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 connected 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 (protons) 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.

There is reason to take Model 1 seriously. It quantitatively explains (ref 9, 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 Radiation.

In working out this model, some problems arose that are connected with it. A fundamental issue arose with respect to the ultra high-energy cosmic rays (UHECR’s) that have been observed. The accelerated expansion of particle space caused by its vacuum potential energy density has also been observed. It became important to ask if a UHECR could be a super particle that tunneled into particle space and decomposed leaving vacuum potential energy and a UHECR proton. A bubble in the density of gamma rays centered on the galactic center has also been noted that may also be connected with this process. These problems will be addressed here.

The Problem

The UHECRs

Blasi (Blasi, 1) describes the problem of a set of ultra high-energy cosmic rays (UHECRs), which are observed in an energy range where there should be no cosmic rays. The reason is as follows. A cosmic ray is usually a very high-energy proton. When it interacts with the earth’s upper atmosphere, it produces gammas that penetrate to earth and are detected there. It was found, using the standard model of particle physics, that a proton with energy above a certain energy (the GZK cutoff ~ 4×10¹⁹ eV or ~ 4×10¹⁰ GeV), interacts with the microwave background in particle space to form other particles (pions). Since microwave background is everywhere, protons with extremely high energy (i.e. from super nova etc.) should not last very long in particle space. This means that particle space should be dark above this energy unless the source is common within our galaxy and close to our solar system. Yet such sources (neutron stars, AGN’s, white dwarfs, radio lobes, etc) are not common enough in our neighborhood of the galaxy to account for the UHECR’s we observe. Furthermore the observed UHECR’s are omni directional, and the particles from neutron stars, AGN’s, white dwarfs and radio lobes are not (Blasi, 2). Here, we investigate where these cosmic rays come from.

The Accelerated Expansion of Space

The expansion of space has been tied to the potential energy density in particle space. The particles exist in particle space controlled by a single new scalar field, f. The energy density ρ and pressure p equations that result are as follows (Peebles, 396):

ρ = ø’ ²/2+ V; and p = ø’ ²/2 – V)

Where:

V = a potential energy density

ø = a new real scalar field

ø’ ²/2 = a kinetic energy term = ρ – V

Now, we expect V to be a slowly varying function of time, because the mass of the black hole is large, so it must change slowly, and the mass is the source of V. Also the same logic says the time derivative of the field must also be small. Further, V must be inversely proportional to r, because the field’s potential energy comes from the black hole, and the black hole’s potential energy falls off with r. We note that there is an r small enough so V is large enough to make a significant contribution to the stress-energy tensor. Finally, The kinetic energy term is expected to be slowly varying with time, because the black hole is massive, and new mass will not change the overall mass much, and so the field will vary slowly with time. Thus there is an r close to the center of the black hole where the pressure will turn negative. Also, this condition will eventually fail at a large enough radius. Finally, at a radius large enough, the falling V will reach the intergalactic value, and flatten. This flat intergalactic value will be the observed intergalactic accelerated expansion potential energy density of ~10^-4 GeV/cc (Kane, 112), where the potential energy term dominates the kinetic energy term. Below we will investigate where this flat intergalactic potential energy density comes from.

The Observed Data

The UHECRs

The observations, as described in Blasi (Blasi, 2) are as follows. Cosmic rays have been observed from ~ 0.1 GeV up to 3 x 10¹¹ GeV. We note:

A total of 59 events have been observed above 4 x 10¹⁰ GeV. The spectrum of these events from ~5 GeV to ~10⁶ GeV has a power law increase with slope of ~ 2.7. From ~10⁶ GeV to ~10¹⁰ GeV, the slope increases to ~ 3.1. At energies larger than 10¹⁰GeV, the spectrum begins to flatten out.
The 59 events appear to be isotropic on the large scale..
On the small scale, 5 possible doublets and 1 possible triplet were found.
The primaries appear to be mostly protons. A recent study indicates less than 30% are possible photon primaries.

It should be noted that there is an observed increase in the number of gamma rays in the center of our galaxy. This must come from a gamma ray source density bubble centered on the galactic center.

The Accelerated Expansion of Space

Two teams of astronomers determined the distance of super novas by use of their red shifts, and found that the universe is undergoing an accelerated expansion. A Nobel prize was awarded for their work.

