Abstract

In a previous paper (ref 1, AP4.7), a self-consistent theory called Model 1 was developed to answer some questions in astrophysics on dark matter and dark energy. 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.
• After the big bang exhausts itself, super particles that remain in vacuum space 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.  

Here, we explore the cycling of the universe to see how it may work in order to repeat many times and become Cycle 1 of many cycles in a cyclical universe. 

 

The Problem

In Model 1 we investigated our universe as it starts with a big expanding bang and ends with a small, contracting sink that expands into a new bang. It is logical to ask if the new bang has the proper characteristics to expand into a new universe similar to the one we inhabit. It appears possible that the universe does not have a single beginning and ending. Instead, it may recycle and regenerate itself many times. If it does regenerate, we ask if it can recycle forever. Here we take the elements of Model 1, and see if it can be one element of a complete self-destructing and self-regenerating universe is possible (called Cycle 1 of many cycles in a Cyclical Universe). If this recycling is possible, we ask how many cycles can be repeated. As we accomplish this task, we will check with the observed data on the universe to see if they support this concept.

 

The Solution

We propose a complete self-connecting and sustaining cyclical universe, and check the consequences. We start the investigation by checking Cycle 1 to see if it can satisfy the observables we see at the present time. As a starting point to describe the Cycle, we will use the big bang, but it is not the beginning of this cyclical universe as will be seen. To describe the Cycling, we will describe each stage of development of the universe stage by stage. We will also postulate three initial conditions for the big bang taken from Model 1.

1. A high temperature, low entropy bubble of energy that enters particle space.
2. The laws of physics are the same as ours, and the potential energy is high in this initial energy bubble at the beginning of the big bang (See reference 10, AP4.7P for a description of how this condition arises).
3. There is a feint tracery of a cosmic net made up of super particles in a separate space (quantum vacuum space-to be referred to as vacuum space) called dark matter. Super particles in vacuum space are separated from particle space by a potential barrier shell.

At the end of the cycle, we will check to see how well the initial conditions are regenerated by attempting to form a new universe like ours capable of supporting life.

Implicit in this proposal and used as a basis for generating Cycle 1 are the following theories.

• On the small scale, the simplest form of the Standard Model of particle physics will be used to move from energy to matter, because it is well tested.
• On the large scale, General Relativity will be used to describe galaxies and black holes, because it is well tested.
• At the intersection, Loop Quantum Gravity (Smolin, 250) will be used, because it has some initial successful tests.

 The stage-by-stage development is as follows (see ref 8. AP4.7N for more details)

1. Stage 1 starts with a huge, concentrated high-energy, low entropy bubble entering particle space with high potential energy (see Postulates 1 and 2). Note also that there is a feint cosmic web remnant of dark matter (Postulate 3). It moves through a stage where there is an expanding space, a gas of simple particles (quarks and electrons), a cloud of photons, and very little anti matter. It then moves to a gas of simple matter (baryons and electrons) in particle space, forming on the tracery of the cosmic web. At the end of this stage (see Appendix 1), there are atoms and molecules of hydrogen and helium forming loosely organized galaxies in space on the feint cosmic web, and a slowly expanding space between the galaxies, and that is what we observe.
2. Stage 2 starts in particle space with wispy galaxies forming on a cosmic web and a localized but expanding concentration of photons. It moves through this stage by forming black holes in the huge initial stars that have formed as part of the wispy galaxies. These initial black holes transfer particles to vacuum space by forming super particles, which then form up on the existing feint cosmic web and strengthen it, as shown in Appendix 2.
3. Stage 3 starts in particle space with proto spiral galaxies forming on a stronger cosmic web, but with central black holes in many of them as shown in Appendix 3. These central black holes form halos of dark matter (shielded super particles) around each galaxy, and strengthen the existing nodes in the web. They also start making new connections between these nodes (galaxies) in the galactic web as shown in Appendix 3. At the same time, they start the leakage of super particles through the barriers in vacuum space, which shows in particle space as dark energy and Ultra High Energy Cosmic Rays (UHECR’s). There are few of these second-generation galaxies with significant concentrations of carbon through iron elements. The photons in the photon cloud have stretched to longer wavelengths by that time due to the expansion of the universe. 
4. Stage 4 starts in particle space with spiral galaxies forming on a strong cosmic web. The galaxies are well formed and starting to collide and form elliptical galaxies. The number of second-generation galaxies with significant concentrations of the elements carbon through iron and beyond in their suns is large and increasing. The black holes, dark matter, dark energy and UHECR’s are increasing. At the end of this stage there will be a high mean energy in the vacuum space super particles, so a slight amount of energy with high temperature and high potential energy will be spilling into particle space. This stage is described in more detail in Appendix 4.
5. When the mean energy particles of the super particle distribution reach the potential energy of vacuum space, the true big bang begins.  However, not all of the energy in vacuum space reaches particle space. Only the super particles in the mid to high-energy zone of the distribution pass into particle space. The low energy super particles remain as the faint cosmic web tracery. These high-energy super particles collide and disrupt into energy, forming a high-energy blob. The remaining super particles provide the charges that determine the laws of physics for the formation of new particles and super particles from the high-energy blob. Note that the old universe has generated the high-energy blob, the high potential energy, and the feint tracery of the old cosmic net, so the postulates shown above are produced. The details of the new conditions are given in Appendix 5.
6. We reach the recycle point here and particle space ends with the residuals in particle space and vacuum space left over from the big bang. Thus, we end up with some low to moderate temperature matter with high entropy that cannot recycle and participate in future cycles. This matter is effectively “dead”. We discuss the impact of these residuals in Appendix 6.

