Quantization of weak gravitational waves in a closed Fridman model

The problem of quantization of free tensor fields in a curved space-time is considered for the example of quantization of weak gravitational waves. The distinctive feature of quantization in a curved space-time is the violation of the homogeneity of time by the expansion of the Universe and the related nonconservation of energy. This last circumstance means that s is impossible to construct a “good” Hamiltonian. The problem can be resolved because of the spatiai homogeneity and the associated integral conservation law.