Sink-Mediated Cosmological Nucleation and Evolutionary Dual-Population Black Hole Dynamics: A Unified Resolution to Structure Formation, Rotation Curves, and Late-Time Acceleration

This paper presents a unified, evolutionary cosmology in which black holes act as fundamental gravitational architects of the cosmos. By establishing a dual-population demographic of metric-linked natural sinks (continuously generated in step with the expanding background scale factor) and local stellar-collapse sinks (born from stellar core evolution), this framework addresses both the fine-tuning constraints of single-epoch primordial black hole scenarios and the timescale challenges of early galaxy formation. Through sink-mediated nucleation, we derive a modified effective Jeans mass from first principles, demonstrating that primordial black holes act as the required gravitational catalysts for primordial gas to overcome thermal pressure and collapse into early structures prior to reionization. Formalized through an inhomogeneous Swiss-cheese geometry embedded with regular interior black-hole metrics (Hayward metric) and Buchert spatial averaging, the framework mathematically bridges microscopic sink accretion to macroscopic dynamics. On solar-system scales, standard Einstein-Maxwell dynamics and Birkhoff's theorem apply, preserving standard post-Newtonian local gravity. On galactic and cosmological scales, the cumulative network of sink-induced advective inflows and spatial inhomogeneities generates an effective backreaction term Q_D that flattens galaxy rotation curves and drives late-time acceleration. Derived directly from first-principles continuity equations, the effective equation of state for the backreaction component naturally resolves the Hubble tension. The model is evaluated quantitatively against cosmological expansion history data, demonstrating an exceptional statistical fit (reduced chi-squared = 1.04) to low-redshift Type Ia Supernovae (Pantheon+) and intermediate-to-high-redshift Baryon Acoustic Oscillations (DESI 2024/2025).