Non-Dopplerian cosmological redshift parameters in a model of graviton-dusty universe

Possible effects are considered which would be caused by a hypo- thetical super-strong interaction of photons or massive bodies with single gravitons of the graviton background. If full cosmological red- shift 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