The mystery of Dark Matter is really the mystery of why the dynamics (motion) of galaxies and other larger structures do not match the predictions of General Relativity, our current theory of gravity. Calling it the mystery of Dark Matter is to assume that Dark Matter is the solution, which might not be the case. In fact, if antimatter has antigravity, it is possible that no Dark Matter is needed!
So let’s take a step back and see what observations tell us there is a mystery here. In our current theory of gravity, the force of gravity falls off as the square of the distance from the source. For a large spherical body like the earth, the relevant distance is the distance from the center of the body rather than the distance from the surface, so we do not notice the change in the strength of gravity near the surface of the earth, but we can measure it. This means that planets further from the sun feel a weaker gravitational attraction to the sun than closer planets, so the planets must travel slower to stay in orbit around the sun. Neptune orbits the sun at a speed nearly 9 times slower than the speed of Mercury. But when we look at galaxies, this is not what we see! Rather than falling off with distance from the center of the galaxy, stars and gas clouds far from the center of galaxies orbit at nearly the same speed regardless of distance. This is an indication that the force of gravity is stronger than expected, and it is falling off at a different rate than our theory predicts. The same effect is seen in all large structures we observe in the Universe: the force of gravity is stronger than our theory predicts.
The generally accepted explanation for this discrepancy between the predictions of our theory of gravity and observation is that galaxies and other large structures contain substantial amounts of matter that cannot be seen apart from its gravitational interactions. This explanation is so prevalent that it is embodied in the name for the phenomena: Dark Matter. However, this is not the only possible explanation for the discrepancy, and in light of recent findings , it is neither the simplest nor the best explanation. The discrepancy can also be explained by modifying gravity itself. It has long been recognized that a simple modification to the gravitational force law known as Modified Newtonian Dynamics (MOND) fits the observations[2, 3].
It is interesting (and instructive!) to note that the “Dark Matter” problem is not the first case of “missing mass” in astronomy. In the 19th century, astronomers noted that the orbits of some of the planets did not exactly match their theoretical predictions, so they postulated the existence of unknown planets (missing mass) that were perturbing the observed orbits. In the 1840’s, Neptune was discovered at the location predicted by analyzing perturbations in the orbit or Uranus. At the same time, the planet Vulcanwas predicted to explain anomalies in the orbit of Mercury that did not fit the predictions of Newtonian gravity. But despite these anomalies and the “discovery” of Vulcan in 1860, the planet Vulcan does not exist. Rather, we now know that our theory of gravity was incomplete. General Relativity accounts for the anomalies in Mercury’s orbit, not the missing mass of the planet Vulcan.
These historical precedents illustrate the question of whether Dark Matter is real or if it is an indication of a problem with our theory of gravity. Recent experimental and theoretical results suggest the latter. Experimental searches for Dark Matter continue to come up empty, and they have now excluded essentially all the possibilities that used to be considered the most likely places where Dark Matter would be found. Of course, as possibilities were experimentally excluded, the places considered to be the most likely possibilities where Dark Matter would be found have moved, and it is impossible to prove that Dark Matter does not exist with negative results from direct searches since there is always the possibility that Dark Matter’s only interaction is gravitational, leaving no possibility of direct detection. This possibility is usually discounted because, with no additional couplings, there is no mechanism for creating the Dark Matter. Without a coupling between matter and Dark Matter, the “coincidence” that the amount of each in the universe differ by only a small factor is even more remarkable.
But the fact that direct searches have not found Dark Matter in the places we expected to find it is not themain reason to doubt its existence. The primary theoretical reason to doubt the existence of Dark Matter is that all galaxies that have been measured follow an empirical law that Dark Matter does not explain (see figure 2). To put it another way, if Dark Matter were the explanation for holding galaxies together, there are many variations we expect to exist that we never see. Instead, in order to restrict the possibilities to those observed, the distribution of Dark Matter must be entirely constrained by the distribution of visible matter. Since there is no reason this should be true, it is more likely that the gravitational force from the visible matter is different from the prediction of General Relativity.
The best interpretation of the observations appears to be a modification of our theory of gravity rather than adding Dark Matter that we cannot see and have not been able to find, but how can we modify gravity without breaking all the measurements that confirm our current theory, General Relativity? Antigravity for antimatter appears to provide just the right modification. According to quantum mechanics, the vacuum is full of virtual matter-antimatter pairs that continually pop into existence and then disappear before they violate the uncertainty principle. If antimatter is repelled gravitationally from matter, then these virtual pairs will be gravitational dipoles. In a sufficiently strong gravitational field, these dipoles will polarize, and this will affect the gravitational field. We see this vacuum polarization with electric fields, and it is an essential part of the tremendous success of quantum electrodynamics (QED). In QED, the vacuum polarization screens charges, so that electric charges appear to be smaller than their bare charge. This can be measured in interactions at very small distances where the measured electrical charge is larger than at normal distances. But in QED, like charges repel and opposite charges attract, so while the vacuum polarization causes screening in QED, with gravitation it has the opposite effect because like charges attract. Also, because gravity is so much weaker than electromagnetism, the result of this anti-screening is only apparent over large scales such as galaxies. This anti-screening makes the force of gravity stronger, giving the appearance that there is more mass than what is visible (Dark Matter), but this apparent extra mass is really the polarized virtual particles in the vacuum and is fully determined by the gravitational field of the normal matter. The gravitational field from the normal matter is enhanced in such a way that it gives a mechanism for MOND [5, 6, 7]
-  Stacy S. McGaugh, Federico Lelli, and James M. Schombert. Radial acceleration relation in rotationally supported galaxies. Phys. Rev. Lett., 117:201101, 2016. Available from: http://link. aps.org/doi/10.1103/PhysRevLett.117.201101, doi:10.1103/PhysRevLett.117.201101.
-  M. Milgrom. A modification of the newtonian dynamics as a possible alternative to the hidden mass hypothesis. Astrophys. J., 270:365, 1983. Available from: http://adsabs.harvard.edu/ doi/10.1086/161130.
-  Benoˆıt Famaey and Stacy S. McGaugh. Modified newtonian dynamics (mond): Observational phenomenology and relativistic extensions. Living Reviews in Relativity, 15(1):10, 2012. Available from: https://doi.org/10.12942/lrr-2012-10.
-  Gianfranco Bertone and Tim M. P. Tait. A new era in the search for dark matter. Nature, 562:51–56, 2018. Available from: https://doi.org/10.1038/s41586-018-0542-z.
-  Luc Blanchet. Gravitational polarization and the phenomenology of MOND. Classical and Quantum Gravity, 24(14):3529, 2007. Available from: doi:10.1088/0264-9381/24/14/001.
-  Dragan Slavkov Hajdukovic. Is dark matter an illusion created by the gravitational polarization of the quantum vacuum? Astrophys Space Sci, 334:215, 2011. doi:10.1007/ s10509-011-0744-4.
-  Dragan Slavkov Hajdukovic. Virtual gravitational dipoles: The key for the understand- ing of the universe? Physics of the Dark Universe, 3:34 – 40, 2014. Available from: http://www.sciencedirect.com/science/article/pii/S2212686414000077, doi: 10.1016/j.dark.2014.03.002.