R-layer Mode Theory XIII: Quantum Tension Cosmology and Observational Predictions

Volume XIII develops Quantum Tension Cosmology, a unified framework in which dark matter phenomenology, galactic dynamics, and cosmic acceleration emerge from a single quantum field of tension—the R-layer. This volume builds upon the structural foundations of earlier R-layer Mode Theory volumes and introduces a fully quantum description of the tension field, its equilibrium configurations, and its observational consequences. At galactic scales, the R-layer behaves as a quantum field governed by a Schrödinger–Poisson system with a uniquely selected Mexican-hat potential. This potential produces a Gaussian quantum tension core at the centers of galaxies, eliminating singularities and resolving the core–cusp problem without invoking particle dark matter. The resulting gravitational potential differs slightly from the black hole potential, leading to testable predictions for: the S2 stellar orbit around Sgr A*, the Event Horizon Telescope (EHT) ring radius, thickness, and central brightness. At cosmological scales, the homogeneous background tension Θ0(t) grows exponentially, driving late-time cosmic acceleration without a cosmological constant. Local gravitational potentials modulate the effective expansion rate, producing: the Hubble tension (local vs. global H0), directional dependence of H(z), anisotropic growth rate fσ8, large-scale anisotropies consistent with recent observations. The R-layer framework provides a decoration-free alternative to ΛCDM, requiring no particle dark matter, no cosmological constant, and no ad hoc feedback prescriptions. It yields a coherent explanation of: flat rotation curves, core-like galactic density profiles, cluster-scale mass deficits, CMB acoustic peak modifications, anisotropic cosmic expansion. Volume XIII concludes with a comprehensive list of falsifiable predictions across stellar, galactic, and cosmological observations, positioning Quantum Tension Cosmology as a unified and testable alternative to standard cosmology.