The Solution

The UHECRs

Model 1 predicts high-energy cosmic rays with the following characteristics.

Super particles will tunnel through the barrier between vacuum space and particle space with energies in a Gaussian distribution in the range ~10¹⁰to10¹⁹ GeV. The portion of the super particle Gaussian less than 10¹¹GeVis reduced because the vacuum space potential energy attenuates the super particles if they have kinetic energy less than this value (see Appendix 1). Note that the cosmic rays less than 1017 GeV are attenuated because they come from super particles in vacuum space with energy less than the potential energy of vacuum space (see Appendix 1). In particle space, they are unstable, so they break down (through spontaneous symmetry breaking) into extremely high-energy protons, giving up the extra potential energy to the particle space vacuum (becoming dark energy). The resulting protons in particle space will have energy in the range 10¹⁰ to 10¹⁹ GeV..
The super particles in vacuum space have a Gaussian distribution with a mean, which depends on the age of the universe. Thus:

– For a young universe, the mean will be low (energy range ~10¹⁰ to ~10¹¹ GeV), because the super particles coming in from the black hole (see ref 3, AP4.7C) meet a relatively large, empty vacuum space, so they expand into the volume and their temperature goes down.

– For an early mature universe, the mean will be modest (energy range ~10¹¹ to ~10¹² GeV), because the addition of more energetic super particles will have increased the particle temperature and density in vacuum space, and the cosmic net is beginning to build, so conditions are right for making galaxies.

– For a middle aged universe, the mean will be medium (energy range ~10¹² to 10¹⁸ GeV), because the super particle temperature and density will have increased enough to generate a mature cosmic net (see ref 4, AP4.7B), and the generation of galaxies along the net will be rapid.

– For an old universe, the mean will be high (energy range ~10¹⁸ to 10¹⁹ GeV), because the super particle temperature and density will have increased enough to be near to the Planck energy preparing for a new big bang.

The protons that result from super particles in particle space will be isotropic in velocity direction on the large scale, because they come from an isotropic distribution of super particles in thermodynamic equilibrium in vacuum space.
On the small scale, doublets and triplets can form from reactions with resident particles in particle space.
Ultra high-energy protons will result from the super particles, but collisions with particles in particle space can also cause ultra high-energy gammas.
Because there is a bubble in the density of the super particles centered on the galactic center (see ref 5, AP4.7, there will be a bubble in the density of the protons that have tunneled out of the super particle barrier shell centered on the galactic center. By colliding with resident dust and gas, these ultra high-energy protons will cause a bubble in the density of gammas centered on the galactic center. This bubble has been observed, as noted above.

We note that the cosmic rays of Model 1 are omni-directional, and so match the UHECRs that are observed..

The spectrum of the UHECR’s matches the Model 1 spectrum for early in the “mature universe” stage. The (~10¹¹ to 10¹² GeV) slope shows the spectrum of ordinary cosmic rays plus the rising contribution of the cosmic rays caused by the high-energy tail of the super particle Gaussian. The rollover beyond ~10¹⁰ GeV is caused by the peak and then the drop-off of super particles as the Gaussian tails off. The isotropy, the doublets and triplets and the dominance of protons match the data satisfactorily.

Note that a shift (if any) of the GZV cutoff to a higher value has no impact on this match, because it only impacts what happens to the particles after entering particle space. Such a shift makes other sources for UHECR’s possible in terms of the cutoff. However, the generation sources and the spectrum of the protons produced do not appear to match those observed. Nonetheless getting cosmic ray data for events up to 10¹⁹ GeV will clarify this issue by showing any new cutoffs.

The Accelerated Expansion of Space.

