Can the universe be described by a wavefunction?

Suppose we assume that in gently curved spacetime (a) causality is not violated to leading order (b) the Birkoff theorem holds to leading order and (c) CPT invariance holds. Then we argue that the `mostly empty' universe we observe around us cannot be described by an exact wavefunction $\Psi$. Rather, the weakly coupled particles we see are approximate quasiparticles arising as excitations of a `fuzz'. The `fuzz' {\it does} have an exact wavefunction $\Psi_{fuzz}$, but this exact wavefunction does not directly describe local particles. The argument proceeds by relating the cosmological setting to the black hole information paradox, and then using the small corrections theorem to show the impossibility of an exact wavefunction describing the visible universe.