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 Schr\"odinger 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 shorterwavelength)
modes of $\zeta$ as an environment. We show that inflation produces phase
oscillations in the wave functional $\Psi[\zeta(\mathbf{x})]$, 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.
