Particle decay in post inflationary cosmology

TL;DR

This paper develops a non-perturbative, cosmology-aware decay law for scalar particles during radiation and matter eras, revealing how expansion influences decay rates, thresholds, and particle populations in the early universe.

Contribution

It introduces a cosmological Fermi's Golden Rule and an adiabatic approximation to compute decay laws accounting for expansion effects, including time dilation and redshift.

Findings

Decay law transitions from stretched exponential to exponential with time.

Expansion modifies decay rates, making them smaller than in Minkowski spacetime.

Energy uncertainty from expansion allows heavier decay channels temporarily.

Abstract

We study scalar particle decay during the radiation and matter dominated epochs of a standard cosmological model. An adiabatic approximation is introduced that is valid for degrees of freedom with typical wavelengths much smaller than the particle horizon ($\propto$~Hubble radius) at a given time. We implement a non-perturbative method that includes the cosmological expansion and obtain a cosmological Fermi's Golden Rule that enables one to compute the decay law of a parent particle of mass $m_1$, along with the build up of the population of daughter particles of mass $m_2$. The survival probability of the decaying particle is $P(t)=e^{-\widetilde{\Gamma}_k(t)\,t}$ with $\widetilde{\Gamma}_k(t)$ being an \emph{effective momentum and time dependent decay rate}. It features a transition time scale $t_{nr}$ between the relativistic and non-relativistic regimes and for $k \neq 0$ is always smaller than the analogous rate in Minkowski spacetime, as a consequence of (local) time dilation and the cosmological redshift. For $t \ll t_{nr}$ the decay law is a "stretched exponential" $P(t) = e^{-(t/t^*)^{3/2}}$, whereas for the non-relativistic stage with $t \gg t_{nr}$, we find $P(t) = e^{-\Gamma_0 t}\,(t/t_{nr})^{\Gamma_0\,t_{nr}/2}$. The Hubble time scale $\propto 1/H(t)$ introduces an energy uncertainty $\Delta E \sim H(t)$ which relaxes the constraints of kinematic thresholds. This opens new decay channels into heavier particles for $2\pi E_k(t) H(t) \gg 4m^2_2-m^2_1$, with $E_k(t)$ the (local) comoving energy of the decaying particle. As the expansion proceeds this channel closes and the usual two particle thresholds restrict the decay kinematics.