Does Hawking cosmology provide a natural explanation and improved prediction algorithm for galactic rotation curves and cluster velocity dispersion? How can we get to the truth of the universe? How successful has humanity been in exploring the universe? Do we humans know where we are in the universe? How old is the universe? How old are the oldest stars?

Hawking’s cosmology logically leads to an observed multiverse. Hawking’s cosmology argues it is a superposition of at least three 3-dimensional universes in a 4-dimensional space, of which two dimensions overlap with our universe. Nothing that could disturb the superposition exists outside it. This explains why dark ma,er causes a linear decrease in gravity with distance to visible mass at large radii in galaxies. To support this, the visible ma,er distribution in the disks and bulges, calculated by the SPARC team, and the observed rotation velocities have been used. Lelli and Mistele showed that the common way to project dark ma,er halos around galaxies cannot be valid. General Relativity seems to need these halos too, but in this article it is shown a valid alternative is to model dark ma,er as three added wire-like masses in the centre of galaxies. Bekensteins TeVeS follows another path, but still can be used to compute the decay of the contribution of dark ma,er to gravity with the expansion of space. This explains the rapid development of large galaxies in the early universe as reported by Labbé. A new prediction method for rotation velocities, that works at all radii in galaxies, is 19 to 27 % more accurate than MOND and TeVeS. In galaxy clusters the improvement of the predicted velocity dispersions is 44 to 57 % over a huge range of cluster masses. Keywords: dark ma,er; galaxies; clusters; SPARC; multiverse; superposition; linear gravity, naturalness The hypothesis of dark ma,er is a way to explain why among other galaxies seem not to obey Newton’s law of gravity. As well, dark ma,er is needed to explain the statistical distribution of ‘cold’ and ‘hot’ spots in the background radiation, that would still need the existence of (much) dark ma,er vs. baryonic ma,er to be understandable in terms of Big Bang nucleosynthesis, as well as ma,ers like gravitational lensing. Nevertheless, there exist several alternative approaches to account for the additional gravity it yields, like Modified Newtonian Dynamics (MOND) [1-2], Bekenstein’s TensorVectorScalar gravity (TeVeS) [3] or Covariant Emergent Gravity (CEG) [4]. But, they assume dark ma,er does not really exist, and so leave the other ma,ers mentioned up here, and the gravity in galaxy clusters, see Banik [2], unresolved. Besides that, they do not give a natural explanation for the concepts and additional fields they introduce. Therefore, in the article in hand the existence of dark ma,er is the starting point. As recommended by Banik in Symmetry [2], a hybrid approach will be presented. It is based upon the real existence of dark ma,er and so as to describe its effect on gravity, it applies the cylindrically symmetric solution of the Einstein field equations from Levi-Civita [5] as described by Santos [6]. It will be argued that it logically follows from Hawking’s Cosmology [7,8]. It solves the problem that Lelli and Mistele [9] showed, that the common way to project dark ma,er halos around galaxies cannot be valid, since the alternative naturally assumes dark ma,er is distributed like the visible ma,er in a galaxy, but in a wire-mass shape, consistent with [5] and [6]. The hypothesis gives a natural explanation of dark ma,er, why it is undetectable and why its gravity shows behaviour as described in general by TeVeS theory, which in the Newtonian limit resembles MOND and is employed as well in the paper in hand. The term naturalness is extensively discussed by Hossenfelder [10] (p. 57). In short it means that a theory is without fine-tuned constants. General Relativity (GR) in galaxies seems to need the said halos too so as to properly include the effect of dark ma,er, but in this paper an alternative is proposed and argued: three orthogonal wiremasses of dark ma,er through the galaxy centre based upon [5] and [6]. Or, alternatively, GR must be modified with some additional terms to make correct solutions possible without these halos. Bekenstein’s TeVeS [3] follows that alternative path and is employed in this paper too as a useful tool, because he studied the evolution in time, but only as a mathematical description of dark ma,er. This goes together well with this hypothesis, since it considers dark ma,er to be in the galaxies in the form of a wire-mass, described by a linear mass density, a,racted by the visible ma,er, instead of in halos. This is why this hypothesis is called hybrid in the above. In this paper the Spier Space Telescope satellite data of 175 galaxies, SPARC, as processed and reported by Lelli et al. [11] and Starkman et al [12] are used to assess several predictions that follow from this theory. The mass-to-light ratio has been used as the only