On Quantum Mechanics in Friedmann-Robertson-Walker Universe

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.