Classical Entanglement Structure in the Wavefunction of Inflationary Fluctuations

Abstract

We argue that the preferred classical variables that emerge from a pure quantum state are determined by its entanglement structure in the form of redundant records: information shared between many subsystems. Focusing on the early universe, we ask how classical metric perturbations emerge from vacuum fluctuations in an inflationary background. We show that the squeezing of the quantum state for super-horizon modes, along with minimal gravitational interactions, leads to decoherence and to an exponential number of records of metric fluctuations on very large scales, $\lambda/\lambda_{\rm Hubble}>\Delta_\zeta^{-2/3}$, where $\Delta_\zeta\lesssim 10^{-5}$ is the amplitude of scalar metric fluctuations. This determines a preferred decomposition of the inflationary wavefunction into orthogonal "branches" corresponding to classical metric perturbations, which defines an inflationary entropy production rate and accounts for the emergence of stochastic, inhomogeneous spacetime geometry.