Black Hole Universe Cosmology: Geometric Inflation via Non-Minimal Coupling

We present a computational validation of the Black Hole Universe (BHU) hypothesis, demonstrating that our observable cosmos can originate from the interior of a parent black hole via metric inversion. Using non-minimal scalar coupling ξRφ² as the inflationary mechanism, we identify the critical parameter ξ = 100 that produces precisely N = 61.7 e-folds, solving the horizon and flatness problems without exotic matter. Geometric constraints yield Rs/RH = 1.096, validating Gaztañaga's duality condition. We implement reheating physics via perturbative decay Γφ̇² → ρr and discuss the connection to entropic gravity, proposing that dark sector phenomena emerge from finite horizon entropy of the parent spacetime.