The problem of why the Pioneer Anomaly's anomalous acceleration is the same order of magnitude as the square root of the dark energy density though in the wrong direction has bugged me since 2002. Of course both dark energy and dark matter density are same order of magnitude .73 vs .23 of critical density for a flat space universe found in the inflation model. But why large-scale cosmology shows up on the small scale of our solar system is the problem and why there is a hollow volume from Sun out to orbits of the outer planets is another mystery.

REVIEWS OF MODERN PHYSICS, VOLUME 82, JANUARY–MARCH 2010

Influence of global cosmological expansion on local dynamics and kinematics

Matteo Carrera*

Institute of Physics, University of Freiburg, Hermann-Herder-Straße 3, D-79104 Freiburg,

Germany

Domenico Giulini†

Institute for Theoretical Physics, University of Hanover, Appelstraße 2, D-30167 Hannover,

Germany

Published 28 January 2010

"Attempts to estimate the influence of global cosmological expansion on local systems are reviewed. Here “local” is taken to mean that the sizes of the considered systems are much smaller than cosmologically relevant scales. For example, such influences can affect orbital motions as well as configurations of compact objects, like black holes. Also discussed are how measurements based on the exchange of electromagnetic signals of distances, velocities, etc. of moving objects are influenced. As an application, orders of magnitude of such effects are compared with the scale set by the apparently anomalous acceleration of the Pioneer 10 and 11 spacecrafts, which is 10^−9 m/s^2. There is no reason to believe that the latter is of cosmological origin. However, the general problem of gaining a qualitative and quantitative understanding of how the cosmological dynamics influences local systems remains challenging, with only partial clues being so far provided by exact solutions to the field equations of general relativity."