EFT Beyond the Horizon: Stochastic Inflation and How Primordial Quantum
  Fluctuations Go Classical
  We identify the effective theory describing inflationary super-Hubble scales
and show it to be a special case of effective field theories appropriate to
open systems. Open systems allow information to be exchanged between the
degrees of freedom of interest and those that are integrated out, such as for
particles moving through a fluid. Strictly speaking they cannot in general be
described by an effective lagrangian; rather the appropriate `low-energy' limit
is instead a Lindblad equation describing the evolution of the density matrix
of the slow degrees of freedom. We derive the equation relevant to super-Hubble
modes of quantum fields in near-de Sitter spacetimes and derive two
implications. We show the evolution of the diagonal density-matrix elements
quickly approaches the Fokker-Planck equation of Starobinsky's stochastic
inflationary picture. This provides an alternative first-principles derivation
of this picture's stochastic noise and drift, as well as its leading
corrections. (An application computes the noise for systems with a sub-luminal
sound speed.) We argue that the presence of interactions drives the
off-diagonal density-matrix elements to zero in the field basis. This shows why
the field basis is the `pointer basis' for the decoherence of primordial
quantum fluctuations while they are outside the horizon, thus allowing them to
re-enter as classical fluctuations, as assumed when analyzing CMB data. The
decoherence process is efficient, occurring after several Hubble times even for
interactions as weak as gravitational-strength. Crucially, the details of the
interactions largely control only the decoherence time and not the nature of
the final late-time stochastic state, much as interactions can control the
equilibration time for thermal systems but are largely irrelevant to the
properties of the resulting equilibrium state.
