Tensor–vector–scalar gravity, developed by Jacob Bekenstein in 2004, is a relativistic generalization of Mordehai Milgrom's Modified Newtonian dynamics paradigm. The main features of TeVeS can be summarized as follows:
These components are combined into a relativistic Lagrangian density, which forms the basis of TeVeS theory.
Details
MOND is a phenomenological modification of the Newtonian acceleration law. In Newtonian gravity theory, the gravitational acceleration in the spherically symmetric, static field of a point mass at distance from the source can be written as where is Newton's constant of gravitation. The corresponding force acting on a test mass is To account for the anomalous rotation curves of spiral galaxies, Milgrom proposed a modification of this force law in the form where is an arbitrary function subject to the following conditions: In this form, MOND is not a complete theory: for instance, it violates the law of momentum conservation. However, such conservation laws are automatically satisfied for physical theories that are derived using an action principle. This led Bekenstein to a first, nonrelativistic generalization of MOND. This theory, called AQUAL is based on the Lagrangian where is the Newtonian gravitational potential, is the mass density, and is a dimensionless function. In the case of a spherically symmetric, static gravitational field, this Lagrangian reproduces the MOND acceleration law after the substitutions and are made. Bekenstein further found that AQUAL can be obtained as the nonrelativistic limit of a relativistic field theory. This theory is written in terms of a Lagrangian that contains, in addition to the Einstein–Hilbert action for the metric field, terms pertaining to a unit vector field and two scalar fields and, of which only is dynamical. The TeVeS action, therefore, can be written as The terms in this action include the Einstein–Hilbert Lagrangian : where is the Ricci scalar and is the determinant of the metric tensor. The scalar field Lagrangian is where is a constant length, is the dimensionless parameter and an unspecified dimensionless function; while the vector field Lagrangian is where while is a dimensionless parameter. and are respectively called the scalar and vector coupling constants of the theory. The consistency between the Gravitoelectromagnetism of the TeVeS theory and that predicted and measured by the Gravity Probe B leads to, and requiring consistency between the near horizon geometry of a black hole in TeVeS and that of the Einstein theory, as observed by the Event Horizon Telescope leads to So the coupling constants read: The function in TeVeS is unspecified. TeVeS also introduces a "physical metric" in the form The action of ordinary matter is defined using the physical metric: where covariant derivatives with respect to are denoted by TeVeS solves problems associated with earlier attempts to generalize MOND, such as superluminal propagation. In his paper, Bekenstein also investigated the consequences of TeVeS in relation to gravitational lensing and cosmology.
Problems and criticisms
In addition to its ability to account for the flat rotation curves of galaxies, TeVeS is claimed to be consistent with a range of other phenomena, such as gravitational lensing and cosmological observations. However, Seifert shows that with Bekenstein's proposed parameters, a TeVeS star is highly unstable, on the scale of approximately 106 seconds. The ability of the theory to simultaneously account for galactic dynamics and lensing is also challenged. A possible resolution may be in the form of massive neutrinos. A study in August 2006 reported an observation of a pair of colliding galaxy clusters, the Bullet Cluster, whose behavior, it was reported, was not compatible with any current modified gravity theories. A quantity probing General Relativity on large scales for the first time has been measured with data from the Sloan Digital Sky Survey to be consistent with GR, GR plus Lambda CDM and the extended form of GR known as theory, but ruling out a particular TeVeS model predicting. This estimate should improve to ~1% with the next generation of sky surveys and may put tighter constraints on the parameter space of all modified gravity theories. TeVeS appears inconsistent with recent measurements made by LIGO of gravitational waves.