fi,ing parameter to fit the baryonic rotation velocity, and hence the baryonic gravitational acceleration, in each galaxy to the observed values near the centre of the galaxies. After that, the hypothesis in hand is used to predict the additional gravitational acceleration at all radii without any further fi,ing and to compare the predictions with the observed values. After a brief introduction of Big Bang theory in chapter 2.1 and Hawking’s cosmology in chapter 2.2 and some other indispensable literature about quantum systems in chapter 2.3, MOND and TeVeS will be discussed in chapter 2.4. This forms the fundament for the proposal presented in chapter 3. In chapter 3 the proposal will stepwise be derived in a logical manner from Hawking’s cosmology and String theory. In chapter 4 this will all be worked out. Firstly, an interpretation of the MOND like behaviour of dark ma,er as a sum of two fields will be proposed. Secondly, the natural basis for this will be explored in chapter 4.2 and in chapter 4.3. In the rest of chapter 4, the hypothesis for dark ma,er will be elaborated and its consequences and behaviour will be explored. In chapter 5, six testable predictions are proposed and proved, one using the work of Levi-Civita, and in chapter 5.3 an improved alternative to MOND for the prediction of rotation velocities as well as velocity dispersions in clusters in the Newtonian limit is presented. In chapter 5.4 TeVeS will be elaborated and used to prove a prediction about the evolution in time of the gravitational acceleration by dark ma,er. It will be shown this evolution gives a much improved prediction for dispersion velocities in a wide range of NGC and Abell clusters. In chapter 6 the conclusions and suggestions for further work are presented. 2. Hawking´s Cosmology and Superposition State of Universe, MOND and TeVeS In this chapter the fundament for the proposal of chapter 3 will be laid, by giving an overview of existing theories that contain vital building elements. 2.1. Big Bang Theory The line of thought of the universe as a quantum system is an elaboration of Hartle & Hawking [7]. The universe, according to the Big Bang theory, comes from an infinitesimal small point in which only elementary particles existed in the form of a plasma, with an extremely high temperature [13] (pp. 127-136) and as a result was in a quantum state, see chapter 4. The originally extremely high temperature is still visible and measurable in the so-called background radiation. Its properties are direct evidence that the universe originated from a hot Big Bang stage. The Big Bang theory is also a logical extrapolation of the expansion of the universe that we observe, among other things due to the redshift of the spectrum of the radiation of stars, but also of the history/evolution of stars and galaxies as visible through our telescopes. In addition, the nonuniform distribution of stellar objects as quasars over the different redshifts proves the universe is not static.Moreover, Big Bang theory can quantitatively explain many phenomena, such as the distribution over the various elements of the mass in the universe, the cosmic composition, based on nuclear physics. The fact that it is dark at night also proves that the universe cannot be infinitely large and infinitely old, because then the entire sky would be filled with light from stars. So, our universe indeed has a beginning. Moreover, the Big Bang theory forms a well-cohesive whole with astronomy and the rest of physics. 2.2. Hawking´s Cosmology and String theory Somewhere at the beginning, our universe has been in a quantum state, because thatʹs where one ends upon extrapolating the expansion of the universe back to the very smallest starting point, [7-8] have derived solutions to the wave function of the universe as proposed by Evere, [14] and further elaborated by DeWi, [15]. As derived and explained by Hartle & Hawking [7] these solutions must satisfy the Wheeler-DeWi, equation. Hartle & Hawking [7] show the Wheeler-DeWi, equation has the following form:Where | ѱ⟩ is the wave function of the universe and where Ĥ(x) is called the Hamiltonian constraint, [7]. The Hamiltonian, in this case derived from General Relativity [7], describes the total energy of a system and Ĥ is the Hamiltonian operator [16] (p. 27). The so-called constraint described by (1) follows from the total energy of the universe being zero, gravitational energy cancelling out the mass energy. Hawking’s & Hartle’s solutions of this equation describe a universe that has no beginning, the Hartle-Hawking state, [7]. Hawking [8] explains this in simpler terms as well: time must have been indeterminate there on the smallest scale in that quantum state, because of the extreme gravitational warpage of space-time at that moment, [8] (p. 172). The time t=0 therefore is not precisely defined and at these scales time reduces to a fourth spatial dimension. So, the universe has no exact measurable beginning. Hawking calls this the ‘no-boundarycondition’, [8] (pp. 172-173). It