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 anti-Zeno effect. If heavy dark matter is produced via annihilation of a lighter species, sub-threshold production yields an enhanced abundance. We discuss several possible cosmological consequences of these effects.

我们从空间平坦辐射主导的宇宙学中的第一原理研究跃迁率和横截面。我们考虑一个标量粒子模型来研究由对湮灭产生的散射和重粒子，得出更一般的结论。S-矩阵公式不适合在快速扩展的宇宙学中研究这些无处不在的过程。我们引入了一种物理驱动的绝热膨胀，它依赖于在给定时间比粒子视界小得多的波长。这种扩展中的主要顺序支配了过渡率和横截面。几个重要和一般的结果是宇宙学红移和有限粒子视界的直接结果：（i）违反局部洛伦兹不变性，（ii）在有限时间内生产横截面冻结，抗-芝诺效应。如果通过较轻物种的湮灭产生重暗物质，则亚阈值产生会增加丰度。我们讨论了这些效应的几种可能的宇宙学后果。