6. Conclusion and discussion

In 1980, the conclusive observation from the flat rotation curves of spiral galaxies was that there existed a significant "mass discrepancy" in spiral galaxies, which was greater if larger distance scales were involved. The flat rotation curves indicated that either Newton's universal law of gravitation and hence the General Theory of Relativity [43] required modification at galactic distances or significantly more mass than the visible mass was required to be present within each galaxy.

The possible mass discrepancy within a galaxy led to the dark matter hypothesis whereby each spiral galaxy is embedded within a huge spherical halo of dark matter. The only alternative to dark matter was considered to be an appropriate modification of Newtonian gravity to provide the required extra gravitational field at large (galactic) distances.

Initially, the dark matter hypothesis was favored, since, at that time, a significant modification of Newtonian gravity was not considered a viable alternative. However, the dark matter hypothesis has several problems: (1) the nature of the proposed dark matter is unknown, although it is considered to be mainly nonbaryonic matter, (2) a dark matter halo has not yet been detected directly, (3) the density profile of a typical halo is required to be fine-tuned in order to produce the observed flat rotation curve of a spiral galaxy, and (4) the lack of dark matter in large globular clusters, which have about the same mass as the smallest dwarf galaxies that are considered to have considerable amounts of dark matter, is a mystery.

Several hypothetical particles have been suggested for the nonbaryonic component of dark matter but, to date, no clear evidence for the existence of any of these particles (axions, WIMPS, or sterile neutrinos) has been obtained.

More recently, modified gravity theories such as the MOND theory have gained popularity, since they overcome most of the problems associated with the dark matter hypothesis. In particular, Mond theory describes the flat rotation curves of spiral galaxies without finetuning, and the globular clusters' lack of dark matter is expected to arise from their much smaller size relative to a dwarf galaxy.

The gravitational interaction of the GM, identified with the very weak, universal, and attractive residual QCD color interactions acting between ordinary matter particles, is essentially equivalent to that of the MOND theory, in that both describe successfully the flat rotation curves of spiral galaxies and the Tully-Fisher relation. However, the GM quantum theory of gravity, based upon a quantum field theory, provides not only a general underlying theory of gravity and hence a more physical understanding of the MOND theory but also a possible understanding of the so-called dark energy causing the observed accelerating expansion of the universe. Indeed, the GM quantum theory describes both dark matter and dark energy in terms of two intrinsic properties of the residual QCD color interactions: antiscreening at galactic distances and finite range at cosmological distances.

The continuing success [44, 45] of the MOND theory together with the underlying GM quantum field theory of gravity is a strong argument against the existence of undetected dark matter halos consisting of unknown matter embedding galaxies.

However, a direct empirical proof of the existence of dark matter is claimed to be provided by two colliding galaxies known as the "bullet cluster" [46]. Observations of the bullet cluster indicate that during the merging process, the dark matter, deduced from gravitational lensing, has passed through the collision point, while the baryonic component of matter, deduced from X-ray emission, has slowed down due to friction and has coalesced within a central region of the combined cluster. This separation of the two kinds of matter is claimed to provide evidence for dark matter. Unfortunately, a similar separation of the regions of non-Newtonian gravity in the MOND and GM gravity theories are expected to occur in the merging of two galaxies such as the bullet cluster, so that these modified gravity theories also describe the merging of the bullet cluster.
