  We study the decay of scalar fields, in particular the inflaton, into lighter
scalars in a De Sitter spacetime background. After providing a practical
definition of the rate, we focus on the case of an inflaton interacting with a
massless scalar field either minimally or conformally coupled to the curvature.
The evolution equation for the expectation value of the inflaton is obtained to
one loop order in perturbation theory and the decay rate is recognized from the
solution. We find the remarkable result that this decay rate displays an
equilibrium Bose-enhancement factor with an effective temperature given by the
Hawking temperature $H\slash{2 \pi}$, where $H$ is the Hubble constant. This
contribution is interpreted as the ``stimulated emission'' of bosons in a
thermal bath at the Hawking temperature. In the context of new inflation
scenarios, we show that inflaton decay into conformally coupled massless fields
slows down the rolling of the expectation value. Decay into Goldstone bosons is
also studied. Contact with stochastic inflation is established by deriving the
Langevin equation for the coarse-grained expectation value of the inflaton
field to one-loop order in this model. We find that the noise is gaussian and
correlated (colored) and its correlations are related to the dissipative
(``decay'') kernel via a generalized fluctuation-dissipation relation.
