List of contents
The shape of nucleons and the quark cylinder.
The quark crystal
The equivalent masses of the cylinder and crystal structures.
It is shown that there may exist at least two different forms of dark matter fashioned from existing baryonic matter, specifically, neutrons. The structures developed are considerably more massive than the number of particles from which they are formed and are argued to be candidates for dark matter since they have no electrical charge, no electrons, hence no chemistry and no photonic emission. They can only interact with each other and other baryons through the agency of gravity. Further, one of the forms is much more likely to clump than the other and raises the possibility that there are large-scale formations of different types of the substance, one of which may more easily be disrupted than the other.
This may present further challenges for astronomical experimenters in the task of observing and identifying dark matter, for, on a large scale the distribution of dark matter within, for example, a galaxy may be unique to that constellation. In addition, detection of these structures on a small scale, by the usual method of collision with other matter, may be rendered difficult, if not impossible, for the structures can only be accelerated to high speeds by interacting with intense gravitational fields.
The concept of dark matter has its origin in the study by Zwicky in 1933 of the Coma cluster. He determined that the outlying galaxies in the cluster were moving substantially faster than the calculated velocities based upon the visible mass in the cluster and proposed that the cluster must be composed of over 90% of matter which could not be seen. He christened this matter, dark matter. His calculations were disparaged at the time, but modern estimates agree, fairly closely with this value.
Since the discovery of these anomalous velocities, observations, made by different methods, have established unequivocally that, throughout the universe dark matter is ubiquitous. A fairly comprehensive survey of the evidence for the existence of dark matter may be found in .
Over the years many attempts have been made to explain the nature of dark matter by physicists, principally by the invention of new particles, none of which has, to date been detected, despite heroic efforts so to do. A specific example of a new particle is the axion, favoured by Wilczek  and which had been devised for a problem not connected with dark matter. The non-appearance of these new particles has led to the suggestion that dark matter is not a new particle, but may be some exotic combination of ordinary matter. Some proposals for these combinations are reviewed briefly in the article by Hossenfelder & Lubick, .
It is in this spirit that we present in the following work, two combinations of the same particle of ordinary baryonic matter, namely, the neutron. It is shown that both structures have the property of substantially greater mass than the constituent particles in addition to all of the attributes of dark matter, viz; no electrical charge, no electrons and hence no chemistry and no photonic emission. The model of the vacuum used here is that explained at length in .
The model of the vacuum developed in  exists in two modes, one of which, the sterile mode is considered to be overwhelmingly dominant, in the temporal sense, in the evolution of the universe. The other mode, called the free vacuum mode exists only fleetingly but is of prime importance, for it is posited to be associated with particle formation and the various heatings of baryonic matter described in .
We proceed to examine the free vacuon mode to determine the frequency intervals over which the energy equivalents of the dark matter and baryonic matter are released into space.
These frequency intervals may viewed as proxies for time intervals, and, it is shown that, in the positioning of the frequency intervals close to the inception frequency of the universe it may be inferred that the time intervals for the formation of dark and baryonic matter from the energy released into space, were extremely small.
The energy, associated with the total amount of baryonic matter in the universe is given by:
In this formula is the number of baryons in the universe, considered to be constant outwith the inception phase; the mass, of a baryon is taken to be that of a proton, viz, , although in view of the particle of which the structures are composed, then, pedantically, the mass of the neutron would be more appropriate.
Now, the model predicates that the above energy is directly associated with the liberation of free vacuons into space.
The subscripts on indicate the beginning ‘i’ of the release of free vacuons, whilst ‘f’ denotes the end of the phase.
It is shown in  that if we adopt Eddington’s number of for the number of baryons in the universe, then the number of enclosures, is . From (1) and (2) we get:
Hence, the baryonic matter frequency interval,
If we denote the total masses of dark and baryonic matter in the universe as and , respectively, then it follows from equation (2) that we may write:
Outwith the dark and baryonic matter formation phases, which will be shown to occupy very short time intervals in the evolution of the universe, no more of these matters are made beyond the inception phase and hence the masses of dark and baryonic matter are thereafter constant in time. It then follows that the LHS of equation (4) is, throughout virtually the whole life of the universe, constant. Further, if we divide above and below by the volume, , of the universe at any time the magnitude of the ratio is unchanged, but the LHS now becomes the ratio of the mass densities of dark, to baryonic, matter.
We may determine the magnitude of the density ratio from the results of the WMAP probe . It was found that the current baryonic matter and dark matter mass densities, as proportions of the critical mass density were 4.6% and 24%, respectively.
There is no requirement to determine the actual densities in the modified version of equation (4), for it is plain that the ratio has magnitude, Hence, from equation (4), given that the baryonic frequency has already been established, the dark matter frequency interval is calculated to be:
The shape of nucleons and the quark cylinder.
The Standard Model of particle physics regards the nucleons to be of spherical shape. In the case, specifically of the proton and neutron, it is more correct to say that the quarks, of which these particles are composed are constrained within a spherical envelope.
In keeping with the assertions in  we posit that during the initial stage of the dark matter frequency interval, which we will show should be positioned at the inception of the universe, baryonic matter, wholly in the form of atomic hydrogen was produced. It is in the extreme compression of this matter that it is converted completely into neutrons which are subsequently deformed into the elements of the structures proposed for dark matter.
Montgomery and Jeffrey , propose that the nucleons are not spherical but exist in the form of triangular ovoids with a quark at each vertex. Whilst their work is principally concerned with the structure of the atomic nucleus and attributes structure to the arrangements of the electrical charges of the quarks, it is extended here to describe possible candidates for dark matter.
Given that the initial shape of the neutron is that of a triangular ovoid, then, under the extreme conditions at the inception of the universe we posit that, in the limit, the triangular ovoid may be deformed into a plane equilateral triangle, as shown in Fig1.
illustration not visible in this excerpt
It may be noted that the quarks are located inside the triangle and at the vertices, but are as depicted for the purpose of clarity. If electrical forces are the principal agents of action between neutrons, then the above configuration may be used to show why neutron-neutron pairing does not occur, despite the nucleon having no net charge. The reader is invited to superimpose a copy of the above on the figure. It will be found that there is no orientation where the charges are all attractive. This argument is used by Montgomery and Jeffrey to show that all pairings of neutrons in this superimposed configuration are unstable.