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

The minisuperspace Wheeler–DeWitt equation for a complex vacuum field reduces, via U(1) factorisation and Friedmann elimination, to a one-dimensional problem on a Gromov-truncated cosmological billiard of finite hyperbolic area. The solution is oscillatory: an infinite sequence of bounce peaks accumulating at the singularity, each suppressed by a fixed factor, with the singularity itself at zero probability. A Green's-function echo phase discriminates Vilenkin, Hartle–Hawking, and landscape boundary conditions, and power-spectrum modulation is confined to trans-Planckian scales, giving automatic consistency with Planck.