Pioneer Anomaly in Perturbed FRW Metric
  In this manuscript, it is shown that the Pioneer anomaly is the local evidence for an expanding universe. In other words, its value is a direct measure of the Hubble constant while its sign shows the expanding behavior of the dynamics of the universe. This analysis is obtained by studying the radial geodesic deviation of the light rays in the perturbed Friedmann-Robertson-Walker metric in the Newtonian gauge. 
Hossein Shojaie
astro-ph.CO gr-qc