHR coupling is fixed (gamma=1), relaxing to O(10-3) along the m - gamma degeneracy, excluding any macroscopically significant departure from standard horizon thermodynamics. Freeing the MHR coupling parameter or the entanglement amplitude raises the inferred Hubble constant to h 0.70 - 0.71, reducing the CMB-SH0ES tension from about 4 sigma to about 1.2 - 2.6 sigma, but no scenario fully resolves it within a flat universe. The Bayesian log-evidence nevertheless disfavors every extension relative to CDM in all dataset combinations (-16 Z-1): the improved fits obtained when the SH0ES calibration is included reflect an absorption of the Hubble tension by the additional parameters rather than genuine evidence for modified horizon entropy.