On the Possibility of Our Universe as the Interior of a Black Hole: Mathematical Foundations and Observational Tests

We present a rigorous investigation of the hypothesis that our observable universe resides within the interior of a black hole in a parent universe. After theoretical refinement and peer review, we report four principal results. (1) The Black Hole condition rS = RH is shown to be a fundamental algebraic identity for any flat FLRW universe at critical density, directly linking FLRW kinematics to black hole geometry. (2) Applying Israel junction conditions to the non-comoving apparent horizon demonstrates a non-zero jump in extrinsic curvature; the resulting surface stress-energy mathematically represents the necessary physical mass accretion from the exterior. (3) The corrected Kantowski-Sachs interior volume integral yields an effective cosmological constant Λeff ≈ 6/rS², which yields Λeff/Λobs ≈ 2.87—a theoretically robust O(1) agreement within the ambiguity of quantum gravity boundary terms. (4) An illustrative fit of the BHU accretion-driven dark energy evolution to DESI DR1 BAO data shows that the model successfully traverses the observationally preferred region, with the specific w₀-wₐ curve constituting a falsifiable prediction. Finally, we distinguish between global KS-induced CMB anomalies and localized features, identifying specific predictions for upcoming surveys.