  We propose a suitable vacuum state for a quantized Dirac field interacting
with a classical scalar field in a Friedman-Robertson-Walker-Lemaitre
spacetime. This state is constructed from an extended version of the adiabatic
expansion of the associated Fourier modes of the field. We compute the full
renormalized stress-energy tensor. For any given initial time, this
instantaneous vacuum can always be chosen to have vanishing Fourier modes for
the renormalized stress-energy tensor. We check the consistency of the solution
for several inflationary models.