makes it impossible to trace the development of our universe from the beginning to this time in a deterministic ‘bo,om-top’ way and, hence, there is a need for a statistical ‘top-down cosmology’, considering all possible alternative histories of the universe. He states that as a consequence of this, at the very beginning time acted as a fourth spatial dimension, ”In the early universe-when the universe was small enough to be governed by both general relativity and quantum theory, there were effectively four dimensions of space and none of time”, [8] (p. 172) This is the starting point of the proposal of this paper. String theory, however, suggests as much as eleven dimensions, but using the minimum of four is more economical and easier to understand. The quantum aspects of the Big Bang become clearer when considering so-called ‘double-slit’ experiments, with a light beam split in two that are directed at a wall with two narrow slits. Especially the variant where only one photon is fired at a time. The same interference pa,erns then arise as with continuous beams of photons, so the probability waves of single photons interfere with themselves, as it were. One photon behaves as if it passed through both slits. That can only happen if the photon itself follows all possible alternative paths simultaneously, as it were like a split probability wave. So, the behaviour of the single photon can be seen as a superposition of all possible alternative paths it follows, so alternative histories, [8] (p.104). The superposition causes wave interference and that determines the paths the photon follows in the experiment.Hawking’s and other’s point about the probabilities is that a quantum experiment will only have a certain outcome when it is performed. The Big Bang can be regarded as such an experiment [8] p. 179), where the universe in the quantum state may have had a statistical probability distribution of many ‘alternative histories’, following the interpretation of Feynman. Maybe 10500 ones as String theory and the more general M theory suggest, [8] (pp. 152 and 181). At page 77 Hawking states that “the universe does not have a single existence or history, but rather every possible version of the universe exists simultaneously in what is called a quantum superposition”.This does not a-priori imply we still are in a real a state of superposition between all, or part of these alternative histories now, but this paper will argue that this is indeed the case with our universe for a specific part of these histories. The parameters and hence the quantum state of our universe are known now. Our universe has known single values for the fundamental parameters and constants. Of all the ‘alternative histories’, ours is the one that has come true. The experiment has been performed; we know the outcome. This is only possible when there is an observer to the experiment, [8] (pp. 107 and 179). This where the idea of an ‘observed universe’ of Hawking and others like Wheeler comes from. The assumption is that man or other sentient beings can perform this role of external observer, as Hawking and Wheeler argue, based upon the ‘delayed-choice’ experiment by Wheeler, see Zeilinger’s overview [17]. That shows that the moment of time where the observer enters the history is not relevant [8] p. 106-107), which is consistent with Zeilinger’s interpretation and conclusions in [17] and the citation in chapter 5.5. The ideas in Hawking’s cosmology [7] are consistent with certain approaches to quantum gravity, such as String theory. The idea from Hawking that space and time are quantum phenomena are central themes in quantum gravity research. The Feynman path integrals that Hawking uses, are an important computational method in quantum gravity, especially in the context of Euclidean quantum gravity. This is explained by himself in [7]. This work provides an early foundation for later developments in quantum cosmology, like String theory, and the idea that gravity itself is a quantum phenomenon. From String theory, the assumption in the article in hand of more dimensions in a multiverse has been taken over, which thus is consistent with taking Hawking’s cosmology as a starting point for the theory of the article in hand. But, there yet is no direct evidence for String theory. Future experiments in gravitational waves, particle physics and cosmology could provide clues. If the LHC or future accelerators find supersymmetry, it would be a boost for String theory and hence the assumption of the article in hand. But, String theory does shed light on the behaviour of black holes. Strominger and Vafa [18] in 1996 showed that in String theory the entropy of certain extremal black holes exactly matches the Bekenstein-Hawking formula [18]. They calculated the number of microscopic states of D-branes and found a perfect match. Maldacena [19] in 1999 introduced the AdS/CFT correspondence, a duality rooted in String theory, that couples gravity in a (D+1)-dimensional anti-de Si,er space to a D-dimensional conformal field