Abstract

In a previous paper (ref 1, AP4.7), a self-consistent theory called Model 1 was developed to answer ten major connected questions in astrophysics. The most important of these questions are:

• How can dark matter be explained and described?
• How can dark energy be explained and described?
• Where do the ultra high-energy cosmic rays that occur in the energy range beyond the GZK cutoff come from?

Model 1 appears to successfully answer these questions. The unique features of this model are:

• There are two spaces in the universe, particle space and quantum vacuum space. A potential barrier separates them. One space contains visible matter, and the other space contains dark matter.

• There is a cycling of mass-energy between these spaces through the black holes that connect them. Particles pass from particle space through black holes where they are converted into super particles that operate with unified force. They then pass into the high-energy vacuum space where they become dark matter operating behind the potential barrier.

• Dark matter particles interact with each other and form a slowly changing halo centered on a galaxy. Corridors of dark matter forming a cosmic web, which guide the development of new galaxies, connect the bubbles of dark matter to each other.

• There, behind the potential barrier, the dark matter particles gain energy, build up in number and eventually exceed the ability of the barrier to contain them. They then explode back into particle space as a big bang. This process repeats to make a series of new universes.

• After the big bang exhausts itself, super particles continue to tunnel through the barrier into particle space. The super particles are unstable and break down into particles with ultra high kinetic energy. In doing so, they give up potential energy into particle space. The potential energy gradually builds up to become the dark energy that we observe as the cause of our accelerating, expanding universe. The extreme energy protons are observed as cosmic rays with energy between the energy of force unification and the Planck energy, which is beyond the GZK cutoff.  

There is reason to take Model 1 seriously. It quantitatively explains (see ref 12, AP4.7D):

• The origin, characteristics and operation of dark matter.
• The origin, characteristics and operation of dark energy.
• The origin, characteristics and operation of the Ultra High Energy Cosmic Rays (UHECR) that have been observed in the energy range beyond the GZK cutoff.
• The huge disparity in the different estimates of the vacuum potential energy.
• The large-scale cutoff and asymmetry in the Microwave Background Energy.

In working out this model, some problems arose that are connected with it. One of those problems concerns the operation of the big bang. According to Model 1, when the dark matter particle energy exceeds the barrier shell potential energy, the dark matter particles pass over the barrier into particle space as a big bang. Here, however, we must ask, How did these particles gather from the huge observable universe to the site of the big bang? Also, what happens to the residual dark matter after the big bang ceases? Finally, how does the residual dark matter influence the development of the microwave background radiation and the galaxy formation in particle space? This paper will address these problems in detail

 

The Problem

AP4.7 Appendix 1 (ref 1, AP4.7) shows the equation for the barrier that provides containment for super particles (dark matter). It is obvious that when the kinetic energy exceeds the potential energy barrier, the super particles flow out. This equation does not, however, answer the questions:

1. How do the dark matter super particles gather for the big bang from the whole observable universe, which is huge?
2. What happens to the residual dark matter after the Big bang ceases?
3. How does the residual dark matter influence the development of the cosmic microwave background radiation and the galaxy formation in particle space?

In this paper, we will address each of these questions, and find answers thathelp solve other troubling problems in cosmology.

 

The Solution

We will address the above questions one at a time here.

1. Gathering the Dark Matter for the Big Bang

In reference 3, AP4.7B, we describe the formation of super particles (dark matter) in some detail, so it is not necessary to repeat that description. Here we start with a description of the passage of super particles out of the black hole into intergalactic space.

