Field-theoretical formulations of MOND-like gravity

Modified Newtonian dynamics (MOND) is a possible way to explain the flatgalaxy rotation curves without invoking the existence of dark matter. It ishowever quite difficult to predict such a phenomenology in a consistent fieldtheory, free of instabilities and admitting a well-posed Cauchy problem. Weexamine critically various proposals of the literature, and underline theirsuccesses and failures both from the experimental and the field-theoreticalviewpoints. We exhibit new difficulties in both cases, and point out the hiddenfine tuning of some models. On the other hand, we show that several publishedno-go theorems are based on hypotheses which may be unnecessary, so that thespace of possible models is a priori larger. We examine a new route toreproduce the MOND physics, in which the field equations are particularlysimple outside matter. However, the analysis of the field equations withinmatter (a crucial point which is often forgotten in the literature) exhibits adeadly problem, namely that they do not remain always hyperbolic. Incidentally,we prove that the same theoretical framework provides a stable and well-posedmodel able to reproduce the Pioneer anomaly without spoiling any of theprecision tests of general relativity. Our conclusion is that all MOND-likemodels proposed in the literature, including the new ones examined in thispaper, present serious difficulties: Not only they are unnaturally fine tuned,but they also fail to reproduce some experimental facts or are unstable orinconsistent as field theories. However, some frameworks, notably thetensor-vector-scalar (TeVeS) one of Bekenstein and Sanders, seem more promisingthan others, and our discussion underlines in which directions one should tryto improve them.Comment: 66 pages, 6 figures, RevTeX4 format, version reflecting the changes in the published pape