The Appendices shown give the procedure and the mathematics for each step. The data that either supports or denies Cycle 1 is mostly given in the references cited. The conclusions that can be reached from this information and those data will be given in the next section.

 

Summary and Conclusions.

We have shown that it is possible, in theory, that our universe recycles and regenerates itself in a series of cycles starting with Cycle 1. This recycling universe has been formed from the elements of Model 1, and it is called the Cyclical Universe. We have also noted that the observable characteristics of this cyclical universe appear to match the observations we have of our universe. We have finally found that this recycling does not appear to last forever. The mass-energy of the Cyclical Universe passes through the high-energy low entropy vacuum space, then a moderate energy particle space, and finally ends up as residuals at low energy and high entropy spread widely in particle space. This residual matter cannot be recycled without raising the temperature, and the concentration of the matter, and thus lowering the entropy. This situation raises the question: What happens next to the mass-energy of the universe? In reference 10, AP4.7P, we propose another final recycling procedure that starts with a complete and total big bang as the next step to restore the high entropy condition.

 

Appendix 1

We start with energy at high temperature in particle space and high vacuum potential energy (Postulate 1, above). The energy must convert to matter in a time determined by the uncertainty principle:

            δt = h/2πδE.

Also matter must convert to energy by the same equation. Now particle space expands because vacuum space is losing potential energy into particle space. The temperature drops. The kinetic energy drops. We see that particle space started with a high potential energy in this mix of energy and particles (Postulate 2, above), so the potential energy in particle space still dominates, and pressure is negative. Space expands rapidly.  The potential energy now generates particles as matter and anti matter, so potential energy drops. Again charge is conserved, but baryons are not. All the particles and forces of the standard model gradually freeze out through spontaneous symmetry breaking while the mixture cools. The matter and anti matter particles annihilate each other as they freeze out, and a sea of photons is formed. The speed of light, which started high in the early, high-energy phase of the expansion, reduces as the energy drops (ref 9, AP4.7M). Thus, the material in particle space, which started at equilibrium as a mixture of matter and anti matter particles annihilating each other, now becomes matter and anti particles annihilating each other, but not in equilibrium. 

The details of the process that generates particles are important now. In the formation of matter and anti matter, our current particle data show that there is roughly one matter baryon excess for 10¹⁰ photons in particle space (ref 2, AP4.7A). This result can happen only if (Kane, 290):

• Conservation of baryon number is violated.
• Charge-parity (CP) is violated.
• Particle space is not in thermodynamic equilibrium while the above conditions are satisfied.