• Super particles near the black hole center are expanded into the diffusion shell by the expansion of space under the influence of the high potential energy (see Appendix 1)
• The super particles inside their barrier shells in the highest energy range (near Planck energy) diffuse out of the black hole diffusion shell with circular speeds higher than 2.99 x 10¹⁰ cm/sec (see Appendix 2). Thus the super particle has a circular speed that is beyond the particle space event horizon speed and is free from the black hole, speeding toward the galaxy edge. Some kinetic energy is lost by the super particles in the electromagnetic fields immediately surrounding the event horizon, and some is lost in the shock zones around solar systems in the galaxy, and in the shock zone just beyond the edge of the galaxy at the interface with intergalactic space. In a band near the galaxy’s edge, the super particle’s mass becomes dominant over the visible matter, and becomes the dark matter halo around the galaxy (ref 3, AP4.7B).
• Many of the super particles that are gathered by black holes in the low to mid-energy range of the energy distribution remain within the black hole’s event horizon as super particles. Thus the super particles that result from conversion of particles escape more slowly than they are formed, because the black hole gravity limits escape to those in the high-energy range. Therefore the super particles that remain within the event horizon and in the diffusion shell remain to gain energy and density
• The super particles that escape from all the galaxies finally end in intergalactic space (and especially in the cosmic web), as high energy shielded super particles. Some of these super particles will tunnel through their shells into particle space providing ultra high-energy protons (UHECRs or cosmic rays) and potential energy, but most add to the energy of the super particles in particle space. The energy of the super particles does not degrade because the collision probability is low. By addition of new high-energy super particles the average energy of the super particles in intergalactic space (especially the cosmic web) eventually increases to near the barrier potential energy (see Appendix 3).
• The diffusion zones in the black holes are also being heated by the addition of particles through the event horizon. The diffusion zone in one of these black holes in a dense group of galaxies finally gains the average energy needed (near Planck energy) to start a large-scale flow of super particles over the barrier shell into particle space. If the average energy in the cosmic web is also near the Planck energy, a sustainable big bang has started (Appendix 4). This is the first, principal black hole.
• The flow of super particles in the first principal black hole reverses the super particle diffusion direction from flow toward the galaxy edge to flow toward the black hole center (see Appendix 5). This draws the super particles in from the event horizon and eventually from the edge of the galaxy. Then the super particles come from other galaxies along the cosmic web corridors. All of this movement happens at a speed much greater than 2.99 x 10¹⁰ cm/sec because the average super particle energy in the web has become close to the Planck energy (Appendix 2). Note that this rapid accumulation of mass-energy in a small zone causes space to curl tightly around the first principal black hole, which reduces the distances between galaxies dramatically, and facilitates the flow. Now we have the flow from the cosmic web needed to sustain a true big bang. Note also that the flow from the first principal black hole cannot become a true big bang until the average super particle energy and density in intergalactic space is high enough (near the Planck energy) to sustain it. Until this energy is achieved, flows from many black holes will start, send high-energy particles into intergalactic particle space and then sputter and die, thus contributing to the space potential energy and kinetic energy of intergalactic space and the cosmic web. We see that the progress toward a big bang is inevitable. However we must also note that some high-energy super particles will be lost in each cycle. Then after enough cycles have happened, the number of super particles at high energy will be reduced to the point that a big bang will no longer happen (see Appendix 4).

2. The Residual Dark Matter after the Big Bang Ceases

A residual cosmic web in vacuum space remains after the big bang remains as follows. There will always be some super particles in the low energy tail of the distribution of super particles, so some will remain after the big bang ceases. The spatial distribution of the dark matter remaining in vacuum space is determined by the diffusion term in the velocity equations of Appendix 3. Since there is a density term n in the denominator, the dense cosmic web corridors will empty out slower than the spaces between the corridors. Thus, after the big bang ceases, there will be a feint shadow of the old cosmic web in the new universe curved into a much smaller volume by the collected mass around the big bang site. This will guide the formation of the Cosmic Microwave Background and the galaxies of the new universe (see 3, below)

3. The Influence of the Dark Matter on Galaxies and CMB radiation

Galaxy Formation.

