  Moving from the consideration that matter fields must be treated in terms of
their fundamental quantum counterparts, we show straightforward arguments,
within the framework of ordinary quantum mechanics and quantum field theory, in
order to convince readers that cosmological perturbations must be addressed in
term of the semiclassical limit of the expectation value of quantum fields. We
first take into account cosmological perturbations originated by a quantum
scalar field, and then extend our treatment in order to account for the
expectation values of bilinears of Dirac fermion fields. The latter can indeed
transform as scalar quantities under diffeomorphisms, as well as all the other
bilinear of the Dirac fields that belong to the Clifford algebra. This is the
first of a series of works that is intended to prove that cosmological quantum
perturbations can actually be accounted for in terms of Dirac fermion fields,
which must be treated as fundamental quantum objects, and their dynamics.
