  After a brief summary of decoherence and quantum to classical transition in
cosmology we focus on the study of quantum decoherence of cosmological
perturbations in inflationary universe, that does not rely on any environment.
This is what `intrinsic' in the title refers to -- a closed quantum system. The
question is, does its quantum perturbations decohere with an inflationary
expansion of the universe. A dominant view which had propagated for a quarter
of a century asserts yes, based on the belief that the large squeezing of a
quantum state after a duration of inflation renders the system effectively
classical. This paper debunks this view by identifying the technical
fault-lines in its derivations and revealing the pitfalls in its arguments
which drew earlier authors to this wrong conclusion. We use a few simple
quantum mechanical models to expound where the fallacy originated: The highly
squeezed ellipse quadrature in phase space cannot be simplified to a line, and
the Wigner function cannot be replaced by a delta function. These amount to
taking only the leading order contributions in seeking the semiclassical limit
and ignoring the subdominant contributions where quantum features reside. Doing
so violates the bounds of the Wigner function, and its wave functions possess
negative eigenvalues. Moreover, the Robertson-Schrodinger uncertainty relation
for a pure state is violated. For inflationary cosmological perturbations, in
addition to these features, entanglement exists between the created pairs. This
uniquely quantum feature cannot be easily argued away. Indeed it could be our
best hope to retroduce the quantum nature of cosmological perturbations and the
trace of an inflaton field. All this point to the fact that a closed quantum
system, even when highly squeezed, evolves unitarily without loss of coherence;
quantum cosmological perturbations do not by itself decohere.
