http://arxiv.org/abs/astro-ph/0505310 Authors: Michael A. Ivanov Comments: 20 pages, 4 figures, LaTeX. Contribution to the 1st Crisis in Cosmology Conference (CCC-1), which will be held in Moncao, Portugal, 23-25 June 2005 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: 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 that 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. Some features of a new paradigm are discussed. In a frame of this model, every observer has two different cosmological horizons. One of them is defined by maximum existing temperatures of remote sources - by big enough distances, all of them will be masked with the CMB radiation. Another, and much smaller, one depends on their maximum luminosity - the luminosity distance increases with a redshift much quickly than the geometrical one. If the considered quantum mechanism of classical gravity is realized in the nature, than an existence of black holes contradicts to the equivalence principle. 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. Also, every massive body would be decelerated due to collisions with gravitons that may be connected with the Pioneer 10 anomaly.