Particle decay in post inflationary cosmology

We study a scalar particle of mas m1 decaying into two particles of mass m2 during the radiation and matter dominated epochs of a standard cosmological model. An adiabatic approximation is introduced that is valid for degrees of freedom (d.o.f.) with typical wavelengths much smaller than the particle horizon (? Hubble radius) at a given time. We implement a nonperturbative method that includes the cosmological expansion and obtain a cosmological Fermi’s Golden Rule that enables one to compute the decay law of the parent particle with mass m1, along with the build up of the population of daughter particles with mass m2. The survival probability of the decaying particle is P(t)=e??˜k(t)t with ?˜k(t) being an effective momentum and time dependent decay rate. It features a transition timescale tnr between the relativistic and nonrelativistic regimes and for k?0 is always smaller than the analogous rate in Minkowski spacetime, as a consequence of (local) time dilation and the cosmological redshift. For t?tnr the decay law is a “stretched exponential” P(t)=e?(t/t*)3/2, whereas for the nonrelativistic stage with t?tnr, we find P(t)=e??0t(t/tnr)?0tnr/2, with ?0 the Minkowski space time decay width at rest. The Hubble timescale ?1/H(t) introduces an energy uncertainty ?E?H(t) which relaxes the constraints of kinematic thresholds. This opens new decay channels into heavier particles for 2?Ek(t)H(t)?4m22?m12, with Ek(t) the (local) comoving energy of the decaying particle. As the expansion proceeds this channel closes and the usual two particle threshold restricts the decay kinematics.