Observational Validation of the AMDCF Spacetime Memory Framework via CAMB CMB Simulations

In this study, we rigorously test the Adaptive Memory-Driven Coupling Framework (AMDCF) against high-precision cosmological data by integrating it with the standard CAMB (Code for Anisotropies in the Microwave Background) library. Using the Planck 2018 cosmological parameters, we compute the baseline ΛCDM power spectrum and apply a non-Markovian Memory Tensor (M_μν) correction. The results demonstrate that the AMDCF model successfully reproduces the primary acoustic peaks of the CMB, while predicting subtle sinusoidal oscillations in the residuals. These oscillatory deviations remain strictly within the ±2% observational error bounds of the Planck satellite. By treating the primordial plasma as a memory-driven viscous medium, the AMDCF framework offers a deterministic, geometric alternative to exotic dark matter, fully respecting the Bianchi identities and energy conservation. Testable Predictions for Future Cosmological Surveys While the current AMDCF model remains fully consistent with the Planck 2018 data (remaining within the ±2% observational error bounds), it yields a highly specific and testable prediction. The non-Markovian memory term introduces a subtle sinusoidal oscillation in the CMB power spectrum residuals (M_{\mu\nu}(\ell) \propto \sin(\ell/75)). This "memory footprint" is currently masked by the instrumental noise of the Planck satellite. However, we predict that next-generation high-precision CMB experiments, such as CMB-S4, Simons Observatory, or LiteBIRD, will possess the sensitivity required to detect these specific oscillatory deviations in the residuals. Furthermore, the 3D parameter space analysis demonstrates that the amplitude of the first acoustic peak (\ell \approx 220) is modulated by the memory coupling parameter. Future precision data will allow cosmologists to directly measure the accumulated historical memory of the universe (M_{\mu\nu}), providing a definitive observational test for the existence of non-Markovian spacetime.