We review attempts to estimate the influence of global cosmological expansion on local systems. 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. We also discuss how measurements based on the exchange of electromagnetic signals of distances, velocities, etc. of moving objects are influenced. As an application we compare orders of magnitudes of such effects with the scale set by the apparently anomalous acceleration of the Pioneer 10 and 11 spacecrafts, which is 10 −9 m/s 2 . We find 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.

McVittie's spacetime is a spherically symmetric solution to Einstein's equation with an energymomentum tensor of a perfect fluid. It describes the external field of a single quasi-isolated object with vanishing electric charge and angular momentum in an environment that asymptotically tends to a Friedmann-Lemaître-Robertson-Walker universe. We critically discuss some recently proposed generalizations of this solution, in which radial matter accretion as well as heat currents are allowed. We clarify the hitherto unexplained constraints between these two generalizing aspects as being due to a geometric property, here called spatial Ricci-isotropy, which forces solutions covered by the McVittie ansatz to be rather special. We also clarify other aspects of these solutions, like whether they include geometries which are in the same conformal equivalence class as the exterior Schwarzschild solution, which leads us to contradict some of the statements in the recent literature.

Abstract. We give a rigorous derivation of the general-relativistic formula for the two-way Doppler tracking of a spacecraft in Friedmann-Lemaître-Robertson-Walker (FLRW) and in McVittie spacetimes. The leading order corrections of the so-determined acceleration to the Newtonian acceleration are due to special-relativistic effects and cosmological expansion. The latter, although linear in the Hubble constant, is negligible in typical applications within the Solar System. PACS numbers: 95.30. Sf, 04.20.Cv