1 | Up to now, all the dark-matter–particle candidates still elude both direct and indirect non-gravitational detection. | |
2 | However, a way to effectively reproduce an apparent universal force law from an exotic dark component could be to enforce an intimate connection between the distribution of baryons, the dark component, and the gravitational field through, e.g., a fifth force effect. This possibility will be extensively discussed in Section 7, notably Section 7.9 | |
3 | The first four sections provide the observational evidence for the MOND phenomenology through the different appearances
of ![]() |
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4 | Arguably, a non-static, expanding or contracting Universe was an a priori prediction of general relativity in its original form, lacking the cosmological constant. | |
5 | However, the WIMP miracle seems to fade away with modern particle physics constraints [23![]() |
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6 | The simplest WIMPs are their own antiparticle. | |
7 | In addition, the time-averaged value of the deceleration parameter ![]() ![]() |
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8 | ![]() |
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9 | We have that ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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10 | As we shall see (Section 5 and 6), MOND was constructed to predict a relation ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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11 | The factor 10 arises from the commonly adopted definition of the virial radius of the dark matter halo at an overdensity of
200 times the critical density of the Universe [332![]() |
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12 | Note that [180] claimed to measure a slope of 3 for the BTFR, but they relied on unresolved line-widths from single dish
21 cm observations to estimate rotation velocity rather than measuring ![]() ![]() |
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13 | The difference in phase space between gas and dark matter also prevents the accretion of tidal gas onto any dark
matter sub-halos that may be present. It does not suffice for a tidal tail to intersect the location of a sub-halo in
coordinate space, they must also dock in velocity space. The gas is moving at the characteristic velocity of the entire
system (typically ![]() ![]() |
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14 | Note that this correlation with acceleration was looked at notably because it was pointed to by Milgrom’s law (see Section 5). | |
15 | The Pioneer anomaly has an amplitude on the order of ![]() ![]() ![]() ![]() |
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16 | Note that such wiggles are often associated with spiral arm features (the existence of which in LSB galaxies being itself challenging in the presence of a massive dark matter halo, see Section 4.2), and hence associated with non-circular motions. It is conceivable that such observed wiggles are partly due to these, but the effect of local density contrasts due to spiral arms on the tangential velocity should be damped by the global effect of the spherical–dark-matter halo, which is apparently not the case. | |
17 | Note that many of these relations were scrutinized during the last 30 years because they were pointed to by Milgrom’s law. Thus, this law has already achieved the important role of a theoretical idea, i.e., to point and direct observations and their arrangement | |
18 | Of course, there is also a natural length scale associated with this acceleration constant, ![]() |
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19 | Note that the denominator ![]() ![]() ![]() |
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20 | Note that the main motivation for modifying dynamics is not to get rid of DM, but to explain why the observed gravitational field in galaxies is apparently mimicking a universal force law generated by the baryons alone. The simplest explanation is, of course, not that DM arranges itself by chance to mimic this force law, but rather that the force law itself is modified. Note that at a fundamental level, relativistic theories of modified gravity often will have to include new fields to reproduce this force law, so that dark matter is effectively replaced by “dark fields” in these theories, or even by dark matter exhibiting a new interaction with baryons (one could speak of “dark matter” if the stress-energy tensor of the new fields is numerically comparable to the density of baryons): this makes the confrontation between modified gravity and dark matter less clear than often believed. The actual confrontation is rather that between all sorts of theories embedding the phenomenology of Milgrom’s law vs. theories of DM made of simple self-uninteracting billiard balls assembling themselves in galactic halos under the sole influence of unmodified gravity, theories, which currently appear unable to explain the observed phenomenology of Milgrom’s law. | |
21 | Generally covariant theories approaching these classical theories in the weak-field limit will then also be classified under this same MOND acronym, even if they really are Modified Einsteinian Dynamics (see Section 7) | |
22 | The Newtonian mass density also satisfies the continuity equation ![]() |
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23 | In general relativity, the first two terms ![]() |
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24 | Let us note in passing that it would not be the first time that the kinetic action would be modified as special relativity
does just this too, changing for a single particle ![]() ![]() ![]() ![]() ![]() ![]() |
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25 | Such non-local theories, which also have to be nonlinear (like any MOND theory) are not easy to construct, and there is presently no real fully-fledged theory, which has been developed in this vein, although hints in this direction are summarized in Section 7.10. | |
26 | Following the dielectric analogy (Section 5.1), this is akin to Maxwell’s first equation, Gauss’ law, in terms of free charge
density ![]() ![]() ![]() ![]() ![]() |
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27 | This is similar to the Palatini formalism of GR, where the present auxiliary acceleration field is replaced by a connection | |
28 | Confusing these two interpolating functions ![]() ![]() ![]() ![]() |
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29 | In principle, ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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30 | In principle, one could make ![]() ![]() ![]() ![]() ![]() ![]() |
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31 | Note that, among the freedom of choice of that function, one could additionally even imagine that the ![]() ![]() ![]() |
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32 | It is interesting to note that different MOND theories offer (very) different answers to the generic question “acceleration
