  The decoherence mechanism is believed to be possibly connected to the quantum
to classical transition of the primordial cosmological perturbations in the
early universe. In this paper, we extend our previous analysis on decoherence
in a fermion and scalar quantum field theory coupled via the Yukawa interaction
in the Minkowski spacetime, to the inflationary de Sitter background. We treat
the scalar field as the system and the fermions as the environment, and both
the fields are taken to be massless. We utilise a non-equilibrium effective
field theory formalism, suitable for open quantum systems such as this. We
assume that an observer measures only the Gaussian 2-point correlator for the
scalar field, as the simplest realistic scenario. In order to compute the von
Neumann entropy generated at late times as a measure of the decoherence, we
construct the one loop renormalised Kadanoff-Baym equation, which is the
equation of motion satisfied by the 2-point correlators in the closed time path
Schwinger-Keldysh formalism. These equations account to the self energy
corrections. Using this, we next construct the one loop corrected statistical
propagator for the scalar, which is related to its phase space area, to compute
the von Neumann entropy. We also compute the variation of the von Neumann
entropy with respect to relevant parameters. We note the qualitative similarity
between our findings and the scenario where both the system and the environment
are scalars. Our result is also qualitatively similar to an earlier one found
by using the influence functional technique for a massive Yukawa theory.
