  Possible effects are considered which would be caused by a hypothetical
superstrong interaction of photons or massive bodies with single gravitons of
the graviton background. 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. From another side, in this case every
massive body, slowly moving relatively 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.