As seen above, we have the super particles rushing out of vacuum space in a big bang, and a feint shadow of the old cosmic web imprinted in particle space but much contracted by the mass around the big bang site. The super particles rushing out of vacuum space will tend to condense around the old contracted cosmic web corridors of residual dark matter, but the tendency will be inhibited by the faintness of the residual web. Nonetheless, the old web provides the seeds for galaxy formation as the new particles condense out of the new big bang. This pattern is needed, because galaxies trying to form from scratch without a dark matter seeds are unstable. Thus the galaxies of the new universe will tend to concentrate near the cosmic web from the old universe (see ref 3, AP4.7B for details).  

Microwave Background Radiation

First, let us consider the implications of the microwave background data. The pattern of the spatial fluctuations in the microwave background indicates two special things.  (Smolin, 206).

• There is a large peak with smaller peaks on each side, which indicates that the matter filling the universe was resonant. The wavelengths of the resonant modes tell us how big the universe was when it first became transparent. Thus it had a finite size, and the size was not larger than the current size of the observable universe.
• There is very little energy in the largest wavelength. Now this may be only a statistical fluke. However, if this piece of data is correct, it indicates a cutoff at ~ R which is the distance over which the cosmological constant curves the universe (~ 10 billion light years). Beyond this distance, the modes are much less excited. Thus it appears that the fluctuations disappear at scales above R.

Now the most widely accepted theory for the early universe, Inflation seeded with quantum fluctuations, would predict a universe that is uniform on a scale much larger than R from very soon after the big bang. This is because there is no special physical reason for inflation to stop at a size R, and produce a cutoff. Thus the energy in the fluctuations should be more or less flat over the range of distances we can observe up to R. So Inflation does not appear to match the spatial spectrum of the background radiation.

On the other hand, Model 1 predicts a new universe that starts as a local zone drawing in a feint shadow of dark matter from the old vacuum space and sending it out from the area around a principal black hole. This forms a new, tiny, growing zone of highly curved space where particles condense near the remnants of an old, contracted cosmic web. The growth of this universe diminishes as the potential energy causing the expansion is diluted and used up forming particles. Then the potential energy begins to increase again as super particles tunnel out from vacuum space and release their potential energy in order to become particles. In all of this action, the size of this new matter filled universe is locked with R. Thus the size of the universe and the principal spatial mode of the background radiation are locked together from the start of the big bang. So Model 1 appears to predict the observed spectrum of the microwave background radiation.

Testing Model 1 with Data

In this paper, we have seen how Model 1 can quantitatively predict:

• How most of the dark matter of the universe can be gathered from an old cosmic web to a big bang site and spilled into particle space in a new big bang.
• How this new big bang will have a residual cosmic web to guide formation and growth of new galaxies.
• How this new structure of galaxies will fit the spatial fluctuations of a new cosmic microwave background radiation.

These predictions form a strong argument for the gathering of dark matter for a new big bang as the old one matures and thus the correctness of Model 1.

Summary and Conclusions

A model (Model 1) has been developed in AP4.7 that predicts dark matter, dark energy and extremely high-energy cosmic rays, which are observed in the energy range beyond the GZK cutoff. As part of this model, a set of super particles was predicted in a new space (vacuum space) that constitutes this dark matter, and generates this dark energy and the extremely high-energy cosmic rays. In this paper, we have asked how super particles gather from the enormous observable universe to the site of the big bang. We also asked what happens to the residual dark matter after the big bang ceases. We asked finally, how the residual dark matter influences the development of the microwave background radiation and the galaxy formation in particle space. We have obtained answers to all of these questions, and found that they are intrinsically imbedded in Model 1. Thus, Model 1 is compatible with all known data of this kind.

