Quantum decoherence during inflation from gravitational nonlinearities

We study the inflationary quantum-to-classical transition for the adiabatic curvature perturbation zeta due to quantum decoherence, focusing on the role played by squeezed-limit mode couplings. We evolve the quantum state Psi in the Schrodinger picture, for a generic cubic coupling to additional environment degrees of freedom. Focusing on the case of minimal gravitational interactions, we find the evolution of the reduced density matrix for a given long-wavelength fluctuation by tracing out the other (mostly shorter-wavelength) modes of zeta as an environment. We show that inflation produces phase oscillations in the wave functional Psi [zeta(x)], which suppress off-diagonal components of the reduced density matrix, leaving a diagonal mixture of different classical configurations. Gravitational nonlinearities thus provide a minimal mechanism for generating classical stochastic perturbations from inflation. We identify the time when decoherence occurs, which is delayed after horizon crossing due to the weak coupling, and find that Hubble-scale modes act as the decohering environment. We also comment on the observational relevance of decoherence and its relation to the squeezing of the quantum state.