Field-theoretical formulations of MOND-like gravity
By Jean-Philippe Bruneton, G. Esposito-Farèse. 2007
167 citations recorded by the source corpus.
Modified Newtonian dynamics (MOND) is a possible way to explain the flat galaxy rotation curves without invoking the existence of dark matter. It is, however, quite difficult to predict such a phenomenology in a consistent field theory, free of instabilities and admitting a well-posed Cauchy problem. We examine critically various proposals of the literature, and underline their successes and failures both from the experimental and the field-theoretical viewpoints. We exhibit new difficulties in both cases, and point out the hidden fine-tuning of some models. On the other hand, we show that several published no-go theorems are based on hypotheses which may be unnecessary, so that the space of possible models is a priori larger. We examine a new route to reproduce the MOND physics, in which the field equations are particularly simple outside matter. However, the analysis of the field equations within matter (a crucial point which is often forgotten in the literature) exhibits a deadly problem, namely, that they do not remain always hyperbolic. Incidentally, we prove that the same theoretical framework provides a stable and well-posed model able to reproduce the Pioneer anomaly without spoiling any of the precision tests of general relativity. Our conclusion is that all MOND-like models proposed in the literature, including the new ones examined in this paper, present serious difficulties: Not only they are unnaturally fine-tuned, but they also fail to reproduce some experimental facts or are unstable or inconsistent as field theories. However, some frameworks, notably the tensor-vector-scalar one of Bekenstein and Sanders, seem more promising than others, and our discussion underlines in which directions one should try to improve them.
View Paper: https://www.semanticscholar.org/paper/fe49bf574828e4ef6e02f48ae05f0fbbf4a70d76
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Citations in the corpus
- Theory of dark matter superfluidity (2015, background): “The square-root form is necessary to ensure that the action makes sense for time-like field profiles and that the Hamiltonian is bounded from below [69].”
- Disformal invariance of second order scalar-tensor theories: Framing the Horndeski action (2013, result): “21 (2004) 38173829 [40] J.”
- Imperfect Dark Energy from Kinetic Gravity Braiding (2010, background): “[50] (see also the most recent paper [57] and older works [58, 59, 60, 61]) and claim that this superluminality does not imply any inconsistencies.”
- The relativistic pulsar-white dwarf binary PSR J1738+0333 - II. The most stringent test of scalar-tensor gravity (2012, background): “In particular, Bekenstein introduced specific scalar-vector couplings to avoid superluminal propagation, but this is actually not necessary to respect causality (Bruneton 2007; Bruneton & Esposito-Farèse 2007; Babichev, Mukhanov & Vikman 2008).”
- Modified Newtonian Dynamics (MOND): Observational Phenomenology and Relativistic Extensions (2011, background): “The corresponding ?̃?-function for n ≥ 2 has a very peculiar shape of the type shown in Figure 3 of [81] (which might be considered a fine-tuned shape, necessary to account for solar system constraints).”
- Beyond the Cosmological Standard Model (2014, unknown): “Moreover, the relation of the sum of metric potentials to the mass distribution is very close to that of GR in scalar-tensor theories that we have considered [959].”