 

Appendix 1

The general relativity energy conservation equation (Peebles, 395) is,

            r’ = -3 (r + p) a’/a

            Where:

            p = pressure

            r = energy density

            r’ = rate of change of energy density

            a = space expansion factor

            a’ = rate of change of space expansion factor

There are conditions when the net pressure is negative,   

            p < –r/3

Then the Robertson-Walker line element and thus the spatial distances diverge. The divergent condition applies when:

            p =  ø’ ²/2 – V

            Where:

            V = a potential energy density

            ø = a new real scalar field

Here, it is found (ref 3, AP4.7B) that V is a slowly varying function of f and the initial value of the time derivative of f is not too large. Then the kinetic energy f’ ²/2 is small compared to V, and the pressure is negative, and depends on V. Then the particles expand under the expansion pressure of V, and the attractive pressure of gravity in the black hole is broken.

Appendix 2 The Speed of light at Extreme Energy

In order to make constant speed of light and constant Planck length compatible, Amelino-Camelia and Magueijo (Amelino-Camelia, 6 and ref 8, Magueijo, 251 and ref 6, Magueijo, 31) developed a modified light speed relation. This relation shows that when the energy increases enough, the speeds of particles and photons increase to values greater than the speed of light in a vacuum. This relationship has been developed further, and incorporated into Model 1 in reference 13, AP4.7M. There it was found, using the theory of granulated Planck space, that the velocities of particles in vacuum space reach extreme values much higher than 2.99 x 10¹⁰ cm/sec, when the super particle energy (E_sp) approaches E_pl in barrier space during a big bang. For super particles in barrier space the potential energy is slightly less than the Planck energy. Thus when super particles gain enough energy to operate freely in barrier space, they are operating in the zone 10¹⁹< E < 1.22 x 10¹⁹ GeV. At the same time, they are passing over the barrier into particle space in a big bang. Here we see that the particle has about the same energy as the Planck granule, so it does not notice the potential energy edge of a Planck granule until it meets a disruption in space such as that at an edge of a galaxy, the boundary of a corridor in the cosmic web or at the edge of the observable universe. Thus since the length of travel for a particle is n Planck lengths long, and N is the number of disruptions along the travel length, then the distance traveled is nl_p, and time used for this travel is just Nt_p, between each disruption, then:

            v = nl_p/ Nt_p ½[(1 + (E_smo+ E_ske)/(E_smo+E_ske– V_so)]

                = 2.99 x 10¹⁰ n/N ½[(1 + (E_smo+ E_ske)/(E_smo+E_ske– V_so)]

Now, since:

            (E_smo+E_ske) > V_so

And

            n/N >> 1

Then:

            ½[(1 + (E_smo+ E_ske)/(E_smo+E_ske– V_so)] ~ 1

So:

            v >> 2.99 x 10¹⁰ cm/sec during the big bang

Note that the same argument holds for super photon velocity

Thus we are able to conclude that according to Model 1, the super particle (and super photon) velocity is large enough to allow for the gathering of particles to the big bang from the entire observable universe when the super particle energy approaches the Planck energy and starts to flow out into a big bang,. This velocity is not infinite, however. This extreme velocity cannot happen in particle space or in vacuum space at lower energies, however. Light speed is constant in particle space at 2.99 x 10¹⁰ cm/sec except at very low temperatures, as relativity requires.

Appendix 3 The Heating of Vacuum Space

The shielded super particles inside the event horizon of a black hole are in a broad energy distribution. Those particles in the high end of this distribution have a high enough speed to pass through the event horizon, but those in the medium to low end do not. They must gain energy to pass out into the galaxy. Thus the super particles that reach intergalactic space are high energy. Some tunnel through the barrier into particle space and decay into UHECR’s and the potential energy that causes the accelerated expansion of particle space. To explain further, we must use the expansion equation.

 

p = f’ ²/2 – V₀

 

During the later part of the expansion phase of the big bang, there are still old super particles in the shadow web of residual dark matter that the new particles from the big bang meet as they expand. They continue to tunnel into particle space and provide high-energy particles and potential energy to particle space. The potential energy V₀ is dwindling, since it is being used to form particles, but it is increasing also from the tunneling super particles. The field f is increasing too as follows.

