The relativistic theory of [38] depends on two fields, an “Einstein metric”
and a scalar field
. The
physical metric
entering the matter action is then given by a conformal transformation of the Einstein
metric47
through an exponential coupling function:
Varying the action w.r.t. , the scalar field yields, in a static configuration, the following modified Poisson’s equation for the scalar field:
and the It was immediately realized [38] that a k-essence theory such as RAQUAL can exhibit superluminal
propagations whenever
[80
]. Although it does not threaten causality [80
], one
has to check that the Cauchy problem is still well-posed for the field equations. It has been
shown [80
, 360] that it requires the otherwise free function
to satisfy the following properties,
:
However, another problem was immediately realized at an observational level [38, 40]. Because of the
conformal transformation of Eq. 75
, one has that
in the RAQUAL equivalent of Eq. 73
. In other
words, as it is well-known that gravitational lensing is insensitive to conformal rescalings of the metric,
apart from the contribution of the stress-energy of the scalar field to the source of the Einstein
metric [40, 81
], the “non-Newtonian” effects of the theory respectively on lensing and dynamics do not at
all correspond to similar amounts of “missing mass”. This is also considered a generic problem with any
local pure metric formulation of MOND [441
].
http://www.livingreviews.org/lrr-2012-10 |
Living Rev. Relativity 15, (2012), 10
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