Quantum particle production in a homogeneous isotropic universe from states described by a density matrix

A study is made of particle production in an arbitrary external field from states described by quadratic density matrices; the spectra of the particles are found. It is shown that when scalar particles are produced in a Friedmann universe from a state described by a thermal density matrix the main contribution to the total number of produced particles is made by those that arose from statistical effects, though the back reaction of the produced particles on the metric is small.