Infrared dynamics of a light scalar field in de Sitter
  Inertial observers in de Sitter are surrounded by a horizon and see thermal
fluctuations. To them, a massless scalar field appears to follow a random
motion but any attractive potential, no matter how weak, will eventually
stabilize the field. We study this thermalization process in the static patch
(the spacetime region accessible to an individual observer) via a truncation to
the low frequency spectrum. We focus on the distribution of the field averaged
over a subhorizon region. At timescales much longer than the inverse
temperature and to leading order in the coupling, we find the evolution to be
Markovian, governed by the same Fokker-Planck equation that arises when the
theory is studied in the inflationary setup.
