Curvature Memory Cosmology — Ver.6 Emergent Late-Time Cosmic Acceleration from Geometric Curvature Memory

This work presents Version 6 of the Curvature Memory Cosmology framework, an effective macroscopic cosmological model in which late-time cosmic acceleration emerges from geometric curvature memory rather than from an explicit dark-energy component. The model introduces a dimensionless curvature-memory function D(a), motivated by the nonlinear dynamics of modified f(R)-type curvature evolution, and uses it to construct an effective expansion relation for the Hubble function H(z). Cosmic acceleration is interpreted as an emergent large-scale geometric phenomenon associated with the cumulative evolution of curvature and the macroscopic response of the spacetime substrate. In contrast to purely conceptual formulations, this version develops a quantitative observational framework. The model is tested against combined cosmological datasets, including Type Ia supernovae (Pantheon+SH0ES), BAO measurements, structure-growth data through fσ8(z), and CMB distance priors. The same underlying expansion dynamics are used consistently for all observables, avoiding independent parametrizations for each dataset. The results indicate that the curvature-memory model remains compatible with the standard early-time matter-dominated cosmological evolution, provides statistically comparable and in some cases slightly improved agreement relative to ΛCDM within the combined analysis, and remains consistent with low-redshift structure-growth constraints. AIC/BIC comparisons suggest statistical preference within the present dataset, although this does not constitute a definitive exclusion of the ΛCDM paradigm. Additional numerical consistency tests examine early-time recovery, parameter stability, sound-horizon behavior, deceleration-parameter evolution, statefinder diagnostics, and spherical-collapse consistency. The work also discusses the limitations of the present effective formulation and identifies future directions, including full perturbation theory, CMB likelihood analysis, Boltzmann-code implementation, and a dedicated SH0ES–Planck split-fit study of the Hubble tension. The present version should be understood as a phenomenological and observationally testable macroscopic framework, not as a complete microscopic theory of gravity. It represents a quantitative development of the earlier Elastic Vacuum / Infinite Dimensionless Vacuum cosmological program.