Chapter VII: The Effect of UG Theory on Cosmology

Modern cosmology relies on the Freidman-Lemaitre-Robertson-Walker (FLRW) metric. The FLRW metric is an exact solution of Einstein’s field equations of general relativity under the assumption of a simply connected, homogeneous, isotropic expanding or contracting universe. The Freidman-Lemaitre-Robertson-Walker model serves as a first approximation for the evolution of the universe, however additional models have been added to provide for the deviation of the observed universe from homogeneity and isotropy. In order to understand the impact that the UG theory may have on cosmology, it is essential to first understand to what extent the UG theory is compatible with the general theory of relativity.

Section VII-1: The General Theory of Relativity and Unified Gravitation

For most engineering and scientific applications, the quantitative differences between Newton’s theory of gravitation and Einstein’s relativistic theories are insignificant. Special relativity and general relativity become important when velocities within the system of interest approach the speed of light, or in environments of high matter densities such as collapsed stars, neutron stars or black holes, or for analyzing systems of cosmological proportions.

Whereas Newton’s potential energy equation is given by , the UG potential energy is described by

In contrast to Newtonian gravitation, the UG potential energy is a non-linear function of the mass of the fundamental test particle. Following equation 2-1-5, the acceleration of a non-relativistic test particle of mass interacting with a particle of mass at rest at the origin of the frame of reference is given by , instead of the Newtonian . Therefore, within the potential energy oscillation zone at distances of the order of or , the trajectory and acceleration of a free falling test particle becomes dependent on its mass.¹ However, at distances , and , the acceleration of the test particle approaches the Newtonian acceleration of , and becomes virtually independent of its mass .

As the special theory of relativity is restricted to systems with relatively negligible gravitation, the deviation of the UG theory from Newton’s theory of gravitation does not pose any additional conflict that has not already been expressed by the Newtonian theory. However, the general theory of relativity is based on Einstein’s equivalence principle, stating that the trajectory of a free falling test particle depends only on its initial position and velocity, and is independent of its composition (and therefore independent of its mass). Consequently, at short distances such as and , the UG theory is possibly at odds with general relativity.

Regardless of whether or not the UG theory is correct, the viability of the principle of equivalence and general relativity at short distances (under ) is arguable. In general relativity the applicability of the equivalence principle is restricted to distance scales where the gravitational field is uniform (with negligible tidal forces). Therefore, the equivalence principle cannot be applied at short distances, where the Newtonian forces may change drastically with any small deviation in the distance . In addition, quantum effects become substantial at distances . Despite decades of enormous effort, the consolidation of general relativity with quantum mechanics has yet to succeed, raising further doubt about the viability of the equivalence principle at extremely short distances. Furthermore, according to the standard model, the strong interaction and the weak interaction are highly dependent on particle masses, and become dominant at distances of approximately . The exact equations of the strong and the weak forces within the standard model are unknown, however they are not likely to be linear with the mass of the test particle. Therefore, the equivalence principle may not be applied on such small scales, regardless of the validity of the UG theory.

It is important to determine when and where the UG equations substantially deviate from general relativity. According to equation 2-1-5 of the UG theory, the acceleration rates of free falling protons, neutrons and electrons are not identical when they gravitationally interact with ordinary matter at distances less than or of the order of . Therefore, in theory, within this range of distances, a free falling frame is not necessarily an inertial frame, as different free falling particles or objects within the same frame may demonstrate different rates of acceleration.

However, at interaction distances of (where and , thus ), the gravitational force applied on a free falling ordinary particle is virtually Newtonian, and its acceleration is therefore independent of its mass. Consequently, in a UG world composed entirely of protons electrons and neutrons (as well as their anti-particles) the general theory of relativity provides a good approximation at distances of . Consequently, in environments where ordinary matter interactions are dominant and the influence of superheavy particles can be regarded as negligible, the predictions made by general relativity, such as gravitational redshift (or blueshift), gravitational time dilation, the deflection of light by gravity (as in gravitational lensing) and the relativistic precession of apsides, hold true and are compatible with the UG theory.

