Stochastic Inflation as an Open Quantum System

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 space. 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 space, for which the associated Fokker-Planck equation lacks equilibrium solutions until the late-time regime aH≫1.