Growth & Lensing Validation of the MMA-DMF Model: A Baryons-Only Framework Tested Against RSD fσ8, Shear/CMB-Lensing, High-k Lyα P1D, and DESI 2024+ Observations

We present a comprehensive validation of the Modified Matter Dynamics with Dynamic Mass Function (MMA-DMF) cosmological model, a baryons-only framework that reproduces late-time structure formation without invoking cold dark matter (CDM). The model employs a scale-dependent effective gravitational strength µ(a, k) driven by a deterministic scalar field to mimic dark matter’s gravitational effects. We test the model against multiple independent observational probes spanning redshifts 0 ≤ z ≤ 4: redshift-space distortions (RSD) measuring fσ8, cosmic shear and S8 constraints, CMB lensing κκ band-powers from Planck PR3 and ACT DR6, high-k Lyman-α forest power spectra P1D, and the latest DESI 2024+ BAO measurements including the Lyα GCcomb constraint. Our best-fit MMA-DMF45b configuration achieves χ2/dof = 1.019 ± 0.082 across 18 real-data tests with 147 degrees of freedom, demonstrating that carefully constructed modified-gravity scenarios remain observationally viable. The model naturally produces slightly suppressed late-time growth relative to ΛCDM (Sth 8 = 0.772 ± 0.015), potentially alleviating the S8 tension. We provide detailed statistical analyses, parameter constraints, and robustness tests. By Occam’s razor, while dark matter remains the standard paradigm, our results indicate that alternative gravitational frameworks deserve continued investigation as upcoming surveys like Euclid and LSST will provide definitive discrimination between these scenarios.