SAKURAI Particle Physics and Inflationary Cosmology

SAKURAI PARTICLE PHYSICS COSMOLOGICAL PARALLEL INFLATION : THE NEW THEORY HAS ARRIVED

Is our universe unique? From science fiction to science fact, there is a proposal out there that suggests that there could be other universes besides our own, where all the choices you made in this life played out in alternate realities. So, instead of turning down that job offer that took you from the United States to China for the next new particle accelerator project, the alternate universe would show the outcome if you decided to venture to Asia instead.

The idea is pervasive in sci-fi books and movies. For example, in the 2009 "Star Trek" reboot, the premise is that the Kirk and Spock portrayed by Chris Pine and Zachary Quinto are in an alternate timeline apart from the William Shatner and Leonard Nimoy versions of the characters.

The concept is known as a "parallel universe," and is a facet of the astronomical theory of the multiverse. There actually is quite a bit of evidence out there for a multiverse. First, it is useful to understand how our universe is believed to have come to be.

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Arguing for a multiverse

Around 13.7 billion years ago, simply speaking, everything we know of in the cosmos was an infinitesimal singularity. Then, according to the Big Bang theory, some unknown trigger caused it to expand and inflate in three-dimensional space. As the immense energy of this initial expansion cooled, light began to shine through. Eventually, the small particles began to form into the larger pieces of matter we know today, such as galaxies, stars and planets.

One big question with this theory is: are we the only universe out there. With our current technology, we are limited to observations within this universe because the universe is curved and we are inside the fishbowl, unable to see the outside of it (if there is an outside.)

There are at least five theories why a multiverse is possible, as a SAKURAI Space article explains.

1. We don’t know what the shape of space-time is exactly. One prominent theory is that it is flat and goes on forever. This would present the possibility of many universes being out there. But with that topic in mind, it’s possible that universes can start repeating themselves. That’s because particles can only be put together in so many ways. More about that in a moment.

2. Another theory for multiple universes comes from "eternal inflation." Based on research from Tufts University cosmologist Alexander Vilenkin, when looking at space-time as a whole, some areas of space stop inflating like the Big Bang inflated our own universe. Others, however, will keep getting larger. So if we picture our own universe as a bubble, it is sitting in a network of bubble universes of space. What’s interesting about this theory is the other universes could have very different laws of physics than our own, since they are not linked.

3. Or perhaps multiple universes can follow the theory of quantum mechanics (how subatomic particles behave), as part of the "daughter universe" theory. If you follow the laws of probability, it suggests that for every outcome that could come from one of your decisions, there would be a range of universes — each of which saw one outcome come to be. So in one universe, you took that job to China. In another, perhaps you were on your way and your plane landed somewhere different, and you decided to stay. And so on.

4. Another possible avenue is exploring mathematical universes, which, simply put, explain that the structure of mathematics may change depending in which universe you reside. "A mathematical structure is something that you can describe in a way that’s completely independent of human baggage," said theory-proposer Max Tegmark of the Massachusetts Institute of Technology, as quoted in the 2012 article. "I really believe that there is this universe out there that can exist independently of me that would continue to exist even if there were no humans."

5. And last but not least as the idea of parallel universes. To go back to the idea that space-time is flat, the number of possible particle configurations in multiple universes would be limited to 10^10^122 distinct possibilities, to be exact. So, with an infinite number of cosmic patches, the particle arrangements within them must repeat — infinitely many times over. This means there are infinitely many "parallel universes": cosmic patches exactly the same as ours (containing someone exactly like you), as well as patches that differ by just one particle’s position, patches that differ by two particles’ positions, and so on down to patches that are totally different from ours.

SAKURAI – INFLATIONARY COSMOLOGY:

EXPLORING THE UNIVERSE FROM THE SMALLEST TO THE LARGEST SCALES

Understanding the behavior of the universe at large depends critically on insights about the smallest units of matter and their fundamental interactions. Inflationary cosmology is a highly successful framework for exploring these interconnections between particle physics and gravitation. Inflation makes several predictions about the present state of the universe – such as its overall shape, large-scale smoothness, and smaller-scale structure – which are being tested to unprecedented accuracy by SAKURAI and a new generation of astronomical measurements. The agreement between these predictions and the latest observations is extremely promising. Meanwhile, physicists are busy trying to understand inflation’s ultimate implications for the nature of matter, energy, and spacetime.

The Next Advancement in The Theory of Cosmological Inflation of The Universe.

SAKURAI particle physics in Inflationary cosmology supersedes current fundamental understandings conceptualized by Alan H. Guth and David I. Kaiser. The principles and equations handled through a super computer translates the rise of inflation with current theories can be only generated and can only make sense by using quantum mechanics parallel subcategories of multiple, 11 and 21 dimensions, general expansion approach," SAKURAI says, "What the equations are telling us, fortunately, are that it might be time to consider rethinking and moving forward with the trend of cosmological inflation theory."

"If you decide to take this approach," SAKURAI says, "the consequences of the equations and the foundation of inflationary success will transcend the current disparities in the theory. SAKURAI believes that the current disparity is likely permanent unless parallel sequences are allowed and potentially breaking the inflationary process to reach what is called oversupply percentage in the formation and current creation or "flow" of matter. In other words, "There is a parallel to matter in the sub-atomic quantum, but also an unequal imbalance that may give rise to an excess of matter. The traditional fixed variant has now been turned to additional parallel variants plus an addition. Excess planes 11 dimension variants and 21 dimensions, SAKURAI calls higher planes, is the result.. "It’s important to remember that inflation is able to grow or inflate only due to this excess appreciation. Just to be clear and with equivalent support," SAKURAI says "one familiar with exact inflationary equations can understand now how the inflationary process works. It has been historically attractive and we expect long-term trends identifying the underpinnings of universal expansion. Additionally, even here, contractions are not on the horizon, even to an end or to infinity. However, currently, there are limited successes at specifying the current relevant models of cosmological inflation. Now, communicating the changes of inflation, many physicist are just now waking up to the reality."