1). Tunneling super particles bring rest mass and kinetic energy (mass energy m) into particle space as well as potential energy. In fact, more mass energy (10¹⁷ GeV <m< 10¹⁹GeV) is brought in than potential energy (V₀ = 10¹⁷ GeV).

2). The vacuum expectation value (ν) or minimum of the Higgs field (f_m) is proportional to the mass (m), which is building up.

 

ν² = f_m ² = m²/ 2λ

 

Since f_m ² is increasing, f ² must increase. Thus more f ² is added to particle space than potential energy, but it is being added slowly in the early stage of the universe development because of the extremely low density of residual super particles from the prior universe.

3). New particles form into stars and galaxies, and eventually form into new black holes, and start to form new super particles. The density of super particles in intergalactic particle space builds up (see ref 2 AP4.7B).

4). The new potential energy from tunneling super particles forces the total potential energy of particle space to go through a minimum and build up to the level we observe now, but the field f is also building. This is the stage we are in now. As the tunneling continues, the space kinetic energy term (f’ ²/2) will eventually exceed the potential energy term (V₀), and the pressure p will turn positive. Then the acceleration will stop, the expansion will slow, and if there is sufficient mass, the universe will start to shrink.

5). The average super particle energy and density will build up by addition of new high-energy super particles from the new black holes.

6). Eventually, the average super particle energy in intergalactic space and especially the web will near the barrier potential energy (~10¹⁹ GeV), and the stage will be set for a new big bang. The flow of particles toward the principal black hole will concentrate the mass of the universe, and start the shrinkage of the universe toward it. Note that the flow from a principle black hole cannot become a true big bang until the average super particle energy and density in intergalactic space is high enough to sustain the flow.

Appendix 4 The Collection of Particles into the Flow of the Big bang

Note that the increase in super particle density and super particle mean kinetic energy in intergalactic space and the cosmic web toward the Planck level is inevitable. Black holes must preferentially send out high-energy super particles to overcome the black hole gravitational attraction. Thus the super particles in intergalactic space must increase in average energy until halted by the Planck energy. Furthermore, as black holes reach the critical energy (near the Planck energy) and begin a large-scale flow into particle space, they add more high-energy super particles unto intergalactic space. If the average energy of the super particles is not high enough to sustain a big bang, then the added super particles from the flow increases the particle density and mean kinetic energy in intergalactic space. This must continue until the particle density and mean kinetic energy is high enough to sustain a big bang, then the majority of the mass-energy of vacuum space is cleared out into particle space, and the new cycle begins. Remember, however, that there will be a residual number of low energy super particles that remain in a shadow web in particle space because they don’t have enough energy to obtain the speed needed to reach the principal black hole and flow out into particle space before the big bang shuts down. Thus after each cycle there are fewer high-energy super particles and photons available for recycling.

The cosmic microwave background that originally came from super particles becomes a background of energetic photons as the universe shrinks with the gathering of the mass for the big bang.

Appendix 5 The Rush to the Black Hole

We begin with the diffusion velocities of the ionized gaseous components (see Cobine, 51). For ionized particles diffusing from an instantaneous point source, and under the influence of gravity,

            V⁺ = -D⁺/n⁺ dn⁺/dx + K⁺E + K⁺G

            V^– =-D^–/n^– dn^–/dx – K^–E + K^–G

            V^g = K^gG

            Where:

            D = Diffusion coefficient

            K = mobility under the influence of electric or gravitational force 

            V = Ion velocity

            n = Ion concentration

            E = Electric field

            G = Gravitational field tempered by centrifugal force (see below)

            n^g = source of particles from the black hol           

We set:

                        V+ = V- = V^g = V ;  n⁺ = n ^– = n^g = n ;  dn⁺/dx = dn^–/dx = dn/dx

We solve these equations, and get:

                        n= (N_o(r)/4pDt)^3/2 exp(–r²/4Dt)  

            Where:

                        D = (D⁺ K^– + D^– K⁺ ) / ( K⁺ + K^– –  2 K⁺ K^– / K^g ) 

                                    r= Radius from black hole source

                        t= Time

                        N_o(r)=number of particles diffusing from an “instantaneous” spherical source around the black hole center (see ref 3, AP4.7B). 

