Field-theoretical formulations of MOND-like gravity (0705.4043v2)

Abstract: 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 (TeVeS) one of Bekenstein and Sanders, seem more promising than others, and our discussion underlines in which directions one should try to improve them.

• The paper critically examines field-theoretical models that reproduce flat galaxy rotation curves without dark matter.
• It assesses theoretical limitations including fine-tuning, no-go theorems, and challenges in ensuring stability and a well-posed Cauchy problem.
• The study proposes improvements in TeVeS and scalar-tensor approaches, emphasizing implications for solar-system and binary pulsar tests.

Field-theoretical Formulations of MOND-like Gravity: An Analysis

The paper "Field-theoretical formulations of MOND-like gravity" by Bruneton and Esposito-Farese systematically evaluates Modified Newtonian Dynamics (MOND) through the lens of field theory, presenting a critical examination of various attempts to ground MOND-like models within a coherent theoretical framework. The objective is to construct a model that obviates the need for dark matter by modifying gravitational theory to explain astronomical phenomena such as flat galaxy rotation curves. A notable challenge lies in ensuring consistency and stability, while also deriving field equations that admit a well-posed Cauchy problem.

Key Insights and Challenges

1. Resolving Galactic Dynamics without Dark Matter: MOND proposes a modification to Newton's laws at very low accelerations. The challenge is to derive these modifications from a stable and consistent field theory. The paper assesses several theoretical frameworks for MOND and notes their successes and failures from dual perspectives: experimental evidence and field-theoretical consistency.
2. Theoretical Limitations and No-go Theorems: Many MOND models introduced are steeped in fine-tuning, some of which exhibit theoretical redundancies or are contingent upon potentially unnecessary hypotheses. The authors critically evaluate these shortcomings, acknowledging past no-go theorems, while suggesting that the landscape for viable models may indeed be broader than previously acknowledged.
3. Stability and Consistency: A perpetual obstacle has been maintaining model stability while reproducing MOND physics. A central concern is the viability of model formulations within the local and cosmological frameworks, specifically how these models handle predictions, such as those relating to light deflection and other high precision tests of General Relativity (GR).
4. Experimental Incompatibilities: Despite MOND's appeal in certain regimes, challenges persist in recovering empirical consistency with solar-system and binary-pulsar tests. The paper emphasizes that many models either fall short in the solar-test predictions or require unnatural fine-tunings that run counter to Occam's Razor.
5. Proposals for Improving TeVeS Models: The Tensor-Vector-Scalar (TeVeS) models hold potential but are not without limitations. Issues such as instability in the Hamiltonian formulation are addressed, indicating potential paths for improvement. The paper highlights these in discussing models that attempt to reconcile MOND predictions with real-world gravitational measurements.

Implications and Future Directions

The pursuit of a MOND-like theory pushes the frontiers of gravitational physics, challenging the dark matter paradigm core to contemporary cosmological models. While the paper does not declare any MOND formulation as definitively superior, it provides a roadmap for future investigations, especially those involving scalar-tensor theories and disformal couplings. A key takeaway is the confirmation that while MOND-like theories face challenges, they remain invaluable for inspiring nuanced exploration of gravitational phenomena.

The authors' examination of stability and field-theoretical issues reveals productive angles for ongoing research. Specifically, extensions to TeVeS models and novel strategies for engaging with the instability issues could yield promising results. Importantly, empirical compatibility with observations, notably from binary pulsars and gravitational wave detections, remain pivotal areas for further exploration.

In conclusion, "Field-theoretical formulations of MOND-like gravity" offers a thorough critique and synthesis of efforts to underpin MOND within a consistent field-theoretical base. It positions itself as a critical resource for researchers endeavoring to reconcile empirical observations with the theoretical elegance of modified gravitational theories.