H₀-tension in the classical limit of Big Bang quantum cosmology

ΛCDM is challenged by observational tensions between late- and early-time cosmology, most dramatically in the Hubble constant H₀. ΛCDM hereby falls short as an effective infra-red (IR) limit of quantum cosmology. Consistency with general relativity in an effective dark energy Λ=αₚΛ₀~ H²/c² obtains from an IR-coupling αₚ~ to the bare cosmological constant Λ₀~ 1/, where is the Planck constant. A path integral formulation with gauged total phase identifies Λ with the trace of the Schouten tensor J. It predicts the scaling H₀ √6/5H₀^Λ CDM inferred from the BAO, while preserving the age of the Universe. With no free parameters, this first principle model predicts a 9% departure in H₀ between the Local Distance Ladder and the ΛCDM { Planck} measurements with no tension between late and early times. In galaxies, the same IR coupling predicts a sharp transition to anomalous rotation curves below the de Sitter acceleration adS=cH, where c is the velocity of light. Excluded by galaxy models in ΛCDM, it points to ultra-light dark matter of mass mD 3× 10⁻²¹eV consistent with mD 10⁻²²eV of wave-like ψCDM.