Renormalized stress-energy tensor for spin-1/2 fields in expanding
  universes
  We provide an explicit expression for the renormalized expectation value of
the stress-energy tensor of a spin-$1/2$ field in a spatially flat FLRW
universe. Its computation is based on the extension of the adiabatic
regularization method to fermion fields introduced recently in the literature.
The tensor is given in terms of UV-finite integrals in momentum space, which
involve the mode functions that define the quantum state. As illustrative
examples of the method efficiency, we see how to compute the renormalized
energy density and pressure in two interesting cosmological scenarios: a de
Sitter spacetime and a radiation-dominated universe. In the second case, we
explicitly show that the late-time renormalized stress-energy tensor behaves as
that of classical cold matter. We also check that, if we obtain the adiabatic
expansion of the scalar field mode functions with a similar procedure to the
one used for fermions, we recover the well-known WKB-type expansion.
