Experimental constraints on the free fall acceleration of antimatter

In light of recent experimental proposals to measure the free fall acceleration of antihydrogen in the earth's gravitational field, we investigate the bounds that existing experiments place on any asymmetry between the free fall of matter and antimatter. We conclude that existing experiments constrain any such asymmetry to be less than about 10^-7. First we consider contributions to the inertial masses of atoms that encode the presence of antimatter and use precision Eotvos experiments to establish the level at which they satisfy the equivalence principle. In particular we focus on vacuum polarization effects and the antiquark content of nucleons. Second we consider a class of theories that contain long range scalar and vector forces that cancel with one another to some high precision. By construction such theories would be able to evade detection in Eotvos experiments that utilize matter while still allowing for a signal in antimatter experiments. Even taking such cancellation for granted, however, we show that the radiative damping of binary pulsar systems constrains these forces to be significantly weaker than gravity. Furthermore we show that there are limits to the accuracy with which such cancellation can be arranged: first by determining the precision to which scalar charges can track vector charges in the best candidate theories; and, second, by showing that the different velocity dependence of scalar and vector forces necessarily introduces non-cancellation at a quantifiable level.