  It is shown that screening the background of super-strong interacting
gravitons creates for any pair of bodies as an attraction force as well an
repulsion force due to pressure of gravitons. For single gravitons, these
forces are approximately balanced, but each of them is much bigger than a force
of Newtonian attraction. If single gravitons are pairing, a body attraction
force due to pressure of such graviton pairs is twice exceeding a corresponding
repulsion force under the condition that graviton pairs are destructed by
collisions with a body. If the considered quantum mechanism of classical
gravity is realized in the nature, then an existence of black holes contradicts
to Einstein's equivalence principle. In such the model, Newton's constant is
proportional to $H^{2}/T^{4},$ where $H$ is the Hubble constant, $T$ is an
equivalent temperature of the graviton background. The estimate of the Hubble
constant is obtained $H=2.14 \cdot 10^{-18} s^{-1}$ (or $66.875 km \cdot s^{-1}
\cdot Mpc^{-1}$).

General Relativity and Quantum Cosmology