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We propose a suitable vacuum state for a quantized Dirac field interactingwith a classical scalar field in a Friedman-Robertson-Walker-Lemaitrespacetime. This state is constructed from an extended version of the adiabaticexpansion of the associated Fourier modes of the field. We compute the fullrenormalized stress-energy tensor. For any given initial time, thisinstantaneous vacuum can always be chosen to have vanishing Fourier modes forthe renormalized stress-energy tensor. We check the consistency of the solutionfor several inflationary models.

Instantaneous vacuum for Dirac fields with a Yukawa interaction in cosmological space-times