According to the fourth UG postulate, however, massive superheavy particles are produced in environments of extremely high matter density, such as in the vicinity of collapsed stars, neutron stars or non-singular black holes.² When a test particle of mass (or an object composed of particles of mass ) interacts with a massive SHP of mass , the non-linear distance range of the UG force, where the cosine and the sine terms of equation 2-1-5 demonstrate oscillations, increases with the product of the two particles’ masses . Therefore, if extremely large superheavy particles exist at the core of a planet (where the term is of the order of tens or hundreds of thousands of kilometers) or at the core of a galaxy (where is of the order of tens of kiloparsecs),³ the gravitational oscillations create minimum points, arcs or contours. For the case of , ordinary matter (such as the molecules or atoms of an object orbiting a planet, or of galactic interstellar gas) accumulates at the minima, and may create rings or spirals. As the UG oscillations are non-linear functions of the mass of the fundamental test particles, the isolated electrons, protons or superheavy particles may demonstrate substantially different rates of gravitational acceleration on large distance scales. Consequently, a free falling frame, and the free falling objects or particles within the frame, may not accelerate at the same rate, and cannot be assumed to follow the geodesics of curved spacetime geometry. Therefore, in regions of spacetime where rings and spirals are formed, the UG theory demonstrates greater deviation from the predictions of the general theory of relativity. Discrepancies between the results of the UG theory and general relativity, however, are relatively small in subsystems influenced by external SHPs when the subsystems are too mild to generate or sustain SHPs of their own, and their ordinary matter is almost exclusively arranged in the form of neutral atoms, molecules or more complex objects. In such a case, where all of the matter within a local free falling frame is composed exclusively of atoms and molecules of ordinary matter that interact with a strong external SHP, each atom or molecule accelerates as a rigid object. Therefore, all of the free falling objects within the local frame accelerate at the same rate as the frame itself (note that the mass of a neutron is almost equal to the mass of a proton, and the mass of the electrons bonded to the nucleus of the atom is almost negligible relative to the masses of the nucleons. The effect of the bonded electrons on the object’s acceleration can therefore be neglected, and the effect of a neutron on the overall acceleration of the object is nearly identical to that of a proton.⁴ Consequently, the acceleration of the free falling objects is very close to the acceleration rate of a free proton). Therefore, the equivalence principle is valid as long as the frame is sufficiently small to ensure that no significant tidal forces exist within its limits, and as long as the number of free electrons or positrons within the frame is negligible. When a significant number of free electrons or positrons exist within the local frame, their rate of acceleration according to the UG theory may vary from the acceleration of the protons, atoms and molecules within the frame,⁵ as well as from the acceleration of the free falling frame.⁶ Consequently, the equivalence principle is violated, and the frame does not constitute an inertial frame. The same is true for cases where a significant portion of the free falling objects within the given local frame are composed of massive SHP types as well.

Section VII-2: Unified Gravitation and Black Holes

In the previous section it was demonstrated that in a world composed exclusively of ordinary matter, the UG theory would not demonstrate significant deviation from general relativity at distances greater than . In such a scenario, the concept of a black hole event horizon, where neither a particle nor light can escape once trapped below the horizon, is supported by the UG theory.⁷ It is important to note, however, that the UG theory rules out the concept of a black hole as a singularity. The fact that the UG potential energy equation oscillates between sets of maxima and minima, with a potential energy that approaches positive and negative infinities as , requires an infinite amount of energy to physically combine two massive particles. Therefore, matter cannot collapse into singularity. Furthermore, in a universe containing a significant amount of superheavy particles, the UG theory provides a mechanism by which matter trapped within the event horizon of a black hole can eventually escape. As the matter within a black hole collapses toward its center, the pressure and temperature at the core become extremely high, to the point where sufficiently large superheavy particles may be created, generating their own repulsive zones. In cases where the SHP mass becomes sufficiently large, the oscillation range between the newly generated superheavy particles and ordinary matter matches or exceeds the radius of the black hole event horizon prior to the SHP creation. With a sufficiently high quantity of superheavy particles, the repulsive force between SHPs and ordinary matter may overcome the strong attractive forces exerted by the black hole’s ordinary matter on matter located close to the former event horizon, making it possible for matter to escape.

Section VII-3: The Effect of Unified Gravitation on Cosmology - The Big Bang and the Expansion of the Universe

Hubble’s discovery that the universe is not static, but expanding, led to the development of the Big Bang cosmological model, which attributes the beginning of our universe to an explosion from a very dense point singularity at about 14.5 billion years ago. The recent discovery that the universe is expanding at an accelerated rate forced the reintroduction of the cosmological constant, which was initially introduced into general relativity by Einstein in order to maintain a static universe, and later retracted in response to Hubble’s discovery of the expansion of the universe. Throughout its development, the Big Bang model encountered significant problems, a few of which were addressed in the introductory chapter of this book.

An entirely different approach may be taken via the UG theory. The UG interaction between two particles has been demonstrated to produce zones of attraction and zones of repulsion. The UG repulsive force will be shown to account for the creation of large voids and to explain the strong rejection between galactic entities,⁸ which drives galaxies to recede away from each other on large distance scales and leads to the observed continuous, even accelerated expansion of the universe. The interplay between repulsive and attractive zones will be shown to account for the creation of galaxies, as well as for the creation of galactic groups, clusters and superclusters. Expansion due to repulsive forces, rather than due to an expansion of spacetime and subsequent inflation, may provide for a substantially simpler cosmological model, which avoids the paradoxes and inconsistencies inherent in the current Big Bang theory.

