Stochastic Particle Production in a de Sitter Background
  We explore non-adiabatic particle production in a de Sitter universe for a
scalar spectator field, by allowing the effective mass $m^2(t)$ of this field
and the cosmic time interval between non-adiabatic events to vary
stochastically. Two main scenarios are considered depending on the
(non-stochastic) mass $M$ of the spectator field: the conformal case with
$M^2=2H^2$, and the case of a massless field. We make use of the transfer
matrix formalism to parametrize the evolution of the system in terms of the
"occupation number", and two phases associated with the transfer matrix; these
are used to construct the evolution of the spectator field. Assuming short-time
interactions approximated by Dirac-delta functions, we numerically track the
change of these parameters and the field in all regimes: sub- and super-horizon
with weak and strong scattering. In all cases a log-normally distributed field
amplitude is observed, and the logarithm of the field amplitude approximately
satisfies the properties of a Wiener process outside the horizon. We derive a
Fokker-Planck equation for the evolution of the transfer matrix parameters,
which allows us to calculate analytically non-trivial distributions and moments
in the weak-scattering limit.