with respect to what?”. For instance, in the MOND-from-vacuum idea (see [304![]() |
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33 | Thus, a Cavendish experiment in a freely falling satellite in Earth orbit would return a Newtonian result in MOND. | |
34 | For instance, using the “simple” function ![]() ![]() ![]() |
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35 | See also [203] and constraints excluding such functions also from Lunar Laser Ranging [138], neglecting the external field effect from the sun on the Earth-Moon system, since it is three orders of magnitude below the internal gravity of the system. | |
36 | This is why, although the “simple” ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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37 | For the ![]() ![]() ![]() ![]() ![]() ![]() |
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38 | Note that the rotation curves of Figure 20![]() ![]() |
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39 | If one assumes that a lot of dark baryons are present in the form of molecular gas, one can add another free parameter in
the form of a factor multiplying the gas mass[460]. The, good MOND fits can still be obtained but with a lower value of
![]() |
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40 | However, the mass-to-light ratio is not really a constant in galaxies. Thus, Figure 22![]() |
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41 | Separable models have also been investigated in [97]. | |
42 | The conventional baryon fraction of clusters increases monotonically with radius [426], only obtaining the cosmic value of
0.17 at or beyond the virial radius. Therefore, one might infer the presence of dark baryons in cluster cores in ![]() |
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43 | If the action has the units of ![]() ![]() ![]() ![]() |
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44 | With this signature, the proper-time is defined by ![]() |
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45 | Note that, at 1PN, this weak-field metric can also be written as ![]() ![]() ![]() ![]() |
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46 | The derived lensing and dynamical masses are typically very close to each other but the data are not yet precise enough to ascertain that they are exactly identical. | |
47 | The frame associated to the Einstein metric is called the “Einstein frame” as opposed to the “matter frame” or “Jordan frame”, associated to the physical metric. | |
48 | k-essence fields have also recently been reintroduced as possible dark energy fluids, that could also drive
inflation [20, 21, 92]. This name comes from the fact that their dynamics are dominated by their kinetic term ![]() |
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49 | Expressed in terms of ![]() ![]() |
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50 | It is also important to remember that some interpolation functions (Section 6.2) are already excluded by solar system tests, and thus, it is useless to exclude these over and over again. | |
51 | A characteristic matter density ![]() ![]() ![]() |
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52 | In the case of TeVeS and GEA theories, the dark fields do not really count as dark matter because their energy density is subdominant to the baryonic one. | |
53 | This is to be contrasted with the time-like nature of TeVeS and GEA vector fields in the static weak-field limit. | |
54 | And the current ![]() ![]() |
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55 | It can be shown that only the projection perpendicular to the four-velocity enters the field equations deduced from the
action of Eq. 100![]() |
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56 | This equality ![]() |
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57 | However, by this we do not mean that the MOND lensing can be computed from the projected surface
density on the lens-plane as in GR, because the convergence parameter (Eq. 113![]() |
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58 | Note that, in order for the problem to be well constrained, a regularization method was used in order to penalize solutions deviating from the fundamental plane as well as face-on solutions and solutions with an anomalous flux ratio or M/L ratio (see Eq. 21 of [419].) | |
59 | Note, however, that this is not always the case in colliding clusters: Abell 520 actually provides a counter-example to the bullet cluster in which the mass peaks indicated by weak lensing do not behave as collisionless matter should [210]. | |
60 | Even if BAO features are present at high redshift in MOND, it is not clear that low redshift structures will correlate with the ISW in the CMB as they should in conventional cosmology because of the late time non-linearity of MOND. | |
61 | Perhaps the most famous modern example of confirmation bias is in measurements of the Hubble constant [466], where
over many years de Vaucouleurs persistently found ![]() ![]() ![]() |
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62 | At ![]() |
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63 | Determining agreement between independent observations requires that we believe not just the result (e.g., the value of
![]() ![]() ![]() |
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64 | The third possibility actually means either non-local effects in non-local theories (Section 7.10), or the effect of additional fields in local modified gravity theories. The important difference with CDM is that these fields are not simply representative of collisionless massive particles, that their behavior is determined by the baryons in static configurations, and that they can be subdominant to the baryonic density. In theories where their energy density dominates that of baryons, these new fields then really act as dark matter in the early universe, which is also a possibility (see Section 7.6 and 7.9) | |
65 | In TeVeS, the perturbations of the scalar field also play an important role in generating enhanced growth [146]. | |
66 | Ferreira’s talk, Alternative Gravities and Dark Matter Workshop, Edinburgh, April 2006. | |
67 | The ISW effect can be cast as the integral of ![]() |
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68 | Note that the presence of non-baryonic matter in the form of massive neutrinos also helps damping the baryonic acoustic
oscillations [127![]() ![]() ![]() |
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69 | This means that, on surfaces of constant temperature, the densities of the various components (e.g. baryons, neutrinos, additional dark fields) are uniform, and that these components share a common velocity field. | |
70 | [279![]() |
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71 | The observed shock velocity of ![]() ![]() |
http://www.livingreviews.org/lrr-2012-10 |
Living Rev. Relativity 15, (2012), 10
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