  We address the question of unitary implementation of the dynamics for scalar
fields in cosmological scenarios. Together with invariance under spatial
isometries, the requirement of a unitary evolution singles out a rescaling of
the scalar field and a unitary equivalence class of Fock representations for
the associated canonical commutation relations. Moreover, this criterion
provides as well a privileged quantization for the unscaled field, even though
the associated dynamics is not unitarily implementable in that case. We discuss
the relation between the initial data that determine the Fock representations
in the rescaled and unscaled descriptions, and clarify that the S-matrix is
well defined in both cases. In our discussion, we also comment on a recently
proposed generalized notion of unitary implementation of the dynamics, making
clear the difference with the standard unitarity criterion and showing that the
two approaches are not equivalent.