As shown above, the conservation of baryon number was violated as soon as the energy converted to particles. Thus, the energy has reformed as matter and anti matter particles while still in thermodynamic equilibrium due to the high light speed at the high energy existing there. Since there is thermodynamic equilibrium, a roughly equal number of particles and anti particles are produced, because excess particles will convert back to energy, and start again converting into particles and anti particles. The matter and anti matter particles annihilate each other producing photons that eventually become our microwave background. As this process continues, the loss of thermodynamic equilibrium along with the continued CP violation results in an excess of matter particles. Particle space is then left with a large number of photons, and an excess of matter, from which galaxies are formed. This condition is what we observe now. For more details of this process, see ref 3, AP4.7C.

Appendix 2

We start with a gas of simple particles (hydrogen, deuterium and helium), and a cloud of photons in particle space. We need a massive structure for the particles to form around to make galaxies. Computer experiments have shown that gasses need a massive seed of attraction to collapse on to form and maintain galaxies. Without this seed, the resulting contracting swirl is unstable and breaks up. So we postulate a feint cosmic web in a separate space (vacuum space) made up of residual dark matter (postulate 3, below) that the gasses could contract on to form the initial galaxies. Vacuum space is separated from particle space by a potential barrier (see ref 1 AP4.7 for more details) according to the equation:

            [-(h²/8Π²m)∂ ²+V]Ψ = EΨ

            Where:

            V = potential energy of a quantum field

            E = total energy

            (h²/8Π²m)∂ ² = kinetic energy

Here, we identify the potential energy from the curvature of space-time due to mass in a black hole with the potential energy of the Schrödinger equation. The gravitational spatial curvature of a black hole could distort the particle orbital structures enough to increase the internal energy of the particle to the super particle level. Then the creation and destruction operators can be used in the Schrödinger equation to create super particles.

Now, we note:

            E = the energy of the super particle.

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

            Where:

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

            a = the barrier potential width.

Note that we are describing is a spherical shell potential barrier of radius r_o and thickness a around a super particle.

In solving this equation, 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 = a) along with their derivatives.

The solution can be used to generate the transmission through the barrier T , which is as follows:

            If E>V

            T = 1/(1+V₀²sin²(k₁a)/4E(E-V₀)      

            If E<V,

            T = 1/(1+V_o² sinh²(k₁a)/4E(V₀-E),

            Where k₁= (8p²m(V₀-E)/h²)) ^1/2

Here we have set up the equations for a super particle with spherical vacuum barrier of radius r_o and thickness a. Inside the radius is vacuum space. Outside the radius is the barrier shell of thickness a, and outside that is particle space. The rate of passage of a particle through the spherical vacuum barrier is:

            R = T h/2Π k₁

Note that the high initial potential energy is gradually being used up to form the particles, so the spatial expansion is slowing down as a result. The temperature of the matter is reducing as the expansion progresses.

Note also that the cloud of photons from annihilating matter and anti matter is building up where the particles are forming, and making a spatial spectrum guided by the feint cosmic net. The spectrum is peaked because the cloud is localized and has an edge beyond which there are few photons. Because the particles are being formed, the vacuum potential energy is diminishing, and therefore, so is the red shift.  

Appendix 3

We start with galaxies forming on a cosmic net and a localized concentration of photons. The galaxies form black holes at their centers as they contract, and they “feed” on surrounding gasses and stars as they grow. The particles a black hole ingests descend to the radius where it reaches the Planck energy. There they bounce on that boundary, and move into vacuum space and form super particles (for more details, see ref 3, AP4.7C). This formation is accomplished as follows.

The super particles are imbedded in a new scalar field, f. The energy density and pressure equations that result are as follows:

Here, p = Ø’ ²/2 – V)

            Where:

            V = a potential energy density

            Ø = a new real scalar field

            Ø’ ²/2 = a kinetic energy term

The value of V is high enough in the vacuum space zone near the black hole center to overcome the kinetic energy term and generate an expansion condition, and space expands. The expansion of space closer to the black hole than an imbedded particle moves the particle away from the black hole center. The use of potential energy to make particles, and the expansion of space away from the black hole center reduces V below the kinetic energy term (f’ ²/2), and the expansion dies. Then the particle is dragged back through space by the gravitational attraction of the black hole. But the motion of the particles is inhibited by the diffusion process (see the diffusion equations, below).  Thus the particles tend to concentrate at a radius where these three processes balance (r_o).

