Abstract
We consider the Klein-Gordon equation in FRW-like universes which are periodic in a suitable scale of time. In a remarkable sector of solutions, the Floquet theory of differential equations allows for generalizing the notion of particle frequency. In this sense, the sesquilinear form associated with Gordon's current is positive definite when restricted to the sub-sector of positive frequencies.
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Droz-Vincent, P. Positive particle frequencies in some time-periodic universes. Lett Math Phys 36, 277–290 (1996). https://doi.org/10.1007/BF00943280
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DOI: https://doi.org/10.1007/BF00943280