Section VII-4: Galactic Lock Out

As a first step, the UG theory will be shown to predict that sufficiently large and abundant superheavy particles within a galaxy may create a gravitational barrier that rejects, and therefore prevents most of the external ordinary matter from penetrating the galactic disk.⁹ In other words, the galaxy will become “locked,” and its growth halted. Consider, for example, an ordinary drifting object (or test particle) approaching a galaxy from infinity with a potential plus kinetic energy of close to zero.¹⁰ Initially, the object is located far beyond the maximal zonal range of the galactic SHPs and is thus gravitationally attracted by the galaxy’s ordinary matter.¹¹ As it accelerates towards the galaxy, however, the object may reach a distance where it is simultaneously attracted by the galaxy’s ordinary matter and conversely repelled by the galactic superheavy particles. Following equation 4-1-1, the object’s potential energy is given by

Equation 7-1

and the force applied on the object is given by

Equation 7-2

Note that in order to concentrate on the essential factors, the above equations are based on a hypothetical scenario of a simple galaxy containing a single SHP group ( orbiting the center of the galaxy in a circular orbit of radius at a non-relativistic and constant velocity (therefore, of equation 4-1-1 is equal to ,, and equation 4-1-1a converges toward equation 7-1). The vast portion of the galaxy’s ordinary matter is assumed to be distributed symmetrically around the center of the galaxy within a sphere of radius , where . To further simplify the current discussion, the influence of other external bodies is assumed to be negligible, and the effect of the rotation of both the galaxy and its SHP groups on the overall energy of the orbiting object is assumed to be relatively small.

Figures 7-1a and 7-1b display the overall potential energy (via equation 7-1) of an approaching single-particle object of mass , as a function of its distance from the center of a galaxy containing a single SHP of mass , and ordinary matter of a total mass of .¹² The overall gravitational potential energy of the approaching particle due to contributions of the SHP and ordinary matter is indicated in violet. For comparison, the exclusive contribution of the galaxy’s ordinary matter is displayed in blue. Note that in this example, a drifting particle of zero energy cannot come closer than a distance of about from the center of the galaxy (see figure 7-1b). Consequently, the galaxy essentially becomes locked to an inflow of ordinary matter, forbidding the entrance of any external ordinary particle of mass approaching with a potential plus kinetic energy below the maximum of . In addition, no circular orbit can exist between , as within this range of distance both the overall gravitational force and the centrifugal force acting on the particle point outward, and thus cannot cancel each other out.¹³

Figure 7-1a: The blue curve in this figure displays the overall potential energy (derived via equation 7-1) of an approaching single-particle object of mass as a function of its distance from the center of a galaxy containing a spherically symmetric distribution of ordinary matter of a total mass of . The addition of a single non-relativistic SHPof mass near the center of the galaxy is shown to elevate the potential energy of the approaching particle (indicated in violet) and creates a barrier at of that keeps out all approaching particles of mass with an overall potential plus kinetic energy of less than . Within the resultant forbidden zone starting at , a particle of mass cannot be confined in orbit. The minima below provide the locations of galactic rings, where the collapse of these rings results in the production of stars.

Figure 7-1b:The potential energy is displayed over a distance range times greater. An external particle of mass with an overall energy of would be stopped by the SHP-generated barrier at about (or ). The forbidden zone is demonstrated to extend all the way out to . As the distance between the approaching particle and the center of the galaxy increases beyond , the relative contribution of the SHP to the potential energy of the test object declines, and the particle’s potential energy converges toward the Newtonian curve (in blue).

Figure 7-1c: Provides the force associated with the potential energy of the approaching particle using the same parameters as figures 7-1a, 7-1b and equation 7-2. Note the repulsive force above .

In general, the galaxy will begin to lock out ordinary matter when , or, as , when

.

Substituting the approximate location of the maximum contour of the barrier at will provide

where the parameter values used were and . A detailed graphical analysis is displayed in figure 7-1d, providing the mass as the galaxy’s maximum amount of ordinary mass with which the galaxy is still locked to drifting objects composed of ordinary matter.

Section VII-5: The Construction of a Barrier, the Effect of a Barrier on the Fragmentation of a Collapsing Cloud and the Creation of a Series of Distinct Galactic Entities

According to current theory, the stages of star formation and the final state of a star are thought to depend on its overall mass. A star of a mass greater than eight solar masses must pass through successive stages of hydrogen, helium, carbon, neon, oxygen, and silicon fusion at its center. With the passing of each stage, the stellar core becomes increasingly hot and dense. The evolution of stars is regarded as a long sequence of contractions, starting with the initial collapse of a molecular cloud, which is then halted by hydrogen burning, and ending with the formation of a neutron star or black hole. The contraction process pauses several times, as nuclear fusion provides the energy required to replenish the energy lost to radiation and neutrinos, as well as the outward pressure needed to balance the inward pull of the gravitational force. Upon the exhaustion of one type of fuel, the star contracts, heats up and burns the next higher element, usually created at a previous stage. Eventually, a core of iron-group elements is produced. Since no further energy-per-nucleon generating process is available, nuclear fusion is halted and the star is held by the pressure created by electron degeneration. As the amount of energy loss increases, the electrons combine into the iron-group nuclei, raising their neutron number. The energy of the stellar core again reduces to a level where it can no longer balance the inward gravitational forces, and the iron core collapses (at a rate of about a quarter of the speed of light) from approximately the size of the Earth to about in radius, creating a proto-neutron star. The collapse is halted by the short-range repulsive nuclear interactions. Note that according to the UG theory, short-range nuclear interactions are driven by repulsive zones of the UG gravitational equation 2-1-1 at distances of .

