Path-integral quantization and cosmological particle production: An example

Abstract

The Feynman path-integral method is applied to the quantization of a scalar field moving in a cosmological background spacetime. The method is illustrated by computing particle production from the vacuum in a spatially flat, Robertson-Walker spacetime with scale factor $R(t)=t$. The result is a distribution of produced particle pairs which at large energies becomes a thermal distribution with a temperature $T=\frac{\ensuremath{\hbar}c}{\ensuremath{\pi}{k}_{B}R(t)}$. The relation to other methods of quantization is discussed.