Testing for a cosmological influence on local physics using atomic and gravitational clocks

The existence of a possible influence of the large-scale structure of the Universe on local physics is discussed. A particular realization of such an influence is discussed in terms of the behavior in time of atomic and gravitational clocks. Two natural categories of metric theories embodying a cosmic influence exist. The first category has geodesic equations of motion in atomic units, while the second category has geodesic equations of motion in gravitational units. Equations of motion for test bodies are derived for both categories of theories in the appropriate parametrized post-Newtonian limit and are applied to the Solar System. Ranging data to the Viking lander on Mars are of sufficient precision to reveal (i) if such a cosmological influence exists at the level of Hubble's constant, and (ii) which category of theories is appropriate for a description of the phenomenon