Thus, this generalized version is the current “working version” of what is now called TeVeS: a tensor-vector-scalar theory with an Einstein-like metric, an Einstein-Aether-like unit-norm vector field, and a k-essence-like scalar field, all related to the physical metric through Eq. 83. It has been extensively studied, both in its original and generalized form. It has for instance been shown that, contrary to many gravity theories with a scalar sector, the theory evidences no cosmological evolution of the Newtonian gravitational constant and only minor evolution of Milgrom’s constant [145, 39]. However, the fact that the latter is still put in by hand through the length-scale of the theory , and has no dynamical connection with the Hubble or cosmological constant is perhaps a serious conceptual shortcoming, together with the free function put by hand in the action of the scalar field (but see  for a possible solution to the latter shortcoming). The relations between this free function and Milgrom’s can be found in [145, 431] (see also Section 6.2), the detailed structure of null and timelike geodesics of the theory in , the analysis of the parametrized post-Newtonian coefficients (including the preferred-frame parameters quantifying the local breaking of Lorentz invariance) in [173, 372, 391, 450], solutions for black holes and neutron stars in [244, 245, 247, 246, 374, 438, 439], and gravitational waves in [216, 214, 215, 373]. It is important to remember that TeVeS is not equivalent to GR in the strong regime, which is why it can be tested there, e.g., with binary pulsars or with the atomic spectral lines from the surface of stars , or other very strong field effects50. However, these effects can always generically be suppressed (at the price of introducing a Galileon type term in the action ), and such tests would never test MOND as a paradigm. It is by testing gravity in the weak field regime that MOND can really be put to the test.
Finally, let us note that TeVeS (and its generalization) has been shown to be expressible (in the “matter frame”) only in terms of the physical metric , and the vector field , the scalar field being eliminated from the equations through the “unit-norm” constraint in terms of the Einstein metric , leading to . In this form, TeVeS is sometimes thought of as GR with an additional “dark fluid” described by a vector field .
Living Rev. Relativity 15, (2012), 10
This work is licensed under a Creative Commons License.