Just before the initial stage of stellar or galactic formation, when the Brownian pressure created by the gas particles can no longer balance the gravitational force and the collapse of a gas cloud is set in motion, there are no central superheavy particles of substantial mass, and the potential energy curve of a test particle of mass resembles the Newtonian potential energy (displayed by the blue curve in figures 7-1a and 7-1b). As the density of matter, the temperature and the pressure within the core of the collapsed star or galaxy increase substantially following each stage of collapse, the prevalence and the mass of the largest SHPs increase substantially, in accordance with postulate IV. With the production of more massive SHPs, the resultant potential energy of the object (presented by the violet curve) begins to increase and to depart from the Newtonian curve. Eventually, as long as the initial cloud is sufficiently massive, the pressure and temperature at its core will build up to high levels, where the production of superheavy particles yields an adequate number and mass of a dominant SHP type to form a barrier that is capable of deflecting inward-drifting matter, thereby preventing the matter from penetrating the galactic disk. This will occur when (see figures 7-1a and 7-1b). Since the transition to substantially larger SHPs takes place during a sudden and relatively short period of collapse, the rise of the barrier is almost instantaneous. As the barrier emerges, the slope of the potential energy, located between the newly formed outer maximum contour and the adjacent external minimum (at approximately and respectively in figures 7-1a to 7-1c) becomes negative. Consequently, gas and other ordinary matter objects orbiting within this distance range are suddenly subjected to a strong repulsive force and ejected outward in the direction of the external minimum.¹⁴ As the volume of matter within the given distance range is emptied out, a large void is formed. At distances exceeding the outer minimum, the object’s potential energy curve converges toward its Newtonian curve, thereby attracting ordinary matter and allowing for a continuous inward flow of matter. However, the vast majority of the inward flowing matter cannot penetrate the barrier and is instead deflected toward the outer minimum contour, where new centers of collapse may form, resulting in the fragmentation of the galactic entity into a series of sister galaxies. The same process is repeated again and again as the number of sister galaxies increases and the area covered by them expands outwards.

Section VII-6: UG Repulsion and the Generation of Stellar Novae and Supernovae

A similar process may explain what initiates the sudden massive expanding shell of gas and the high levels of radiation generated by stellar novae and supernovae. A sudden and drastic increase in the brilliance of a star is characteristic of a nova, where stellar explosion causes the star to become 10,000 to 100,000 times brighter than the Sun, and the cataclysmic supernova, where the exploding star can become billions of times as bright as the Sun before fading out of view. At its maximum brightness, the exploded star of the supernova may outshine the entire galaxy. Both novae and supernovae are characterized by a tremendous rapid brightening lasting few weeks, followed by slow dimming, and both show spectroscopically blueshifted emission lines, which imply that hot gases are blown outward. It is yet unknown how the collapse of a dying star creates an explosion that generates a massive outflow of gas and matter.

According to the fourth UG postulate, a significant increase in the temperature and pressure of a stellar core leads to the sudden creation of SHPs of significantly larger mass. A large and abrupt increase in temperature and pressure occurs during the initial collapse of the molecular cloud when the star is born, or at various stages of the stellar life cycle described in section VII-5. The initial collapse of a star results in a significant increase in temperature and pressure within the central core, which may produce pairs of substantially massive superheavy particles and anti-particles. ¹⁵

The birth of larger SHPs almost instantaneously elevates the potential energy curve, creating a barrier (for example, see the transition from the blue curve to the violet curve of figures 7-1a and b). Following the discussion of the previous section, the newly formed barrier produces a sudden massive expanding shell of gas, which drives out the vast amount of ordinary matter previously located between the newly formed maximum and the newly formed external minimum. As the temperature in the collapsing core becomes sufficiently elevated, the collapse of the star is halted by the hydrogen burning process, producing higher temperatures and increasing the outward pressure, thus balancing the inward gravitational force within the star. When its supply of hydrogen is nearly depleted, the collapse of the star is resumed. Energy released during this second collapse allows for the production of even larger SHPs, as the temperature and pressure within the stellar core are increased. Hence, the radius of the maximum contour, which is proportional to the dominant SHP of mass , and the radius of the adjacent external minimum, which is dependent on , are shifted outward, resulting in a significantly expanded barrier. The new, extended barrier once again triggers a sudden massive expanding shell of gas. This process is repeated through the series of collapses.

The creation of superheavy particles of greater mass produces a larger number of narrow minima within a shell contained between any two successive minima of the former dominant SHP type, resulting in an enormous number of local collapses toward the new set of minima. This process releases a vast amount of energy in the form of radiation, which together with the massive expanding shell of gas produced by the outer barrier, may explain the phenomenon of a nova or supernova.

A star that has experienced several stages of novae or supernovae is likely to have exhausted a majority of its core hydrogen (and possibly other light elements) and to produce heavier elements. Such a star is also likely to have already shed most of its outer layers via prior novae or supernovae or by its stellar wind (see section VI-2). Therefore, in the later stages of a supernova, a star is likely to lack the spectral lines of the lightest elements, while demonstrating a higher abundance of heavier elements in its spectrum, which may explain the various classifications of supernovae.

