The remarkable feature of GEA theories allowing for the desired enhancing of gravitational lensing
without any on the form of the physical metric is that, writing the metric as in Eq. 73, it can be
shown [431] that in the limit
the action of Eq. 93
is only a function of
and is
thus invariant under disformal transformations
, of the type of Eq. 83
.
These GEA theories are currently extensively studied, mostly in a cosmological context (see Section 9), but
also for their parametrized post-Newtonian coefficients in the solar system [65] or for black hole
solutions [451].
Interestingly, it has been shown that all these vector field theories (TeVeS, BSTV, GEA) are all part of a
broad class of theories studied in [183]. Yet other phenomenologically-interesting theories exist among this
class, such as, for instance, the models considered by Zhao & Li [502, 506, 510] with a dynamical
norm vector field, whose norm obeys a potential (giving it a mass) and has a non-quadratic
kinetic term à-la-RAQUAL, in order to try reproducing both the MOND phenomenology
and the accelerated expansion of the universe, while interpreting the vector field as a fluid
of neutrinos with varying mass [504, 505]. This has the advantage of giving a microphysics
meaning to the vector field. Such vector fields have also been argued to arise naturally from
dimensional reduction of higher-dimensional gravity theories [34, 261], or, more generally, to be
necessary from the fact that quantum gravity could need a preferred rest frame [206] in order to
protect the theory against instabilities when allowing for higher derivatives to make the theory
renormalizable (e.g., in Hořava gravity [64, 195]). Inspired by this possible need of a preferred rest
frame in quantum gravity, relativistic MOND theories boiling down to particular cases of GEA
theories in which the vector field is hypersurface-orthogonal have, for instance, been proposed
in [61, 396].
http://www.livingreviews.org/lrr-2012-10 |
Living Rev. Relativity 15, (2012), 10
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