  We study transition rates and cross sections from first principles in a
spatially flat radiation dominated cosmology. We consider a model of scalar
particles to study scattering and heavy particle production from pair
annihilation, drawing more general conclusions. The S-matrix formulation is ill
suited to study these ubiquitous processes in a rapidly expanding cosmology. We
introduce a physically motivated adiabatic expansion that relies on wavelengths
much smaller than the particle horizon at a given time. The leading order in
this expansion dominates the transition rates and cross sections. Several
important and general results are direct consequences of the cosmological
redshift and a finite particle horizon: i) a violation of local Lorentz
invariance, ii) freeze-out of the production cross section at a finite time,
iii) sub-threshold production of heavier particles as a consequence of the
uncertainty in the local energy from a finite particle horizon, a manifestation
of the \emph{antizeno} effect. If heavy dark matter is produced via
annihilation of a lighter species, sub-threshold production yields an enhanced
abundance. We discuss several possible consequences of these effects.