Section VII-7: The Fragmentation of a Galactic Entity and the Creation of Galactic Substructures

The creation of a series of distinct galactic entities by the collapse of a gas cloud was discussed in section VII-5. In this section, the interplay between attractive and repulsive zones within any galactic entity of a size larger than a typical galaxy (typically of larger than will be shown to provide a possible explanation for the fragmentation of a galactic entity into a group or a cluster of galaxies.

Assume, for example, that a specific galactic entity (the “parent entity”) produced by the collapse of a gas cloud is described by the same parameters used in figures 7-1a to 7-1c, with the exception of and , and adheres to the same set of assumptions. The series of maxima and minima of the potential energy curve of the parent entity is demonstrated in figures 7-2a and 7-2b. As the density of matter in the vicinity of the minima becomes elevated, some of the minima develop into secondary centers of collapse, creating stars or smaller “offspring” galaxies, which generate sufficiently large SHPs of their own to produce a barrier. The secondary stars or galaxies consequently become locked to external drifting matter, diverting nearby matter to collapse at neighboring local minima.¹⁶ As a result, a series of interconnected stars, galaxies or even galactic groups, clusters or superclusters are created at the minima, thereby fragmenting the matter within the galactic entity into a series of substructures. Note that the offspring substructures are separated into groups, where each group occupies a different minimum contour produced by the superheavy particles of the parent entity, and their disk planes should subsequently be oriented tangentially to the respective minima of the galactic parent.

Figure 7-2a:Same as figure 7-1a, using higher values of and. Rings collapse at the minima to produce galactic substructures.

Figures 7-2b:Same as Figure 7-2a displayed on a larger distance scale. The wide void (forbidden zone) which is shown to start at about in Figure 7-2a is shown to extend all the way to , where it starts to converge toward the ordinary matter Newtonian curve (in blue).

Further note that in figure 7-2b the void around the center of the parent galaxy is nearly a perfect sphere with a radius of . However, in a more realistic scenario, where the space within the void is additionally influenced by other galactic entities and the SHP groups move at relativistic speeds, the size and shape of the void become distorted. Consequently, the void may contain few local minima at which some galactic entities may form, and its geometry does not demonstrate perfect spherical symmetry. However, the average density of matter in the void is significantly reduced.

Finally, it is important to note that the process described above, by which a large galactic entity, or “parent” is broken into smaller “offspring” substructures, does not take into account the effect that the rotation of the large SHP groups may exert on the fragmentation of the parent structure. The process of star formation described in Chapters IV-1-2 and VI-4 may be extended to galactic groups, clusters and superclusters, to explain the fragmentation and distribution of galaxies within clusters.

Section VII-8: Gravitational Repulsion Between Galaxies

The rejection of ordinary matter by galaxies provides a mechanism by which galactic entities may repel each other at distances larger than the diameter of a supercluster. Repulsion between two galaxies will be shown to persist over a large range of distances, starting at a slightly larger distance than the oscillation range of ordinary matter of mass with the dominant superheavy particles. The equation that describes the interaction between the two galaxies is given by

Equation 7-3

where and denote the respective masses of the dominant SHP types of the two galaxies, and provide the total number of these SHPs in the respective galaxies, and and are the total mass of the ordinary matter within each of the galaxies. Note that the radii of the two galactic disks (which are close to and respectively) are assumed to be small relative to the distance between their centers. The contributions of additional SHP groups and of other heavenly objects are assumed to be negligible.

The potential energy of the gravitational interaction between two identical galactic entities using the same structure and parameters as the latest example (, and ) is depicted in figures 7-3a and 7-3b. The galaxies are shown to repel each other at distances stretching between (which is the zonal oscillation range between the dominant SHPs and ordinary matter of mass , denoted as ) and (which is the distance between the center of the galaxies and their outermost potential energy minimum, denoted as ). In this example, the distance range of the repulsion between the galaxies is of the order of about one third of the estimated size of the observable universe. Note that the existence of roughly spherical voids around each galactic entity must create a network of non-randomly distributed galaxies that are positioned along two dimensional sheets that form the walls of bubble-shaped regions of space, in agreement with observations.

As demonstrated in figure 7-3a, two isolated galaxies tend to cluster together when the distance separating them is less than the zonal oscillation range between their dominant superheavy particles and ordinary matter of mass , denoted by , causing them to gravitate toward a local minimum. When the distance separating the two galaxies lies between and , the galaxies repel and accelerate away from each other.

The different terms of the force equation can be derived by computing the gradient of equation 7-3, which can be shown to reduce proportionally to either or to within the range , and proportionally to at distances , where the effect of the SHP reduces significantly. At distances greater than , the galaxies begin to attract each other and the UG equations converge toward the Newtonian interactions between the ordinary matter of the given galaxies.

