CMB Peaks and Early-Time Constraints on the MMA–DMF Model (Planck, ACT and Simons)

This paper presents an extensive and technical assessment of early-time observational constraints on the cosmological model Modified Matter Acceleration–Dark Matter Free (MMA–DMF). In response to the persistent tensions that challenge the standard ΛCDM paradigm — notably the 5σ Hubble tension and the continued null results of direct detection experiments for Cold Dark Matter (CDM) particles — the MMA–DMF model proposes a unified cosmological history that relies exclusively on baryonic matter and a scalar-mediated modification of gravity. The scope of this document is strictly focused on the “Primordial Universe” sector (z > 1000), where we test the model against high-precision data from the Planck 2018 release (temperature and polarization), the Atacama Cosmology Telescope (ACT) DR6, and Baryon Acoustic Oscillation (BAO) measurements. We detail the theoretical infrastructure of the model, which introduces a transient radiation “EARLY Bump” (parametrized by fₚeak = 0. 36 and p = 3) and an effective decaying X-component designed to mimic the gravitational potential wells of CDM prior to recombination. Crucially, the analysis shows that the model, under strict “No-Slip” conditions (Φ = Ψ) and General-Relativistic lensing kernels (Σ = 1) during the CMB epoch, reproduces the acoustic scale θ* with 0. 01% precision relative to Planck observations. Numerical results indicate that the model naturally accommodates a local Hubble constant of H₀ ≃ 72 km s⁻¹ Mpc⁻¹ through a geometric modification of the sound horizon (rₛ ≃ 137 Mpc). We conclude, invoking the principle of parsimony, that the MMA–DMF framework provides a phenomenologically viable early-time alternative that fits current data without an explicit CDM component, with the Hubble constant emerging geometrically.