No abstract

Observations of spiral galaxies strongly support a one-to-one analytical relation between the inferred gravity of dark matter at any radius and the enclosed baryonic mass. It is baffling that baryons manage to settle the dark matter gravitational potential in such a precise way, leaving no "messy" fingerprints of the merging events and "gastrophysical" feedbacks expected in the history of a galaxy in a concordance Universe. This correlation of gravity with baryonic mass can be interpreted from several non-standard angles, especially as a modification of gravity called TeVeS, in which no galactic dark matter is needed. In this theory, the baryon-gravity relation is captured by the dieletric-like function µ of Modified Newtonian Dynamics (MOND), controlling the transition from 1/r 2 attraction in the strong gravity regime to 1/r attraction in the weak regime. Here, we study this µ-function in detail. We investigate the observational constraints upon it from fitting galaxy rotation curves, unveiling the degeneracy between the stellar mass-to-light ratio and the µ-function as well as the importance of the sharpness of transition from the strong to weak gravity regimes. We also numerically address the effects of non-spherical baryon geometry in the framework of non-linear TeVeS, and exhaustively examine how the µ-function connects with the free function of that theory. In that regard, we exhibit the subtle effects and wide implications of renormalizing the gravitational constant. We finally present a discontinuity-free transition between quasi-static galaxies and the evolving Universe for the free function of TeVeS, inevitably leading to a return to 1/r 2 attraction at very low accelerations in isolated galaxies.

Field theories with Lorentz (or diffeomorphism invariant) action can exhibit superluminal behavior through the breaking of local Lorentz invariance. Quantum induced superluminal velocities are wellknown examples of this effect. The issue of the causal behavior of such propagation is somewhat controversial in the literature and we intend to clarify it. We provide a careful analysis of the meaning of causality in classical relativistic field theories and stress the role played by the Cauchy problem and the notion of chronology. We show that, in general, superluminal behavior threatens causality only if one assumes that a prior chronology in spacetime exists. In the case where superluminal propagation occurs, however, there are at least two nonconformally related metrics in spacetime and thus two available notions of chronology. These two chronologies are on equal footing, and it would thus be misleading to choose ab initio one of them to define causality. Rather, we provide a formulation of causality in which no prior chronology is assumed. We argue that this is the only way to deal with the issue of causality in the case where some degrees of freedom propagate faster than others. In that framework, then, it is shown that superluminal propagation is not necessarily noncausal, the final answer depending on the existence of an initial data formulation. This also depends on global properties of spacetime that we discuss in detail. As an illustration of these conceptual issues, we consider two field theories, namely, k-essence scalar fields and bimetric theories of gravity, and we derive the conditions imposed by causality. We discuss various applications such as the dark energy problem, modified-Newtonian-dynamics-like theories of gravity, and varying speed of light theories.