Figure 7-3a

Figure 7-3b

Consequently, the velocity with which the two galaxies recede from each other between increases by an amount that is proportional to , and the velocity of two galaxies relative to each other converges quite rapidly to their maximum receding velocity at . As the galaxies drift apart beyond the relative distance , the velocity at which they recede from each other is gradually reduced by the attractive force between them. Whether the attractive force at is sufficiently strong to eventually stop their motion away from each other depends on the value of their potential plus kinetic energy at . A positive initial energy indicates that the galaxies will continue to recede to infinity, whereas a negative initial energy implies that their motion away from each other will eventually come to a halt and begin to accelerate in the reverse direction, back toward one another. In the case of exactly zero energy, their receding will continue forever as the relative distance between the galaxies asymptotically approaches a maximum distance.

Section VII-9: The Expansion of the Universe

According to observation, the universe is expanding at an accelerated rate. Invoking the Copernican principle leads to the conclusion that the same isotropic expansion detected from Earth can be observed at the present time anywhere else in the universe. In the following discussion, the average size of a galactic cluster is denoted as , the average distance between adjacent galactic clusters is denoted as , and the average relative velocity of adjacent superclusters as they recede from each other is given by , where due to the Copernican principle, , and can be shown to be the same everywhere in the universe. Therefore, an observer located in single galactic supercluster views adjacent superclusters located at a distance of as receding at an average velocity of , superclusters located at a distance of as receding at an average velocity of , and so on. This leads to the conclusion that two distant galaxies should recede from each other at a speed proportional to the distance between them. ¹⁷¹⁸¹⁹

As shown in the previous section, two isolated galaxies tend to cluster together when the distance separating them is shorter than , to repel each other at distances between and , or to attract each other at distances which exceed . The velocity of a pair of galactic clusters as they recede from each other was shown to increase, and to asymptotically approach the value of their velocity at . This may explain what causes the expansion of the universe. If the matter of the universe is contained within a sphere of radius , where is of an order of less than or equal to the average , the universe must expand in a uniform manner at an accelerating speed that asymptotically approaches a constant expansion velocity.²⁰

The UG theory further provides a mechanism to explain the observed acceleration of the expansion of the universe. As a substantial number of galactic cores enter into the next stage of collapse, significantly more massive SHPs are produced, thereby increasing the force with which the galactic entities repel each other. Invoking the cosmological principle, this process must occur everywhere in the universe at approximately the same time. Consequently, galaxies and galactic clusters are expected to repel each other with increasing force, escalating the expansion velocity of the universe.

Section VII-10: Additional Comments about Unified Gravitation and the Big Bang Model

The UG theory does not contradict, but can actually support the model of a relatively small and dense universe that at some point in time began to expand. However, there are two fundamental differences between the UG and the Big Bang expansions.

1. While the expansion of the universe according to the Big Bang is assumed to have started in a state of singularity, the term of the maxima of the UG equation 2-1-1 prevents the pre-expansion UG universe from becoming a point singularity.²¹ Consequently, the initial pre-expansion UG Universe is expected to have been relatively small, yet infinitely larger than a singularity, eliminating the problems that arise from the Big Bang assumption that just prior to the beginning of the expansion, the universe was in a state of infinite temperature and infinite density, in which all known theories of physics would break down.

2. The expansion of the universe, according to the UG theory, is driven by the repulsive force between galactic entities, which results in an accelerated expansion as long as the universe did not grow sufficiently large for the distance between a majority of the entities to become larger than of the dominant SHPs in the universe.

These fundamental differences allow a UG-based cosmological model to avoid a number of problems presented by the Big Bang model. In particular, the fact that unified gravitation provides for the possibility of an accelerated expansion of the universe allows for the amount of time elapsed since the start of the expansion to be significantly larger than 14.5 billion years, resolving a potential recurrence of the age dilemma. As aforementioned, the initial size of the UG universe may have been extremely small, yet infinitely larger than a point singularity, and the universe may be substantially older than predicted by the Big Bang model. Consequently, the different regions of the universe had significantly more time to interact than previously estimated, thus avoiding the horizon problem. In addition, the UG model accounts for the observed tendency of matter within the universe to expand uniformly when viewed on large spatial scale, and to cluster when viewed on small spatial scale, therefore avoiding the problem of structure posed by the Big Bang theory. Note that since the UG scenario provides for a massive expansion of an extremely small initial universe, the theory is also consistent with the discovery of an almost uniform cosmic microwave background and with the theory of Big Bang nucleosynthesis. Finally, the expansion of the universe according to the UG theory is driven by the repulsive forces between massive SHPs and ordinary matter, rather than relying on the Freidman-Lemaitre-Robertson-Walker metric. Thus, the requirement that the density of matter and energy in the universe be equal to a critical density (within one part in according to the current Big Bang Theory) is eliminated, thereby avoiding the flatness problem. Consequently, the UG model does not need to rely on the assumption that an inflation process occurred in the early stages of the universe expansion, nor does it require the presence of dark matter and dark energy, and may thus provide a significantly simpler and potentially more stable theory than the current cosmological model.

