Quantum Decoherence During Inflation from Gravitational Nonlinearities

TL;DR

This paper investigates how gravitational nonlinearities during inflation cause quantum decoherence of curvature perturbations, leading to classical stochastic fluctuations, with implications for understanding the quantum-to-classical transition in the early universe.

Contribution

It demonstrates that gravitational nonlinearities induce decoherence of inflationary perturbations, providing a minimal mechanism for the emergence of classicality from quantum states.

Findings

Decoherence occurs after horizon crossing due to weak gravitational coupling.

Hubble-scale modes serve as the environment causing decoherence.

Phase oscillations in the wave functional suppress quantum off-diagonal terms.

Abstract

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.