For updated version—see www.Aquater2050.com/2015/12/

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 extremely high-energy cosmic rays that occur 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 our 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 building and moving bubble centered on a galaxy. The bubbles of dark matter are connect to each other by corridors of dark matter forming a cosmic web, which guides the development of new galaxies.

• There, behind a 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 an endless 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 extreme 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.  

 

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, the dark matter particles pass over the barrier into particle space. 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 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 dark matter flows 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 microwave background radiation and the galaxy formation in particle space?

In this paper, we will address each of these questions, and find answers that help 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 AP4.7C (ref 4), we describe the flow of particles up to the start of the big bang with a series of rate reactions as follows. While in particle space inside r_o, particles can become super particles because the potential energy due to the spatial distortion of the black hole is sufficiently high to allow super particle production. However, with the potential energy inside the new super particles high, the pressure becomes negative according to the equation (see Appendix 1):

 

           p = f’ ²/2 – V)

 

So the space inside the super particles expands, pushing them away from the black hole center. There, the potential energy is reduced, and the super particles convert into particles, giving up potential energy, with no black hole to provide the potential energy needed to replenish them. At the same time, the expansion of space stops at this larger radius, so the pressure becomes positive, and the particles are dragged back inside r_o by gravitation. This process is repeated, thus keeping the density of super particles inside r_o high and with the addition of new particles, increasing..

 

Gradually, the kinetic energy increases enough through energetic particle addition via the black hole to a limited volume, to provide the activation energy needed, and the super particles are bounced against the Planck energy into vacuum space inside the vacuum barrier shell. Then, encased in the protective vacuum barrier shell, they can maintain the potential energy needed to stay super particles away from the black hole central region inside r_o. Then when they are pushed away from the black hole center by the high potential energy, they form into the cosmic web observed as dark matter (see ref 3, AP4.7B). The volume is larger there, however, so the temperature goes down, and the average kinetic energy becomes less than the shell potential energy. The super particle ions that cool enough can recombine into neutral super particles. So a new heating process occurs, where super particles are heated by the addition of energetic super particles encased in potential shells from particle space near the black hole center, until the average kinetic energy reaches the shell potential energy.

 

There, the super particles near the high-energy tail of the distribution flow over the barrier into particle space. This flow starts near the black hole at the center of the highest energy peak in the of dark matter cloud (the principle black hole). Since the super particles in the high-energy tail of the distribution are between the potential energy and the Planck energy, the speed of light is extremely high (approaching infinity) according to the equation (see Appendix 2):

 

            c ~ (3 x 10¹⁰ cm/sec) / (1-E/E_m)

 

           Where:

           E_m = maximum energy = Planck energy

 

So, these extreme energy super particles diffuse rapidly to the principle black hole drawn by a density gradient and the force of the black hole’s gravity. They then rush over the barrier (see Appendix 3). This rush can occur from anywhere in the visible universe, because the speed of light is so high. The rush of high-energy super particles out of vacuum space also truncates the distribution at the high-energy tail. Meanwhile, the heating continues to push the mean energy higher toward the highest energy possible (the Planck energy). At this time in the life cycle of the universe, there are many black holes feeding vacuum space, and the number is increasing, so the heating with new energetic particles accelerates. The super particles are ionized at this high energy. The negative ions (super electrons) move at near the speed of light at this extreme energy. Also, the electric field formed between the positive and negative super particles (see Appendix 3) tends to drag the positive super ions toward the principal black hole and its neighboring black holes. Finally, as demanded by general relativity, the curvature of space is increasing rapidly around the principle black hole where the matter is gathering. Then all dark matter is drawn rapidly toward the general site of the big bang.

 

Thus, we have a condition (the critical condition) where the dark matter super particles in vacuum space are forming a distribution extremely high in kinetic energy and density. The energy distribution has a peak just under the Planck energy. The spatial distribution of dark matter in the visible universe is high and relatively flat with a modest peak around the principal black hole. When this critical condition is reached, the high energy tail of the distribution of dark matter passes over the barrier, and drags with it more by virtue of the gravity of the black holes, the density gradient and the electric field between the positive and negative super particles. This is the true big bang, and it stops when the energy of the dark matter near the principle black hole drops below the energy of the potential barrier.

 

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 new universe (see 3, below)

 

3. The Influence of the Dark Matter

 

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.  

 

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 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 spectrum of the microwave background radiation.

 

Testing Model 1 with Data

This portion of Model 1 must be tested with data. A summary of the tests that support Model 1 including those supplied by this paper are shown here. A much more detailed description of the tests that support Model 1 is given in ref 20, AP4.7D.

1. Model 1 is constructed from elements of general relativity, quantum mechanics and classical physics in their appropriate energy realms. It is self-consistent in each of those realms. 
2. It satisfies all the physical data currently known in areas of dark matter and dark energy. No other model or theory is known that satisfies all these data.
3. It connects with the standard model of particle physics, a general relativity description of black holes, the theory of ionized gasses, the theory of the speed of light at extreme energies, the theory of the Planck high-energy limit of quantum mechanics and the theory of the Higgs field.
4. It predicts the existence of a cosmic ray with energy between ~ 10¹⁷ GeV and ~ 10¹⁹ GeV that can be observed beyond the GZK limit where it should not exist. This cosmic ray has been observed.
5. It predicts the existence of a new low cross section super particle with a barrier shield that can be directly observed. This super particle is now being searched for. Preliminary results are positive.

 

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.

 

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 = f’ ²/2 – V

 

            Where:

            V = a potential energy density

            f = a new real scalar field

 

Here, it is assumed 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 (Amelino-Camelia, 6) develops a modified dispersion relation to account for this. This relation shows that when the energy increases, the speed of light increases. Magueijo (ref 8 Magueijo, 251) describes it thus, “It was as if the speed of light became larger and larger as we approached the border between classical and quantum gravity. At the border, the speed of light seemed to become infinite and absolute space and time could be recovered, not in general, but for one specific length and time- L_p, and t_p …”. This relationship can be quantified under certain conditions with the equation (ref 6 Magueijo, 31)

 

            c ~ (3 x 10¹⁰ cm/sec) / (1-E/E_m)

                       

           Where:

           E_m = maximum energy = Planck energy

 

Appendix 3 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 = Ion or gravitational 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 hole

           

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 a 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 principle contributor.

 

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) is roughly 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 = 1.128c_o

                        And c_o ~ c or less (c_o is limited by the speed of light).

                        And c ~ (3 x 10¹⁰ cm/sec) / (1-E/E_m)

                        And E_m = maximum energy = Planck energy

 

We see that as long as E < E_m but E > V, the speed of light is huge, so the big bang sink can pull super particles from the edge of the observable universe and still pass over a barrier of potential V into particle space. Note that the average kinetic energy of particles in vacuum space early in the life of the universe is much lower than the average kinetic energy of particles late in the life of the universe, so early, the diffusion is only to the edges of a galaxy and a bit beyond. Late, diffusion comes from the edge of the visible universe.

 

References

  1.     L. H. Wald, “AP4.7 DARK MATTER AND ENERGY-FUND PROBS IN ASTROPHYSICS” www.Aquater2050.com/2015/08/

  2.      L. H. Wald, “AP4.7A SUPER PARTICLE CHARACTERISTICS” www.Aquater2050.com/2015/08/

  3.      L. H. Wald, “AP4.7B SHAPING THE DARK MATTER CLOUD” www.Aquater2050.com/2015/08/

4. L. H. Wald, “AP4.7C DARK MATTER RATE EQUATIONS” www.Aquater2050.com/2015/08/
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