BAO and the Full-Shape Matter Power Spectrum P(k) and E-Mode Lensing in the MMA–DMF Cosmology Late-Time Tests of the Dark-Matter-Free MMA–DMF Cosmology

The Modified Matter Acceleration – Dark Matter Free (MMA–DMF) framework proposes a baryon-only cosmology in which the phenomena usually attributed to cold dark matter (CDM) are reproduced by a combination of effective early-time fluids in the background and a scale- and time-dependent scalar coupling that enhances baryonic gravity at late times. In a companion paper (Paper I), MMA–DMF was shown to reproduce the acoustic peaks of the cosmic microwave background (CMB), reduce the sound horizon to rs ≃ 137.2 Mpc and resolve the Hubble tension with H0 ≃ 72 km s−1 Mpc−1 while remaining consistent with Planck and ACT temperature and polarisation spectra. In this work we perform an exhaustive late-time validation of MMA–DMF using real data for baryon acoustic oscillations (BAO), the full-shape matter power spectrum, redshift-space distortions (RSD), the one-dimensional Lyman-α power spectrum and E-mode lensing from both cosmic shear and CMB lensing. We employ a strictly rs-independent (rs-free) BAO pipeline, a modified Boltzmann solver based on class with no CDM species, Markov chain Monte Carlo sampling with emcee, and dedicated leakage-projection and covariance-whitening steps for the power-spectrum and Lyman-α analyses. We find that MMA–DMF provides an excellent description of current BAO and Lyman-α constraints, fits 18 measurements of fσ8(z) with χ2/dof ≃ 1.02, reproduces the Lyman-α flux power spectrum with χ2/dof ≃ 1.05, and matches cosmic-shear and CMB-lensing data with S8 ≃ 0.772±0.015 and AL ≃ 1.03±0.05. The global late-time goodness of fit, χ2/dof ≃ 1.02, is comparable to that of ΛCDM. Information criteria reveal no decisive statistical preference for either paradigm once differences in model complexity are taken into account. This demonstrates that a dark-matter-free cosmology with scalar-mediated growth remains a phenomenologically viable description of BAO, full-shape clustering and E-mode lensing.