Gradually, the kinetic energy increases enough through energetic particle addition to a limited volume, to provide the activation energy needed, and along with the high potential energy available, super particles are formed. The super particles are then bounced against the Planck energy into vacuum space inside the vacuum barrier shell. There, encased in the protective vacuum barrier shell, they are pushed away from the black hole center beyond r_o by the high potential energy (and thus negative pressure). The volume is larger there, however, so the temperature goes down. The radius ~ r_o supports an energy level high enough to ionize the super particles.

Thus, we see that the super particles move radially to a quasi-stable minimum shell around the black hole center to form a source of incoming ionized super particles. This is an impulse source that gives out super particles as long as the black hole is feeding- a time short compared to the life of the galaxy. The particles do not remain at this equilibrium point, however, they diffuse away from it under the influence of the concentration gradient, and the electromagnetic force helped by the expanding space. Thus we have the dark matter cloud generation equations:

             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)  = a Gaussian distribution of particles diffusing from a finite spherical shell  source, where space expansion and the gravitational force balance.

Appendix 4

This is what we observe in our time. We start with galaxies with black holes and dark matter connected to a cosmic web. Super particles will tunnel through the barrier between vacuum space and particle space with energies in a Gaussian distribution in the range ~10¹⁰ to10¹⁹ GeV. The lower portion of the Gaussian (10¹⁰ to 10¹² GeV) is dramatically reduced, however, because the barrier passes high-energy super particles easier than low ones (see Appendix 2). In particle space, they are unstable, so they break down (through spontaneous symmetry breaking) into UHECR’s, giving up their extra potential energy to the particle space vacuum energy density. The resulting protons in particle space will have energy in the range 10¹² to 10¹⁸ GeV (as observed). Now this is a mature universe, and for a mature universe, the mean of the Gaussian will be medium (energy in the range ~10¹⁴ to 10¹⁸ GeV), because the super particles entering the black hole will have increased the temperature and density enough to generate a mature, medium temperature Gaussian distribution of super particles. The potential energy from the tunneling super particles will have built up enough in particle space to pass the declining vacuum energy from the big bang, and achieve the increasing 10^-4 GeV/cc that we observe now.

By now, the cosmic photon background photons have stretched their wavelengths into the microwave (~ 3 deg K) due to the expansion of the universe. The spatial spectrum has a large peak. This matches with the prediction for a new universe that starts as a local zone drawing in dark matter from a large vacuum space and concentrating it before sending it out from the area around a principal black hole. This forms a new, small, growing zone of highly curved space. The growth of this zone is accelerating due to a slowly increasing potential energy density generated by super particles tunneling in from vacuum space and breaking down in particle space to leave their potential energy there. Thus the size of the universe and the principal spatial mode of the background radiation are locked together from the start. For more details, see Ref 5, AP4.7F.

This stage continues by heating up the super particles and ends with the super particles hot enough for some to begin leaking into particle space, but not enough to cascade into a big bang.

Appendix 5

We start with galaxies with black holes, dark matter, an increasing red shift and UHECR’s, and CMB. Gradually, the average kinetic energy of the total dark energy mass increases enough through energetic particle addition via the black hole to a limited volume, until it equals the potential energy of the barrier. 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 (ref 9, AP4.7M). So, these extreme energy super particles diffuse rapidly to the principle black hole drawn by a density gradient sloping toward the black hole and the force of the black hole’s gravity. They then rush over the barrier (see Appendix 2). This rush can occur from anywhere in the observable 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 dark matter is drawn rapidly toward the general site of the big bang (see ref 5, AP4.7F for more details).

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 hole, 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.

A residual cosmic web in vacuum space remains after the big bang exhausts itself 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. Note that the remaining super particles provide the charges that determine the laws of physics for the formation of new particles and super particles from the high-energy blob. This will guide the formation of the new universe, and we have just covered Postulate 3.

Cycle 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, high potential energy space where particles condense near the remnants of an old, contracted cosmic web, and give up potential energy into particle space, and we have just covered Postulate 2. The growth of this universe diminishes as the potential energy causing the expansion is diluted and used up forming particles.

