  We investigate the relaxation and decay of a particle during inflation by
implementing the dynamical renormalization group. This investigation allows us
to give a meaningful definition for the decay rate in an expanding universe. As
a prelude to a more general scenario, the method is applied here to study the
decay of a particle in de Sitter inflation via a trilinear coupling to massless
conformally coupled particles, both for wavelengths much larger and much
smaller than the Hubble radius. For superhorizon modes we find that the decay
is of the form eta^{Gamma1} with eta being conformal time and we give an
explicit expression for Gamma1 to leading order in the coupling which has a
noteworthy interpretation in terms of the Hawking temperature of de Sitter
space-time. We show that if the mass M of the decaying field is << H then the
decay rate during inflation is enhanced over the Minkowski spacetime result by
a factor 2H/[pi M]. For wavelengths much smaller than the Hubble radius we find
that the decay law is e^{-alpha/[k H C(eta)} with C(eta) the scale factor and
alpha determined by the strength of the trilinear coupling. This result
suggests a suppression of power for long wavelength modes upon horizon
crossing. In all cases we find a substantial enhancement in the decay law as
compared to Minkowski space-time. These results suggest potential implications
for the spectrum of scalar density fluctuations as well as non-gaussianities.
