Abstract
Possible effects, which could be caused by a hypothetical super-strong interaction of photons or massive bodies with single gravitons of the graviton background, are considered. If full cosmological redshift magnitudes are caused by the interaction, then the luminosity distance in a flat non-expanding universe as a function of redshift is very similar to the specific function which fits supernova cosmology data by Riess et al (1998 Astron. J. 116 1009). From another side, in this case every massive body, moving slowly relative to the background, would experience a constant acceleration, proportional to the Hubble constant, of the same order as a small additional acceleration of Pioneer 10, 11.
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