Harmonic cosmology: How much can we know about a universe before the big bang?

Quantum gravity may remove classical space-time singularities and thus reveal what a universe at the big bang could be like. In loop quantum cosmology, an exactly solvable model is available, which allows one to address precise dynamical coherent states and their evolution in such a setting. It is shown here that quantum fluctuations before the big bang are generically unrelated to those after the big bang. While this is derived only in the solvable model, it presents the case of the strongest control on coherence properties; adding ingredients to a realistic model could only increase the complexity. A reliable determination of pre-big bang quantum fluctuations of geometry would thus require exceedingly precise observations.