According to Model 1 (see ref 3, AP4.7C), the super particles that tunnel out from Vacuum space yield enough vacuum energy in particle space over 10¹⁰ years to account for the 10^-4 GeV/cc needed for the accelerated expansion of space observed now. Now recall the equations:

ρ = ø’ ²/2+ V; and p = ø’ ²/2 – V)

The intergalactic energy density ρ starts very high after the big bang with V dominant so the pressure is negative, causing space to expand. The V is used forming particles and anti particles with an excess of particles (see ref 3, AP4.7C for details), until ø’ ²/2 dominates. Then the pressure turns positive, and space stops accelerated expansion, but continues ordinary expansion with a low value of V. Meanwhile, black holes are forming and generating shielded super particles. Some of the super particles (with extremely high potential energy) are tunneling out through the shields, and decomposing into ultra high-energy protons and giving up V into particle space in the process. If we assume the process of making black holes and the rate of passage of super particles are both roughly linear, the combined process is roughly quadratic, and particle space is gradually filled with potential energy from super particles until it dominates and accelerated expansion starts. If the barrier thickness is ~10^-31 cm, and the potential energy density is ~10⁷²GeV/cc, we get the following result. About half way through the life of the universe, the pressure turns negative, and we get accelerated expansion, and then over 10¹⁰ years the tunneling super particles yield the 10^-4 GeV/cc we observe now. This behavior is what astronomers have observed recently.

Testing Model 1 with Data

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

The UHECR’s that cannot be accounted for by ordinary processes, but are still observed.
The potential energy needed to explain the accelerated expanding universe we observe. .

These predictions form a strong argument for the existence of dark energy derived from dark matter and the correctness of Model 1.

In addition to the above argument, there is a connected argument in favor of the acceptance of Model 1. To construct Model 1 we start with constants from quantum mechanics (Planck energy) and the standard model of particle physics (force unification energy), and choose two new constants (the spherical barrier radius and the barrier thickness). We can then quantitatively explain five observed phenomena that have yet to find a single consistent explanation, namely:

The origin, characteristics and operation of dark matter – see ref 5, AP4.7B
The accelerating expansion of the universe (Dark energy)-see above
The UHECR (cosmic rays) that have been observed in the energy range beyond the GZK cutoff-see ref 12, AP4.7I.
The huge disparity in the different estimates of the vacuum potential-see Kane, 112.
The large-scale cutoff and asymmetry in the Microwave Background Energy-see ref11, AP4.7F.

We have used two equations to obtain two unknowns. The results were then used to satisfy the equations for three other phenomena. This is not possible unless the phenomena are connected and part of a single unified physical process.

In addition to these data tests, there is a significant experiment that could be performed to prove Model1. It may be possible to stimulate the dark matter to force the emission of UHECRs (see ref 8, AP4.7K).

Summary and Conclusions

Ultra high-energy cosmic rays (UHECR’s) and vacuum potential energy density have been studied to find their origin and characteristics. They are found to match the characteristics of Model 1 super particles (dark matter) that have tunneled through the barrier separating vacuum space from particle space in Model. We found that after tunneling, super particles brake down into a UHECR proton and potential energy. The UHECR proton is observed as a cosmic ray. The potential energy is observed as vacuum energy density in particle space. The observed spectrum of UHECR’s appears to match the expected spectrum of an “early mature universe”, which means that the mean energy of the super particle Gaussian distribution of dark matter is at ~10¹² GeV.

Appendix 1

The Barrier Equations

Consider the following non-relativistic three-dimensional time independent Schrödinger equation (see ref 7, AP4.7).

[-(h²/8Π²m)Ñ²+V(x, y, z)]Y(x, y, z) = EY(x, y, z)

Where:

V(x, y, z) = barrier potential

E = particle energy

If we convert to spherical coordinates, and let:

Y(r, q, f) = R(r) Y(q, f)

Where:

Y(l, m) = Spherical Harmonics = (4Π) ^-1/2 , if l = 0 (spherical symmetry)

Now, let:

R(r) = U(r)/r,

then:

Y(r, q, f) = (4Π) ^-1/2 U(r)/r

Now, consider:

[-(h²/2m d²/dr² + V(r)]U(r) = EU(r)

Where:

E = the energy of the particle.

V(r) = V_o[Q(r) – Q(r-w)] = the vacuum potential.

And:

Q(x) = the Heavyside step function of width a starting at x =0

w = the potential zone width.

Note that any solution to the equation is unchanged if the step function is moved along the r axis to r_ob. Then:

1. One can think of starting at 0 and moving to r_ov. Think of this as moving within the super particle itself, so the complex kinetic and potential energy distributions applicable within the particle exist here.

