The graviton background: a new way to quantum gravity
  Graviton pairing and destruction of these pairs under collisions with bodies may lead to the Newtonian attraction. It opens us a new way to a very-low-energy quantum gravity model. In the model by the author, cosmological redshifts are caused by interactions of photons with gravitons of the background. Non-forehead collisions with gravitons lead to an additional relaxation of any photonic flux. Total galaxy number counts/redshift and galaxy number counts/magnitude relations are computed and found to be in a good agreement with galaxy observations. 
Michael A. Ivanov