Bayesian MCMC Fitting and Observational Predictions for Closed S3/Γ Topological FLRW Cosmology

This work builds a complete observational calibration pipeline based on the four-dimensional coupled domain dynamical framework established in the author’s prior ST theoretical series. Earlier derivations within this research programme yielded analytical topological power spectrum solutions, yet lacked quantitative empirical constraints from multi-band astronomical observations. This manuscript develops a modular Bayesian MCMC workflow to constrain signatures of compact multiply connected FLRW spacetimes. The analysis combines full Planck CMB temperature and polarisation measurements, DESI large-scale structure and Lyman-α forest spectroscopic data, high-redshift quasar absorption line samples, synthetic catalogues for Euclid, LSST and SPHEREx optical surveys, and gravitational wave templates for LISA. Five distinct physical models are defined for statistical comparison: standard flat ΛCDM, 3-torus compact geometry, classical single 3-sphere topology, quantum heat-kernel corrected single-sphere solutions, and a hybrid framework unifying topological geometry and modified gravity. Systematic uncertainties originating from seven astrophysical and instrumental sources are fully decomposed, with complete cross-covariance matrices computed for error propagation. Blind gradient signal tests and pure noise null simulations are implemented to quantify false detection probabilities. Joint multi-wavelength analysis yields mild statistical preference for closed geometries over the standard cosmological model. Combined spectroscopic surveys enable 5σ statistical detection of topological oscillatory spectral features, while two independent LISA gravitational wave pipelines provide cross-verification for predictions of compact cosmic manifolds. All posterior parameter sets satisfy three analytical limiting cases derived from the ST master equation. This establishes a consistent theoretical-to-observational research chain matching the astroparticle cosmology scope of The European Physical Journal C.