Concerning the first point, the FLRW solutions have been extensively studied for TeVeS (Sections 7.3
and 7.4, see, e.g., [70]) and GEA (Section 7.7, see, e.g., [515]) theories, for BIMOND (Section 7.8,
see, e.g., [101
]), and for theories based on dipolar dark matter (Section 7.9, see, e.g., [60
]). In
the latter case, the theory [58, 60] has been shown to be strictly equivalent to
CDM out
to first-order cosmological perturbations (but very different in the galaxy formation regime),
together with a natural explanation for
. For the other theories, it has been shown that
the contribution of the extra fields to the overall expansion is subdominant to the baryonic
mass and does not affect the overall expansion [151
]. Such theories can predict an extremely
wide range of cosmological behavior, ranging from accelerated expansion to contraction on
a finite time scale [70]. The key point is that the expansion history mainly depends on the
form of the “MOND function”
for the unconstrained domain
in any of these
theories.
For instance, in TeVeS, in static configurations (see Eq. 85
), and
in evolving homogeneous and isotropic configurations such as the expanding universe. The form of
is clearly constrained from the MOND phenomenology only for
, meaning that a lot of freedom
exists for
. Exactly the same is true in GEA and BIMOND theories [101]. For instance,
Bekenstein [33] originally proposed for TeVeS an
-function (corresponding to
, see Eq. 79
) with a
discontinuity at
(the B04 function on Figure 44
) not enabling galaxies to collapse continuously out
of the Hubble expansion. Afterwards, Zhao & Famaey proposed an improved “mirror-function”
such that the corresponding
-function reproduces the simple
-function (
in Eq. 46
) for
, and
for the cosmological regime
(see Figure 44
, leading to
an acceptable expansion history. However, when connecting a static galaxy to the expanding
universe, the limit
would predict the existence of a singular surface around each
galaxies on which the scalar degree of freedom does not propagate, meaning that it is better to
reconnect the two sides at
(see Section 6.2). In addition, the integration constant
can play the role of the cosmological constant [184] to drive accelerated expansion, but
even some
models can drive late-time acceleration [125], which is not surprising
since k-essence scalar fields were also introduced to address the dark energy problem. In the
case of BIMOND (see Section 7.8), a symmetric matter-twin matter early universe yields a
cosmological constant through the zero-point of the MOND function, thereby naturally leading to
.
All in all, with the additional freedom of a hypothetical dark component in the matter sector, in the
form of, e.g., ordinary or sterile neutrinos, playing with the form of for
in TeVeS, GEA
and BIMOND always allows one to reproduce an expansion history and a Hubble diagram almost precisely
identical to
CDM, justifying the assumption made in Section 8 of an expansion history for gravitational
lensing in relativistic MOND. However, it is important to note that MOND theories are not providing a
unique prediction on this.
http://www.livingreviews.org/lrr-2012-10 |
Living Rev. Relativity 15, (2012), 10
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