It is further important to address what could have initiated the dramatic expansion of the universe. The UG explanation may involve a process similar to the processes described earlier in this chapter for the formation and dynamics of galactic entities. Consider, for example, a universe initially composed of a uniform cloud of gas as it begins to collapse toward its center, toward creating a single high-density core. As the production of sufficiently massive superheavy particles locks the galaxy disk to ordinary matter, excess matter is diverted to nearby secondary centers of collapse, generating a subset of galaxies. As the process is repeated, the collapsing universe becomes filled with galactic clusters and superclusters. Over time, the burning of hydrogen²² is depleted and a second collapse of the galactic core ensues, resulting in the generation of heavier SHP types. At later stages of collapse, the production of sufficiently massive superheavy particles may create repulsion between clusters of galaxies, thus halting the collapse of the universe and initiating an expansion via the mechanisms described in sections VII-8 and VII-9. Eventually, the distance between neighboring clusters will approach the average , and the effect of superheavy particles on the interaction between galactic clusters will become negligible. Consequently, at this point, the universe is expected to once again become compatible with the general theory of relativity. In cases where the amount of energy in the universe is insufficient to allow for continuous expansion, the universe may begin to contract. However, the existence of massive SHPs near the cores of galactic entities will prevent a full collapse, and the density of the universe may begin to oscillate around its average. This may occur as long as the population of massive superheavy particles remains stable over time. In case of significant decline in the SHP population, the universe will begin to collapse and the process described above will begin a new cycle.

Section VII-11: The Galactic Halo and the Transition From a Spiral to an Elliptical Galaxy

The rotation of a galaxy (as well as the rotation of its SHP groups) tends to confine stars and matter within its galactic disk. As discussed, the size of the galactic disk is determined by the radius of the second minima and is given approximately by

Equation 7-11-1

This equation can also be used to estimate the mass of the dominant SHP type. Assuming that the average radius of a galactic disk of a spiral galaxy extends approximately to and that provides that . The same logic used in sections VII-4, 5, and 8 for determining the repulsion between galaxies can be applied to stellar systems, leading to the conclusion that stars may repel each other at certain distances. Hence, the number of stars that can be compressed into the galactic disk is limited. Consequently, in a galaxy containing an excess number of stellar systems that cannot be compressed into the disk must assume orbits within the halo. To quantify this statement, the maximum number of stars that may be contained within the galactic disk is of the order of and the maximum quantity of stars contained in the halo is of the order of respectively, where is the average shortest distance between neighboring stars (therefore, the average stellar repulsion distance). In the case of a galaxy with and , the approximate maximum number of stars within the galactic disk and halo are and stars respectively.²³

The size and mass of a galaxy is determined by the mass of its dominant superheavy particles. Following the discussion of sections VII-4 and 5, the galaxy will eventually become locked to ordinary matter by the production of large SHPs, and the inflow of the gas which fuels the production of new stars will practically cease. Over time, the supply of interstellar gas within the galaxy will become depleted, as interstellar gas is used for the production of new stars, or is ejected from the galaxy in the form of galactic wind (see section VI-2). The resultant galaxy is expected to contain little or no cool interstellar gas or dust, and the majority of its stars are expected to reside within its halo. Furthermore, the galaxy is expected to appear to have no stellar disk, and as little or no new stars are produced, its stellar population is expected to consist of older stars. These characteristics are widely observed in the elliptical classification of galaxies.

Between the time that the galaxy becomes locked to ordinary matter and the depletion of its interstellar gas, a significant amount of matter, energy and angular momentum is lost in the form of galactic wind. Consequently, the rotating core of the galaxy (which is the engine of the galaxy) and its source of energy also lose energy and momentum, as well as matter that is pumped out by the rotating spiral. As a very limited amount of new gas enters the galaxy, the central core is deprived of additional fuel, and since its energy and momentum is reduced, the rate of rotation of the galactic core must slow down.²⁴ As the central core loses some of its mass , and its rotation velocity reduces substantially becomes closer to , the effect exerted on the velocity of the object by the SHP and the central core, which is proportional to , decreases.²⁵ On the other hand, as the number of stars in the halo increases, and the mass and rotational velocity of the central core and the rotational velocity of the SHPs are reduced, the relative influence of nearby matter on the object increases. Consequently, the galaxy rotation curve may deviate substantially from constant velocity.

Section VII-12: Elliptical Morphology and Properties of Elliptical Galaxies

The elliptical shape of a galaxy is known not to correlate well with the rotation of the galaxy as a whole ^{(Caroll & Ostlie, 2007, p. 988)}. A possible reason for the elliptical shape of the galaxy is that relativistic SHP groups distort the otherwise circular equi-potential contours into elliptical ones, in which case the level of ellipticity depends mainly on the velocity of the SHP groups. For the simple case of a galaxy containing a single SHP type of mass , the axes of the minima are given by , or for the outermost substantial minimum, by .

