Parameterised free functions and saddle stresses in modified gravity

Building on previous work, we explore the parameter space of free functions in non-relativistic modified gravity theories more widely, showing that in fact the two broad regimes present have similar functional forms between different models. Using different parameterisations, we investigate the effects on scaling tidal stresses as well as attempt to constrain the (hitherto poorly understood) deep MONDian scaling C. We also consider a new intermediate MOND limit in these theories and what it tells us about the transition between these regimes. Finally we suggest a model independent framework, with the aim of constraining the MONDian parameter space using future data, such as the forthcoming LISA Pathfinder mission.