Quantum cosmology of the Gromov bounce: Exact wave function, boundary condition discrimination, and observational consistency

We solve the Wheeler–DeWitt equation on the Gromov-truncated cosmological billiard — the wedge-shaped domain bounded by the BKL curvature wall and the Gromov symplectic wall. The minisuperspace equation reduces from three variables to one through U(1) factorisation and Friedmann constraint elimination. In the corner region, the radial equation is the Euler equation with oscillatory solutions: the bounce wave function is an infinite sequence of probability peaks accumulating at the singularity, each geometrically suppressed, with zero probability at the singularity itself. The Green's function for a Coleman–De Luccia source at the Gromov wall gives the echo phase as a function of the compactification parameters, discriminating between Vilenkin, Hartle–Hawking, and landscape nucleation boundary conditions. The Mukhanov–Sasaki equation on this background is in the non-perturbative regime, but super-horizon mode protection confines the billiard modulation to trans-Planckian scales, ensuring automatic consistency with CMB observations without fine-tuning.