theory. This idea has major implications for the so-called black hole information paradox. The black hole information paradox is the problem that, according to Hawkingʹs calculations, information appears to be lost when a black hole evaporates due to Hawking radiation, which violates the laws of quantum mechanics that require that information is always conserved. Maldacena’s duality suggests that information is not lost but remains encoded in the dual theory. Mathur [20] in 2003 proposed that black holes do not contain a singularity, but instead consist of a complex collection of string states, or a fuzzball. This potentially solves the information paradox, because information can be stored in the quantum structure of the fuzzball instead of being destroyed in a singularity. This all is support for the String theory and hence for the assumptions it makes. In the meanwhile, it is fruitful to explore the potential for a natural explanation of what dark ma,er is, as is done in the article in hand. 2.3. How a Superposition State Can Have Classical Effects Quantum superposition can be forced by a beam-spli,er like in the famous ‘double-slit’ experiment discussed up here. It can be forced as well by a dedicated device like in a Qubit or in an MRI-scanner. A tensor-interaction like in the deuteron may as well yield a superposition state. The la,er will be discussed into more depth in the sequel, since it might be very relevant to the behaviour of our universe. So, quantum effects can affect classical effects through a variety of mechanisms, with microscopic quantum phenomena affecting macroscopic classical phenomena. A deuteron Is a bare proton and a neutron, glued together, without electrons. It forms a vital step in the fusion of helium, and thus of the existence of stars. The binding force between the neutron and the proton is the sum of the resulting forces of the superposition of two quantum spin states, see Bethe [21]. So, this force would not be strong enough if the deuteron were in just one of those states. It is evident this has a huge classical impact. Another example is superconductivity. Superconductivity occurs when electrons behave as a collective quantum mechanical entity, completely eliminating electrical resistance. This has applications in powerful magnets and lossless current transport, Ginzburg et al [22]. In the early stages of the universe, quantum fluctuations caused variations in the density of ma,er, which later evolved into the large-scale structures of the universe such as galaxies and clusters, Guth [23]. Chemical reactions, enzymatic processes and even biological phenomena such as photosynthesis are influenced by quantum mechanical principles, which has macroscopic consequences, McFadden et al [24]. This all is essential to the following part of this paper: as with the single photon in the doubleslit or with the deuteron, our universe could still be in a superposition of multiple histories. The result should be able to interfere with itself very well like the single photon, and forces like gravity might add up like in the deuteron. It will be argued why for electro-magnetism this cannot have a measurable impact. These possibilities for classical effects lead to a testable hypothesis of the nature of dark ma,er. But firstly, MOND and TeVeS theories are briefly visited, because they give a mathematical description of the gravitational effects of dark ma,er of which some starting points are used in the article in hand.

Conclusions and Suggestions for Further Work The hypothesis of dark ma,er is a way to explain why among other galaxies seem not to obey Newton’s law of gravity. As well, dark ma,er is needed to explain the statistical distribution of ‘cold’ and ‘hot’ spots in the background radiation, that would still need the existence of (much) dark ma,er vs. baryonic ma,er to be understandable in terms of Big Bang nucleosynthesis, as well as ma,ers like gravitational lensing and gravity in galaxy clusters. Alternative approaches like MOND and TeVeS work well to describe the flat rotation curves in galaxies as such, but do not give a natural explanation for the concepts and additional fields they introduce. In this paper, as recommended by Banik in Symmetry, a hybrid approach to dark ma,er is presented, in which Bekensteins TeVeS is applied as well, but only as a mathematical tool to describe gravity. But, it should be insisted, the existence of dark ma,er is taken as a starting point in this article. A natural explanation for the nature of dark ma,er is presented based upon Hawking’s cosmology and String theory that has its foundations in it. The conclusion is that the universe consists of four 3-dimensional universes, existing as at least four states of a superposed 4-dimensional multiverse, which each have two overlapping dimensions with the observed universe. For there is nothing outside it that could disturb the superposition state, it could be in that state forever, without de-coherence effects ending it. That is why Hawking and others can speak