Modified Gravity Without Dark Matter

Abstract

On an empirical level, the most successful alternative to dark matter in bound gravitational systems is the modified Newtonian dynamics, or MOND, proposed by Milgrom. Here I discuss the attempts to formulate MOND as a modification of General Relativity. I begin with a summary of the phenomenological successes of MOND and then discuss the various covariant theories that have been proposed as a basis for the idea. I show why these proposals have led inevitably to a multi-field theory. I describe in some detail TeVeS, the tensor-vector-scalar theory proposed by Bekenstein, and discuss its successes and shortcomings. This lecture is primarily pedagogical and directed to those with some, but not a deep, background in General Relativity

The modified Newtonian dynamics—MOND and its implications for new physics

“…3, MOND cannot handle the dynamics of clusters of galaxies without invoking additional unseen matter. An interesting escape is suggested by Sanders [100]. In BSTV cosmology, just as in the PCG one [63], the σ field can undergo oscillations which generate bosonic particles early on.…”

Nonlocal metric formulations of modified Newtonian dynamics with sufficient lensing

“…Indeed, in the case of rotationally supported systems, MOND provides a simple explanation for (i) the Tully-Fisher relation [9], which states that the observed limiting rotation velocity of galaxies, v ∞ , scales as the fourth root of the baryonic mass of the galaxy (see [10] for a recent dramatic confirmation of this relation); (ii) Milgrom's law, stating that the need for dark matter always seems to occur when the gravitational acceleration falls to about a 0 [11]; (iii) Freeman's law, namely that the surface density never exceeds a 0 /G [12]; and (iv) Sancisi's law, i.e., that bumps in the rotation curves are correlated to the baryonic mass [12]. For pressure-supported systems, MOND also explains their typical size R = GM/a 0 and predicts a stellar velocity dispersion σ ∝ (GM a 0 ) 1/4 [13,14], explaining thus the Faber-Jackson relation [15]. MOND also was able to predict properties of low surface brightness galaxies that were eventually confirmed by observation [16,17].…”

Do Modified Newtonian Dynamics Follow from the Cold Dark Matter Paradigm?

“…(See also the plot of the v ϱ dynamical at the last measured point on galaxies as a M/L K function of the rotational acceleration there in Fig. 1 of Sanders 2001. ) 3.…”

“…The acceleration controls the dynamics of all galaxy a 0 system, such as galaxy groups (Milgrom 1998(Milgrom , 2002, clusters (Sanders 1999), and large-scale filaments (Milgrom 1997), where MOND has been shown to explain away the need for DM. It has been pointed out that MOND does not yet explain away DM in the inner part of X-ray galaxy clusters (e.g., The & White 1988;Gerbal et al 1992;Aguirre, Schaye, & Quataert 2001).…”

“…One still has to invoke the presence of (baryonic) DM awaiting to be discovered there. Clusters at large, however (say, within 2 Mpc of the center), are explained by MOND (Sanders 1999).…”