2. One then moves from r_ov to r_ob., so w = r_ob-r_ov.= v. This is vacuum space, so the vacuum potential is V(r) = V_ov[Q(r_ov) – Q( r_ov-v)] = the vacuum potential

3. One then moves from r_ob to r_ob + a, so w = a. this is the space within the barrier itself, i.e. between vacuum space and particle space, so the vacuum potential is V(r) = V_ob[Q(r_ov) – Q( r_ov-v)] = the vacuum potential.

Thus the equation governs passage from the super particle through vacuum space and then through the barrier and into particle space. For convenience, we will let r = 0for solving the equation. Note that what we are describing is two concentric spherical shells with thicknesses v and a wrapped around a super particle. The shell with thickness v is vacuum space. The shell with thickness a is the barrier between vacuum space and particle space.

Note that what we will calculate is the transmission probability density (T = t²= r) or probability of transmission. The solution to the equation is a combination of left and right moving wave functions that are continuous at the boundaries of the barrier (r = 0 and r = w) along with their derivatives.

The solution can be used to generate the transmission through the barrier T (see Ref 8), which is as follows:

If E>V

T = 1/(1+V₀²sin²(k₁w)/4E(E-V₀)

If E<V,

T = 1/(1+V_o² sinh²(k₁w)/4E(V₀-E),

There:

k₁= (8Π²m(V₀-E)/h²) ^1/2

Here we have set up the equations for either of two shells, a vacuum space shell and a barrier shell. The rate of passage of a particle through either spherical shell is

R = T h/2Π k₁

The best fit for the vacuum space sphere and the barrier shell of the very rough data available is:

r_ov= 10^-20 cm

r_ob= 10^-11 cm

a = 10^-31 cm

There are three important cases.

Case 1

E > 10¹⁷ GeV

V_ov= potential energy ~ 10¹⁷ GeV

V_ov/cc = potential energy density ~ 10³² GeV/cc

N = number of super particles in vacuum space = 10⁶⁰ super particles

This is the vacuum space case for particles with potential energy ~ 10¹⁷ GeV-i.e. super particles. We note that super particles with kinetic energy greater than 10¹⁷ GeV move freely in vacuum space. If the kinetic energy drops below 10¹⁷ GeV, however, the probability of operating in and passage through gradually attenuates.

Case 2

E ~ 10¹⁷ GeV

V_ob= 10¹⁹ GeV

V_ob/cc = potential energy density ~ 10⁵⁰ GeV/cc

N = number of super particles in vacuum space = 10⁶⁰ super particles

This is the case of leakage of super particles for the whole universe by tunneling through the barrier. When these particles reach particle space, they break down to ordinary particles and give up their phase change energy (10¹⁹ GeV/sp) into the particle space vacuum energy, or dark energy, which over 10¹⁰ years has made a dark energy of ~ 10^-4 GeV/cc. This is the same dark energy that causes the accelerated expansion of space that requires a potential energy of ~ 10^-4 GeV/cc.

Case 3

E = 10¹⁹ GeV

V_ob= 10¹⁹ GeV

This is the case of big bang passage over the barrier (see ref 3, AP4.7C for details).

References

P. Blasi, “The Highest Energy Particles in the Universe: the Mystery and its Possible Solutions”, arxiv.org/pdf/astro-ph/0110401.pdf
J. Magueijo, New Varying Speed of Light Theories, arxiv.org/pdf/astro-ph/0305457.pdf
L. H. Wald, “AP4.7C DARK MATTER RATE EQUATIONS” www.Aquater2050.com/2015/11/
L. H. Wald, “AP4.7A SUPER PARTICLE CHARACTERISTICS” www.Aquater2050.com/2015/11/
L. H. Wald, “AP4.7B SHAPING THE DARK MATTER CLOUD” www.Aquater2050.com/2015/11/
L. H. Wald, “AP4.7G ORIGIN OF THE NEW REAL SCALAR FIELD” www.Aquater2050.com/2015/12/
L. H. Wald, “AP4.7F GATHERING THE DARK MATTER FOR THE BIG BANG AND ITS IMPACT ON MBR” www.Aquater2050.com/2015/12/
L. H. Wald, “AP4.7K OBSERVATION OF SUPER PARTICLES INSIDE THE BARRIER SHELL” www.Aquater2050.com/2016/01
L. H. Wald, “AP4.7D HOW TO PROVE A THEORY’S CORRECTNESS” www.Aquater2050.com/2016/12/