We derive cosmological expansion, acceleration, and horizon structure as consequences of global coherence-capacity evolution in projection-based effective physics. Building on the theory of coherence capacity and its transport, concentration, and exhaustion, we show that cosmology is not the dynamics of spacetime itself but the global bookkeeping of how a finite stability budget is redistributed over large scales. Under minimal axioms, we obtain generalized Friedmann-type equations governing capacity flow, interpret expansion as a relaxation process under spare coherence capacity, and identify cosmic acceleration as arising from capacity redistribution rather than vacuum energy. Cosmological horizons emerge as global coherence-capacity bottlenecks, analogous to black-hole horizons, and the cosmic arrow of time aligns with irreversible capacity loss. No fundamental inflaton, cosmological constant, or initial singularity is required. The framework is model-independent and yields testable deviations from ΛCDM at large scales, unifying cosmology with gravity, horizons, entropy, and irreversibility as manifestations of coherence-capacity dynamics.