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We study the quantum vacuum definition for spin-(1/2) fields in a Robertson-Walker universe using the coincidence of a local property (singularity structure of the DeWitt-Schwinger kernel) and a global property (energy minimization) and we obtain two kinds of vacua: strong and weak (which coincide with the energy minimization vacuum). The density of particles created during the expansion of the Universe between two weak vacua is found to be finite. However, we prove that the energy-momentum tensor vacuum expectation value is nonrenormalizable.
Chimento et al. (Mon,) studied this question.