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 [22] 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 [431], 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 [122], or other very strong field
effects^{50}.
However, these effects can always generically be suppressed (at the price of introducing a Galileon type term
in the action [22]), 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 [513], 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 [503].

Living Rev. Relativity 15, (2012), 10
http://www.livingreviews.org/lrr-2012-10 |
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