Abstract
We study the freedom in assigning Fock representations to each cosmic time for a canonically quantized free neutral scalar field in spatially homogeneous and isotropic universes. Two requirements are considered: The implementability of the Bogoliubov transformation between Fock representations at different times, and the finiteness of the energy generation rate per unit volume. We show that especially the second requirement completely determines the particle-defining modes corresponding to the Fock representations in the high frequency region for the minimal coupling case. We also show, with no assumption on the expansion law of the universes, that the scalar field should interact with the background geometry through conformal coupling in order that the Bogoliubov transformation between the Hamiltonian diagonalizing Fock representations is implementable.
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