Emergent Time from Cosmic Expansion: A Geometric Reinterpretation of Gravitational Dynamics

I propose that time can be understood as emergent from cosmic expansion rather than being fundamental. Using cosmological perturbation theory with the scale factor a (t) as the primary temporal variable, I show how Einstein's field equations express geometric consistency between local and cosmic scales, validated by the McVittie metric (Φ = Ψ = -m/ (ar) ). A key finding is emergent MOND-like dynamics: when gravitational acceleration falls below cH, cosmic expansion sets an effective floor, yielding v∞ = (GMcH) ^1/4 — matching Milky Way rotation to 91% and explaining the empirical a₀ ≈ cH coincidence. Testable predictions include: (1) epoch-dependent time dilation corrections with β = 1. 0 ± 0. 5, detectable via Euclid/Roman cluster surveys; (2) MOND transition radius rₜransition = √ (GM/cH) ; (3) H₀–density anticorrelation. These distinguish emergent time from standard GR.