  If gravitons are super-strong interacting particles and the low-temperature
graviton background exists, the basic cosmological conjecture about the
Dopplerian nature of redshifts may be false. In this case, a full magnitude of
cosmological redshift would be caused by interactions of photons with
gravitons. Non-forehead collisions with gravitons will lead to a very specific
additional relaxation of any photonic flux. It gives a possibility of another
interpretation of supernovae 1a data - without any kinematics. These facts may
implicate a necessity to change the standard cosmological paradigm.
  A quantum mechanism of classical gravity based on an existence of this sea of
gravitons is described for the Newtonian limit. This mechanism needs graviton
pairing and "an atomic structure" of matter for working it, and leads to the
time asymmetry. 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. It is shown that in this approach the two
fundamental constants - Hubble's and Newton's ones - should be connected
between themselves. The theoretical value of the Hubble constant is computed.
In this approach, every massive body would be decelerated due to collisions
with gravitons that may be connected with the Pioneer 10 anomaly. Some unsolved
problems are discussed, so as possibilities to verify some conjectures in
laser-based experiments.
