Red Shift from Gravitational Back Reaction

Deviations from geodesic motion caused by gravitational radiation have been discussed in the last decades to describe the motion of particles or photons in strong fields around collapsed objects. On cosmological scale this effect, which in the first order is caused by the finite speed of gravitational interaction, is important also in the weak field limit. In this paper the energy loss by transfer to the gravitational potential is determined in a quasi-Newtonian approximation for the examples of a static Einstein universe and for an expanding universe with flat metric. In both cases the resulting red shift is a considerable fraction of the total red shift and requires an adjustment of the age and the matter composition in our models of the universe.