  It is shown that only in the space-times admitting a 1+3-foliation by flat
Cauchy hypesurfaces (i.e., in the Bianchi I type space-times the isotropic
version of which the spatially flat Friedmann-Robertson-Walker space-times are)
the canonical quantization of geodesic motion and quantum-mechanics obtained as
an asymptotics of the quantum theory of scalar field lead to the same canonical
commutation relations (CCR). Otherwise, the field-theoretical approach leads to
a deformation of CCR (particularly, operators of coordinates do not commute),
and the Principle of Correspondence is broken in a sense. Thus, the spatially
flat cosmology is distinguished intrinsically in the quantum theory.