Since the kinetic energy has actually exceeded the shell potential energy to start the big bang, the super particles have enough kinetic energy (at the Planck energy) after flowing into particle space, that collisions can cause complete disruption of the super particle into energy. Note that both positive and negative ions from the ionized gas of super particles are temporarily converted to energy, so charge is conserved. Thus, the super particles will not only flow over the barrier, they will disintegrate into energy as they reach particle space according to the uncertainty principle:

            δt = h/2πδE.

But there are a residual number of super particles with charges from the old universe, and these will guide the formation of new particles according to the laws of physics of the old universe. Thus, we have partially covered Postulate1. We have not completely covered Postulate 1, because the particle space after the new big bang did not recover all of the mass-energy from the prior particle space, and vacuum space. Some was left in the residual particles left in particle space that had not yet entered black holes. More was left in the residual super particles left in the trace cosmic web left in vacuum space.

Appendix 6

The residuals in vacuum space will eventually cycle from their high-energy state down into a widely separated, low energy state in particle space. The residuals from particle space have no place to cycle to, so they gradually build up as low energy residuals that are outside of the active bubble formation zones. We might view this as an entropy build-up zone, and we emphasize that a recycling universe formation procedure cannot last forever. Eventually enough matter ends up in a low energy, high entropy state that nothing can happen to it, unless and until a comprehensive and eternal recycling process takes place that reduces entropy in this matter and restarts the cycles again. Such a process is proposed in reference 10, AP4.7P as an automatic result of the physical characteristics of the system proposed in Model 1.

Appendix 7

The equations above make it possible to estimate the time between big bangs. As mentioned above, the leakage of super particles into intergalactic space is a leakage into the base of super particles in Vacuum space. This base has the galactic bubble of super particles superimposed on it. A galactic bubble is expected to reach the spillover point first, so galactic parameters will be used for this calculation. At the present time, an average galaxy is estimated to have the value ~10⁶⁰ GeV which was built up over ~10¹⁰ years (the lifetime of our universe). The rate of buildup started at 0 because there were no black holes. As the number of black holes increased, the rate increased in vacuum space according to the formula

            R_vt_i² 

            Where:

            R_v = vacuum space rate constant = 10¹⁷ GeV/sec²

            t_i  = time  from the big bang to now = 10¹⁰ years= 3 x 10¹⁷ sec

Now the vacuum potential energy barrier has an estimated value of 10¹⁹ GeV. Also, the super particles build energy from E = 10¹⁷ to 10¹⁹ GeV. Assuming the same buildup rate continues in the future, the time required for the kinetic energy to reach the vacuum potential, and start spilling out into a new big bang is ~10¹⁹ sec or ~10¹² years. Note that this calculation is based on several assumptions, the most important of which is that processes involved are relatively smooth and regular. This may turn out to be incorrect, so the value obtained should be viewed as only illustrative, not accurate. 

 

References.

1. L. H. Wald, “AP4.7 DARK MATTER AND ENERGY-FUNDAMENTAL PROBLEMS IN ASTROPHYSICS” www.Aquater2050.com/2015/07/
2. L. H. Wald, “AP4.7B SHAPING THE DARK MATTER CLOUD” www.Aquater2050.com/2015/07/
3. L. H. Wald, “AP4.7C DARK MATTER RATE EQUATIONS” www.Aquater2050.com/2015/07/
4. L. H. Wald, “AP4.7I THE SUPER PARTICLE AS A COSMIC RAY” www.Aquater2050.com/2015/07/
5. L. H. Wald, “AP4.7F GATHERING FOR THE BIG BANG” www.Aquater2050.com/2015/07/
6. L. H. Wald, “AP4.7J THE COMPLETENESS OF MODEL 1” www.Aquater2050.com/2015/07/
7. L. Smolin, The Trouble with Physics, Boston, New York: Mariner Books, 2006
8. L. H. Wald, “AP4.7N A NEW CONCEPT OF MASS FOR MODEL 1” www.Aquater2050.com/2015/07/
9. L. H. Wald, “AP4.7M VARIABLE SPEED OF LIGHT IN MODEL 1” www.Aquater2050.com/2015/07/
10. L. H. Wald, “AP4.7P RELATIONSHIPS BETWEEN THE PHYSICAL CONSTANTS” www.Aquater2050.com/2016/05/
11. G. Kane, Modern Elementary Particle Physics, Ann Arbor, Michigan, Perseus Publishing, 1993