A Cosmological Model Based on a Pre-Geometric Phase and a Modified Gravity Phase: Towards a Unified Formulation with Holographic Initial Conditions, Cosmological Quantization, and a Five-Dimensional Bulk-Brane Structure

This paper presents the Newton-Mach (NM) model, a novel two-phase cosmological framework consisting of a pre-geometric phase and a subsequent modified-gravity (MG) phase. In the pre-geometric phase, standard general relativity is not assumed; instead, the expansion is driven by the fundamental kinematic law ṙ = -c²/r. This approach naturally avoids the standard infinite-density Big Bang singularity, replacing it with a well-defined boundary. When the comoving radius reaches the minimum effective length at the Planck epoch, the universe undergoes a holographic transition to the MG phase. By introducing a cosmological quantization ansatz based on the Bekenstein-Hawking entropy (N 727 degrees of freedom), the model calibrates to the local H₀ measurement (H₀ 73. 45 km/s/Mpc), offering a unique perspective on the Hubble tension. Furthermore, the NM framework proposes a purely geometric origin for the dark sector. This geometric dark matter profile successfully fits the M31 galaxy rotation curve (_² = 0. 35) without assuming undiscovered dark matter particles. The paper also explores the model's implications for early universe structure formation, providing a qualitative pathway for early massive galaxy seeding relevant to recent JWST observations. Finally, it proposes a geometric resolution to the black hole information paradox, suggesting that evaporation terminates at a stable Planck-hole remnant with a non-singular core.