Condensates and quasiparticles in inflationary cosmology: mass generation and decay widths

Abstract

During de Sitter inflation massless particles of minimally coupled scalar fields acquire a mass and a decay width thereby becoming \emph{quasiparticles}. For bare massless particles non-perturbative infrared radiative corrections lead to a self-consistent generation of mass, for a quartic self interaction $M \propto \lambda^{1/4} H$, and for a cubic self-interaction the mass is induced by the formation of a non-perturbative \emph{condensate} leading to $M \propto \lambda^{1/3} H^{2/3}$. These radiatively generated masses restore de Sitter invariance and result in anomalous scaling dimensions of superhorizon fluctuations. We introduce a generalization of the non-perturbative Wigner-Weisskopf method to obtain the time evolution of quantum states that include the self-consistent generation of mass and regulate the infrared behavior. The infrared divergences are manifest as poles in $\Delta=M^2/3H^2$ in the single particle self-energies, leading to a re-arrangement of the perturbative series non-analytic in the couplings. A set of simple rules that yield the leading order infrared contributions to the decay width are obtained and implemented. The lack of kinematic thresholds entail that all particle states acquire a decay width, dominated by the emission and absorption of superhorizon quanta $\propto (\lambda/H)^{4/3}\,[H/k_{ph}(\eta)]^6 ; \lambda\,[H/k_{ph}(\eta)]^6 $ for cubic and quartic couplings respectively to leading order in $M/H$. The decay of single particle quantum states hastens as their wavevectors cross the Hubble radius and their width is related to the highly squeezed limit of the bi- or tri-spectrum of scalar fluctuations respectively.