The problems connected to propagation of a gravitational field are considered. The law of electromagnetic radiation frequency change in gravitational field is shown. The problem of a gravitational field quantization is investigated. Energy of a graviton is found by two ways. First, on the basis of use quantum gravitational eikonal and Lagrangian of a gravitational field the energy of a solitary graviton is found. It is shown that graviton has the mass proportional to its frequency. Second, due to refusal from symmetric stresses tensor in structure of an energy-impulse tensor the quantum form of the energy-impulse tensor in Einstein's equation is found. It has allowed found the energy of a solitary graviton. Both ways of an energy graviton finding has given the identical result. It is shown that the solution of the Einsteins equation with use of the quantum form of an energy-impulse tensor for the certain direction represents the sum of a gravitational wave and a graviton. It is found out that at approach of a graviton to the massive bodies (double stars) radiating gravitational waves there is a resonant pumping of the gravitational field energy of these bodies to the gravitons with increase in their mass and frequency. It enables registration of the gravitons with the help of the detector located near to massive bodies. The assumption is made that dark energy of a gravitational field is all set of the graviton energies of a space.

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