http://arxiv.org/PS_cache/hep-th/pdf/0506/0506189.pdf Title: Gravitons as super-strong interacting particles, and low-energy quantum gravity Authors: Michael A. Ivanov Comments: 38 pages, 9 figures, Latex. Will be published in 2005 It is shown by the author that 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. A new dimensional constant which characterizes one act of interaction is introduced and estimated. 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. Of course, all of these facts may implicate a necessity to change the standard cosmological paradigm. Some features of a new paradigm are discussed here, too. 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, than 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. It is shown that the predicted and observed values of deceleration are in good agreement. Some unsolved problems are discussed, so as possibilities to verify some conjectures in laser-based experiments.