Thermal Interpretation of Infrared Dynamics in de Sitter

Understand

The infrared dynamics of a light, minimally coupled scalar field in de Sitter spacetime with Ricci curvature $R=12H$, averaged over horizon sized regions of physical volume $V_H=\frac{4\pi}{3}\left(\frac{1}{H}\right)^3$, can be interpreted as Brownian motion in a medium with de Sitter temperature $T_{DS}=\frac{\hbar H}{2\pi}$.

• We demonstrate this by directly deriving the effective action of scalar field fluctuations with wavelengths larger than the de Sitter curvature radius and generalizing Starobinsky's seminal results on stochastic inflation.
• The effective action describes stochastic dynamics and the fluctuating force drives the field to an equilibrium characterized by a thermal Gibbs distribution at temperature $T_{DS}$ which corresponds to a de Sitter invariant state.
• Hence, approach towards this state can be interpreted as thermalization.