  We study scalar fields subject to an equation of the Klein-Gordon type in
nonstationary spacetimes, such as those found in cosmology, assuming that all
the relevant spatial dependence is contained in the Laplacian. We show that the
field description ---with a specific canonical pair--- and the Fock
representation for the quantization of the field are fixed indeed in a unique
way (except for unitary transformations that do not affect the physical
predictions) if we adopt the combined criterion of (a) imposing the invariance
of the vacuum under the group of spatial symmetries of the field equations and
(b) requiring a unitary implementation of the dynamics in the quantum theory.
Besides, we provide a spacetime interpretation of the field equations as those
corresponding to a scalar field in a cosmological spacetime that is conformally
ultrastatic. In addition, in the privileged Fock quantization, we investigate
the generalization of the evolution of physical states from the hyperbolic
dynamical regime to an elliptic regime. In order to do this, we contemplate the
possibility of processes with signature change in the spacetime where the field
propagates and discuss the behavior of the background geometry when the change
happens, proving that the spacetime metric degenerates. Finally, we argue that
this kind of signature change leads naturally to a phenomenon of particle
creation, with exponential production.
