Lyman-α Forest and Baryon Acoustic Oscillations: Achieving ΛCDM-Level Constraints Without Dark Matter in the MMA-DMF20 Framework

We present observational constraints on cosmological distances derived from Lyman-α (Lyα) forest anisotropy and Baryon Acoustic Oscillations (BAO) within the Modified Metric Approach with Dynamic Mass Function (MMA-DMF20) framework—a model that operates without dark matter at any cosmic epoch. The MMA-DMF20 paradigm introduces an effective background component X, realizable as a light scalar field or fluid with large sound speed (cₛ² ≈ 1), that modifies the expansion history H (a) prior to the baryon drag epoch while preserving the standard General Relativity (GR) Euler equation and cosmic microwave background (CMB) acoustic constraints. Critically, X is not a dark matter species: it does not cluster (cₛ² ≈ 1 prevents structure formation), it decays completely into radiation near recombination, and it contributes nothing to late-time dynamics. Through rₛ-free BAO mapping and Alcock–Paczynski geometric tests applied to BOSS DR12 and eBOSS DR16 Lyα data, we demonstrate that MMA-DMF20 achieves parity with ΛCDM predictions at the level of distance measurements. Information criteria (AIC, BIC) on combined Lyα χ² summaries show no statistical preference for ΛCDM over the zero-dark-matter hypothesis when geometric constraints are prioritized. Our findings suggest that, within the explicitly tested scope of BAO geometry and Lyα distance anisotropy, dark matter is not required to match observational data—offering a minimalist alternative rooted in modified gravitational dynamics that satisfies Occam’s razor while maintaining consistency with large-scale structure observations.