Quantum Geometro-Topodynamics: Unitary Topology Transitions, Black Hole Evaporation, and Axionic CMB Birefringence

Abstract

We present a self-consistent framework of Quantum Geometro-Topodynamics that addresses the unitarity of spatial topology change, the black-hole information paradox, and the gravitational CP problem. By formulating the Wheeler-DeWitt evolution in a stratified Hilbert space equipped with a topological measure derived from the Ashtekar-Lewandowski volume, we prove exact norm conservation and detailed balance for topology-changing surgeries. The black-hole singularity is shielded by the Loop Quantum Gravity area cutoff, leading to a unitary transition into a baby universe with a probability of order a few percent and complete information retrieval. Dynamization of the topological vacuum angle yields a non-perturbative axion potential via the dilute-instanton-gas approximation. With the Ray-Singer prefactor geometrically suppressed, the condensate relaxes to zero and accounts for the observed cold dark matter density for a decay constant on the order of 10^11 to 10^12 GeV. The framework is constrained by the Immirzi parameter and the observed dark-matter density. We predict a cosmic microwave background birefringence angle of approximately 0.1 to 0.5 degrees via EB and TB power-spectrum mixing, offering a concrete test for upcoming LiteBIRD and CMB-S4 observations.