of the wave function of the universe in the first place. The superposition leads to the existence of additional baryonic ma,er, but in superposed universes and hence ‘dark’, with gravity that a,racts ma,er in other superposed universes through the 2-dimensional intersections. The 2-dimensionality of the intersections explains both why the additional gravitational acceleration decreases linearly with distance and why electromagnetic waves cannot propagate through it. And this, together with the orthogonality of superposition states, gives a natural explanation for dark ma,er particles being undetectable. Gravity from dark ma,er and visible ma,er is very well interpreted as the sum of two gravitational accelerations. Modelling dark ma,er as a set of three orthogonal line masses with the Levi-Civita metric and adding this to the Schwarzschild metric for a baryonic point mass, gives a valid solution of the Einstein field equations in the weak fields that occur in the galaxies studied and directly leads to the Tully-Fisher relation. In each galaxy, one constant value for the ratio between the surplus acceleration and the sum of all mass-density over distance can be determined. This will be called the ‘linear constant of gravity’, GL. From the values of the calculated baryonic and the observed velocities in galaxies in the SPARC data, an average value for the gravitational constant Gl of the 2-dimensional gravity is deduced: GL ≈ 6.64 ± 0.02 x 10-13 [m3 kg-1 s-2]. This is not a fine-tuned number as meant in Hossenfelder [10], but an empirical value that represents the average effect of the ma,er in the superposed universes as observed in our galaxies. The amount of ma,er in the galaxies in the superposed universes can vary according to their history, which becomes visible in the values of GL that vary from galaxy to galaxy. But this value proved to give a much improved prediction of dispersion velocities in galaxy clusters. The mass-to-light ratio has been used as the only fi,ing parameter to fit the baryonic rotation velocity, and hence the baryonic gravitational acceleration in each galaxy to the observed values near the core of the galaxies. After that, the above-mentioned value for GL is used to predict the additional gravitational acceleration at all radii without any further fi,ing. Applying this value to predict rotation velocities from the baryonic ma,er distribution in a galaxy, upon using the mass density in the plane of rotation, will yield predictions that are on average 10 to 17 % closer to observation than MOND or Bekenstein’s work, TeVeS. With 175 dedicated values of GL, this improves further to 19 to 27 %. The description of dark ma,er as a set of wire-like line masses and the dilution of dark ma,er from galaxies that both follow from the theory in hand, together are fundamental to describe both flat rotation curves in galaxies and the cluster velocity dispersions in a consistent manner. In galaxy clusters, the resulting improvement of the predictions of the velocity dispersions is even much more than in galaxies. Further investigation of the shapes and orientations of dark ma,er halos based upon the linear gravity hypothesis, will yield line-masses with comparable orientation as the ones currently calculated by many researchers, but much more concentrated at the centre of galaxies. This avoids the fundamental problems with the current view of halos surrounding galaxies as recently reported by Mistele and Lelli based upon the SPARC data. Using the work of Levi-Civita and Santos it is shown a consistent relativistic formulation of the hypothesis can be constructed in GR. As an alternative approach, the work of Bekenstein has been elaborated too to study the evolution in time of linear gravity. In the la,er case this has been done following the same steps Bekenstein took with MOND and GR. The solution based upon TeVeS and the FRW metric confirms the prediction of decaying linear gravity from a decreasing concentration of dark ma,er in time, by the expansion of space in accordance with the hypothesis. But then, it becomes clear that somewhere in the past linearised calculations will break down, since then the field was much stronger and numerical approaches are needed. And, perhaps, the said models of Mistele and Lelli used to analyse the SPARC data are accurate enough to falsify or confirm the predicted decay, taking into account the evolution of galaxies in time. And, to check whether GL stays constant over the huge distances, out to 1 Mpc, they analysed. More future work is to implement the linear gravity approach, including the predicted evolution in time, in existing simulation software for the evolution of galaxies to verify whether that will yield be,er agreement with the observed trends, in particular the rapid evolution of large galaxies in the early universe as well as to study how linear gravity can be applied to gravitational lensing, including dark ma,er as a source. The author looks forward to receiving responses to this hypothesis from the field.