The above function tells us that after the “lifetime” of the universe is nearly over, the particle density and kinetic energy functions are high and rather flat with bumps at and around the contributors of super particles, tapering off at the edge of the visible universe. The highest point in the function is at the first principal black hole.

Now, we wish to use these equations for the case of the big bang. When the particle energy at the peak of the principal bump reaches the Planck energy, the super particles start to flow rapidly into particle space. The source N_o(r) has become a sink S_o(r), and:

                        S_o(r) = f(r)∫ ∫ N_o(v,t) dv dt 

            Where:

            ∫ N_o(v,t) dv = the integral over volume of all black hole particle sources in the visible universe.

            ∫ N_o(a,t) dt = the integral over time of all the “instantaneous” particle sources over the lifetime of the universe.

Also, the concentration gradients have reversed, and the diffusion constant D has changed signs, and so the solution is:

                        s = (S_o(r)/4pDt)^3/2 [H(r) – exp(–r²/4Dt)]         

            Where:            

                        H(r) ~ flat with a modest peak near the principle black hole so,

                        H(r) ~ 1

From basic kinetic theory we find:

                        D = Lc/3

            Where:

                        L = 1/npd² and d is the diameter of the shielded super ion.

                        And c = the average velocity = 1.128v

                        And v >> 2.99 x 10¹⁰ cm/sec (see Appendix 2)                     

We see that as long as E is close to the Planck energy, the speed of light is huge, so the big bang sink can pull super particles from the edge of the shrunken and concentrated universe and then pass over a barrier of potential V into particle space. Note that when particles get beyond the horizon of the black holes involved in this process, the mean free path of the super particles is much larger than the galaxies they are in, so the super particles fly free at extremely high light velocity along the gravitational corridors of the cosmic net toward the collection of principal black holes that are at the center of the incipient big bang.

                    

References

1.      L. H. Wald, “AP4.7 DARK MATTER AND ENERGY-FUNDAMENTAL PROBLEMS IN ASTROPHYSICS” www.Aquater2050.com/2015/11/

2.      L. H. Wald, “AP4.7A SUPER PARTICLE CHARACTERISTICS” www.Aquater2050.com/2015/11/

3.      L. H. Wald, “AP4.7B SHAPING THE DARK MATTER CLOUD” www.Aquater2050.com/2015/11/

4.      L. H. Wald, “AP4.7C DARK MATTER RATE EQUATIONS” www.Aquater2050.com/2015/11/

5.      Misner, Thorne and Wheeler, Gravitation, New York, Freeman and Co., 1973.

6.      J. Magueijo, New Varying Speed of Light Theories, arxiv.org/pdf/astro-ph/030545v3.pdf

7.      I. G. Amelino-Camelia, “Testable Scenario for Relativity with Minimum-Length” hep-th/0012238. 

8.      J. Magueijo, Faster than the Speed of Light, Penguin Books, New York, New York, 2003

9.      L. Smolin, The Trouble with Physics, Boston, New York: Mariner Books, 2006

10.  L. H. Wald, “AP4.7I THE SUPER PARTICLE AS A COSMIC RAY” www.Aquater2050.com/2015/11/

11.  G. Kane, Modern Elementary Particle Physics, Ann Arbor, Michigan, Perseus Publishing

12.  L. H. Wald, “AP4.7D HOW TO PROVE A THEORY’S CORRECTNESS” www.Aquater2050.com/2015/12/

13.  L. H. Wald, “AP4.7M VARIABLE LIGHT SPEED IN MODEL 1 www.Aquater2050.com/2015/11/