Observational Constraints on Ramanujan–Bose Interval Cosmology: Full MCMC Analysis with Pantheon+, DESI DR1/DR2, Planck, and Growth Rate Data

We present a comprehensive observational confrontation of the Ramanujan–BoseInterval Cosmology (RBIC) framework using full Markov chain Monte Carlo(MCMC) analysis. Our dataset comprises 1624 Type Ia supernovae from thePantheon+SH0ES compilation with the complete 1701 × 1701 statistical plussystematic covariance matrix, 13 BAO measurements from DESI DR1, updatedconstraints from DESI DR2 [1], 3 Planck 2018 CMB distance priors, and 18independent fσ8 growth rate measurements—yielding N = 1658 real datapoints with zero mock data.Wepromotethe condensate mass ratio Mratio ≡ M∗/ℏH0 fromafixedparameterto a free MCMCparameter, obtaining joint posteriors on {H0, Ωm, α0, Mratio}.The BRB running coupling is constrained to α0 < 0.003 at 95% confidence(consistent with the profile-likelihood result of our earlier analysis), while Mratiois constrained to Mratio > 340 at 95% CL, directly confirming the theoreticalexpectation M∗/ℏH0 ≫ 200 from first principles. The Paper 2/3 fiducial valueα0 =0.019 is excluded at 7.3σ by the full covariance analysis.The RBICframeworksurvives: gravity decoupling (497.6 km2 s−2 Mpc−2, 62.4%),the geometric interval term (74.2 km2 s−2 Mpc−2, 9.3%), and the BRB contribution (13.6 km2s−2Mpc−2, 1.7%) account for 73.4% of the observed Hubbletension. The growth rate data yields S8 = 0.791 ± 0.018, a 0.8% suppression relative to ΛCDM, consistent with KiDS/DES weak-lensing constraints andproviding the first RBIC prediction of the S8 parameter.Real CANDELS galaxy size evolution data [2] confirm βmw = 0.728 andBuchert vorticity 7.8 km2 s−2 Mpc−2. All falsifiable predictions remain valid; theweff(z = 0.5) bifurcation between Path A (−0.97) and Path B (−0.999) willbe resolved by DESI Year-3.