Classical analog of cosmological particle creation

A classical, minimally coupled scalar field in a given background cosmology is discussed. Far from the initial singularity a WKB approximation is valid so that a semiclassical particle number can be defined as an adiabatic invariant. This number is then compared to scalar field parameters near the singularity. Generalization of work by Misner can be used for a nonparticle singularity description. Alternatively, "freezing" of the cosmology at some time $t_0$ after the singularity is required to obtain a particle description there. This procedure is shown to be valid if a WKB regime does exist at $t_0$. It gives unphysical results if a WKB regime does not exist at $t_0$. These classical methods are shown to reproduce the results of the quantum treatment except for zero-point energy terms. It is further shown that the "freezing" procedure is not conformally invariant for a conformally coupled massless scalar field. Grishchuk's result on gravitational wave amplification is reproduced and discussed.