Case for testing modified Newtonian dynamics using LISA pathfinder

Abstract

We quantify the potential for testing MOdified Newtonian Dynamics (MOND) with LISA Pathfinder (LPF), should a saddle point flyby be incorporated into the mission. We forecast the expected signal to noise ratio (SNR) for a variety of instrument noise models and trajectories past the saddle. For standard theoretical parameters the SNR reaches middle to high double figures even with modest assumptions about instrument performance and saddle approach. Obvious concerns, like systematics arising from LPF self-gravity, or the Newtonian background, are examined and shown not to be a problem. We also investigate the impact of a negative observational result upon the free-function determining the theory. We demonstrate that, if Newton's gravitational constant is constrained not be re-normalized by more than a few percent, only contrived MONDian free-functions would survive a negative result. There are exceptions, e.g. free-functions not asymptoting to 1 in the Newtonian limit, but rather diverging or asymptoting to zero (depending on their mother relativistic MONDian theory). Finally, we scan the structure of all proposed relativistic MONDian theories, and classify them with regards to their non-relativistic limit, finding three broad cases (with a few sub-cases depending on the form of the free function). It is appears that only the Einstein-Aether formulation, and the sub-cases where the free-function does not asymptote to 1 in other theories, would survive a negative result without resorting to "designer" free-functions.