Scalar particle creation in an anisotropic universe

Abstract

The problem of quantized scalar field creation in an anisotropic spatially homogeneous background universe is reexamined from a Schrödinger-picture point of view. For each mode a complete set of orthonormal wave functions, ${\psi }_N$, is obtained using the method of Salusti and Zirilli. These wave functions are valid at all times even if there is an initial cosmological singularity and depend only on the solution of the classical equation of motion. The wave functions are fixed completely by requiring the classical solution to have positive-frequency WKB form when the universe reaches the stage of adiabatic expansion. These wave functions are eigenfunctions of a conserved number operator which has the usual particle interpretation in the adiabatic regime. An intitial state near the singularity is chosen as a superposition of the wave functions, ${\psi }_N$, and the particle number in the adiabatic regime is calculated. For plane-wave initial states, which follow the classical behavior near the singularity, the final particle number depends only on the parameters of the initial wave packet. For an initial state which instantaneously diagonalizes the Hamiltonian, an (arbitrary) initial time must be chosen. If the mode in question is in the adiabatic regime at that time almost no particle creation occurs. If it is not adiabatic, creation occurs and becomes infinite if the initial time is taken to be that of the singularity. This creation is a consequence of the failure of particle number to be well defined in this regime. Comparisons with other particle-creation studies are made.