Stochastic inflation as an open quantum system

TL;DR

This paper models stochastic inflation as an open quantum system, deriving a Lindblad master equation for long-wavelength modes by tracing out short-wavelength modes, and explores its implications for de Sitter space dynamics.

Contribution

It introduces a systematic open quantum system framework for stochastic inflation using the Schwinger-Keldysh formalism, deriving a Lindblad equation and extending it to global de Sitter.

Findings

Derived a Lindblad master equation for inflationary modes.

Connected the master equation to a Fokker-Planck equation in certain limits.

Analyzed the late-time behavior of the system in global de Sitter.

Abstract

We reinterpret Starobinsky's stochastic inflation as an open quantum system, where short-wavelength modes act as the environment for long-wavelength modes. Using the Schwinger-Keldysh formalism, we systematically trace out the environment and derive an effective theory for the reduced density matrix, including deviations from exact de Sitter. The resulting master equation is a Lindblad equation, which reduces to a Fokker-Planck equation for the diagonal elements up to higher orders in the slow-roll expansion, while also yielding a more complete equation in phase space. Finally, we extend the formalism to global de Sitter, for which the associated Fokker-Planck equation lacks equilibrium solutions until the late-time regime $aH \gg 1$.