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

TL;DR

This paper investigates how massless particles in de Sitter inflation acquire mass and decay widths through non-perturbative infrared effects, leading to quasiparticles with restored de Sitter invariance and altered fluctuation scaling.

Contribution

It introduces a non-perturbative Wigner-Weisskopf method to analyze mass generation and decay widths of particles during inflation, revealing new infrared effects and decay mechanisms.

Findings

Massless particles gain mass proportional to th or rd power of coupling constants.

All particle states develop decay widths due to superhorizon quanta interactions.

Decay rates increase as particles cross the Hubble radius, affecting scalar fluctuation spectra.

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.