Particle decay in inflationary cosmology

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 ${\eta }^{{\Gamma }_1}$ with $\eta$ being conformal time and we give an explicit expression for ${\Gamma }_1$ 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 $\ll H$ then the decay rate during inflation is enhanced over the Minkowski space-time result by a factor $2H/\pi M$. For wavelengths much smaller than the Hubble radius we find that the decay law is $e$ with $C(\eta )$ the scale factor and $\alpha$ determined by the strength of the trilinear coupling. 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.