The apparent major axis is given by (where the velocity of the SHP group at the time of emission is perpendicular to the distance between the location of the emission and the location of interception of the gravitational signal by the orbiting matter) and the apparent minor axis is given by (where the given velocity and the distance are parallel). Therefore, the observed ellipticity can be defined as . The largest ellipticity observed is approximately , suggesting that , or . Note that in the more realistic case of multiple SHP groups rotating on different rotational planes, the elliptical galaxy may be triaxial without a single preferred axis of rotation.

Section VII-13: The Boxiness vs. Diskiness of Elliptical Galaxies

Figures 7-4a and 7-4b: A calculated disky galaxy (7-4a) drawn using and a calculated boxy galaxy (7-4b) drawn using . Both galaxies share the parameters , , , and .

Ralf Bender, Jean-Luc Nieto and their collaborators proposed that many of the characteristics of elliptical galaxies are related to the degree of boxiness or diskiness that their isophotal surfaces demonstrate ^{(Bender, 1992)}. It remained unclear, however, why a small portion of elliptical galaxies present a boxy appearance, while a majority of elliptical galaxies are disky. Figure 7-4b (calculated via equation 4-1-1a) demonstrates that a galaxy may take on a boxier appearance when the distance is selected to be sufficiently small for a superheavy particle group moving at a relativistic velocity relative to the center of the galaxy. With and , the isophotal surfaces in figure 7-4b demonstrate clear departure from elliptical morphology, particularly with increasing proximity to the galaxy center. Increasing to in figure 7-4a modifies the morphology of the galaxy into a more spherical, or disky morphology.

1 A free falling object is an object that is influenced exclusively by the gravitational force.

2 The UG theory prevents the possibility of singularity (see section VII-2).

3 One parsec () is equal to about , and

4 For further information, see Chapter VIII.

5 In general relativity the term ‘local frame’ refers to a conceptual set of standardized clocks and measuring rods, which are also subjected to acceleration by the local gravitational field.

6 This may be the case for galactic jets, pulsars or any plasma.

7 This is true for any massive object composed exclusively of ordinary matter.

8 The term “galactic entity” refers to either a single galaxy, or to a galactic group (containing 2 to 50 galaxies), galactic clusters (containing 50 to 1000 galaxies), or galactic superclusters (containing more than 1000 galaxies).

9 The same mechanism should exist in stellar systems, and may also exist in planets

10 A “drifting” particle describes a particle with a total potential plus kinetic energy of close to that begins its approach toward the galaxy from a very large distance with a negligible amount of kinetic energy.

11 At distances exceeding the zonal range of the superheavy particles with ordinary matter, the UG contribution of the SHPs is negligible compared with the contribution of the galaxy’s ordinary matter.

12In terms of the more general equation 4-1-1a, the parameters used are , , , , , and .

13A forbidden zone is defined as a spherically symmetric volume of space around the center of a galaxy in which the orbit of an object composed exclusively of ordinary matter cannot be completely confined.

14 For simplicity, it is assumed that the galaxy’s potential energy is dominated by a single group of SHPs and by its ordinary matter. Therefore the maximum associated with is well-defined.

15 The newly generated superheavy particles are ejected from the central core and accelerated to relatively high (relativistic) velocities according to the process described in Chapter III-3 (note that a similar mechanism may solve the long-standing puzzle of why the compact object remaining after a supernova explosion is given a velocity kick away from the core. Observations over the last decade have shown that at birth neutron stars receive a large velocity kick of the order of a hundred to a thousand ^{(Hoflich, Kumar & Wheeler, 2004)}. Within the UG theory, the compact object may be a superheavy particle generated in or near the galactic central core, with sufficient kinetic energy to be ejected out of the central core together with ordinary matter trapped by the SHP zones.

16 Note that the locations of the minima are determined by both the parent entity and its offspring substructures.

17 Note that according to this statement, distant galaxies are expected to recede from each other at superluminal velocity. Superluminal velocities do not contradict the special theory of relativity in this case, as there is no global inertial system at which the velocity between the two galaxies can be measured.

18 Note that the expansion of the universe, according to the current standard model of cosmology, is viewed as the expansion of the intervening space between galaxies, rather than as the expansion of galaxies into an empty space.

19 In accordance with general relativity and the cosmological principle, there is nothing external to the whole system of matter in the universe.

20 However, the speed of two given galactic clusters is likely to vary from the speed expected for the same clusters in isolation, as each one of them is affected by the entire mass of the universe, and not only by the other cluster.

21 See the discussion of singularity in Chapter II and in section VII-2 of this chapter.

22 Recall that the hydrogen burning process is responsible for stopping the initial collapse and thereby prevents the galactic core from collapsing further.

23 Note that an increase in , according to the UG theory, would provide more space for stars to form within the galactic disk. However, the value of is determined by the mass of the dominant superheavy particles in the galactic center. Therefore, as the initial stellar quantity was substantially lower than (or in the current example), the rotation of the galaxy confined all stars located within the maximum contour to the galactic disk, while stars located beyond this maximum were ejected from the galaxy in the form of galactic wind (see section VI-2).

24 Note that upon the occurrence of another stage of collapse, the rotation rate of the galactic core will increase substantially.

25According to equation 6-5.