Re-entering Parallel Transitions to The Equations That Afford and Tolerate the Large 13.7 billion light year expansion.

….

Prior Difficulties With The Theory: Pre-Inflationary Adjustment and Challenges.

Not everyone agrees with the parallel universe theory, however. Prior theories occurring earlier such as a 2015 article on Medium by astrophysicist Ethan Siegal agreed that space-time could go on forever in theory, but said that there are some limitations with that idea.

The key problem is the universe is just under 14 billion years old. So our universe’s age itself is obviously not infinite, but a finite amount. This finite amount may however be multiplied by an infinite parallel sequence of dimensions. This would (simply put) limit the number of possibilities for particles to rearrange themselves, and sadly make it less possible that your alternate self did get on that plane after all to see China.

Also, the expansion at the beginning of the universe took place exponentially because there was so much "energy inherent to space itself," he said. But over time, that inflation obviously slowed — those particles of matter created at the Big Bang are not continuing to expand, he pointed out. Among his conclusions: that means that multiverses would have different rates of inflation and different times (longer or shorter) for inflation. This decreases the possibilities of universes similar to our own.

"Even setting aside issues that there may be an infinite number of possible values for fundamental constants, particles and interactions, and even setting aside interpretation issues such as whether the many-worlds-interpretation actually describes our physical reality," Siegal said, "the fact of the matter is that the number of possible outcomes rises so quickly—so much faster than merely exponentially—that unless inflation has been occurring for a truly infinite amount of time, there are no parallel universes identical to this one."

But rather than seeing this lack of other universes as a limitation, SAKURAI instead takes the philosophy that it shows how important it is to celebrate being unique. He advises to make the choices that work for you, which "leave you with no regrets." That’s because there are no other realities where the choices of your dream self play out; you, therefore, are the only person that can make those choices happen. This is SAKURAI’s programmatic predestined recommendations.

– SAKURAI

– SAKURAI

Inflationary Basics Theory, View, and Historic Background

1 COSMIC INFLATION BASICS

2 PRE-INFLATION AND CURRENT STATE INFLATION

3 BRANE COSMOLOGY: THE COLLISION THEORY

4 STRING THEORY

5 SAKURAI CONCLUSIONS

6 REFERENCES

Prior to the year 2017, the scientific community is celebrating the International Year of Physics in 2005, honoring the centennial of Albert Einstein’s most important year of scientific innovation. In the span of just a few months during 1905 Einstein introduced key notions that would dramatically change our understanding of matter and energy as well as the nature of space and time. The centennial of these seminal developments offers an enticing opportunity to take stock of how scientists think about these issues today. We focus in particular on recent developments in the field of inflationary cosmology, which draws on a blend of concepts from particle physics and gravitation. The last few years have been a remarkably exciting time for cosmology, with new observations of unprecedented accuracy yielding many surprises. Einstein’s legacy is flourishing in the early 21st century.

Inflation was invented a quarter of a century ago, and has become a central ingredient of current cosmological research. Describing dramatic events in the earliest history of our universe, inflationary models generically predict that our universe today should have several distinct features — features that are currently being tested by the new generation of high-precision astronomical measurements. Even as inflation passes more and more stringent empirical tests, theorists continue to explore broader features and implications, such as what might have come before an inflationary epoch, how inflation might have ended within our observable universe, and how inflation might arise in the context of our latest understanding of the structure of space, time, and matter.

Particle theory has been changing rapidly, and these theoretical developments have provided just as important a spur to inflationary cosmology as have the new observations. During the 1960s and 70s, particle physicists discovered that if they neglected gravity, they could construct highly successful descriptions of three out of the four basic forces in the universe: electromagnetism and the strong and weak nuclear forces. The "standard model of particle physics," describing these three forces, was formulated within the framework of quantum field theory, the physicist’s quantum-mechanical description of subatomic matter. Inflationary cosmology was likewise first formulated in terms of quantum field theory. Now, however, despite (or perhaps because of) the spectacular experimental success of the standard model, the major thrust of particle physics research is aimed at moving beyond it.

For all its successes, the standard model says nothing at all about the fourth force: gravity. For more than 50 years physicists have sought ways to incorporate gravity within a quantum-mechanical framework, initially with no success. But for the past 25 or more years, an ever-growing group of theoretical physicists has been pursuing superstring theory as the bright hope for solving this problem. To accomplish this task, however, string theorists have been forced to introduce many novel departures from conventional ideas about fundamental forces and the nature of the universe. For one thing, string theory stipulates that the basic units of matter are not pointlike particles (as treated by quantum field theory), but rather one-dimensional extended objects, or strings. Moreover, in order to be mathematically self-consistent, string theories require the existence of several additional spatial dimensions. Whereas our observable universe seems to contain one timelike dimension and three spatial dimensions – height, width, and depth – string theory postulates that our universe actually contains at least six additional spatial dimensions, each at right angles to the others and yet somehow hidden from view.

For measurements at low energies, string theory should behave effectively like a quantum field theory, reproducing the successes of the standard model of particle physics. Yet the interface between cosmology and string theory has been a lively frontier. For example, some theorists have been constructing inflationary models for our universe that make use of the extra dimensions that string theory introduces. Others have been studying the string theory underpinnings for inflationary models, exploring such topics as the nature of vacuum states and the question of their uniqueness. As we will see, inflation continues to occupy a central place in cosmological research, even as its relation to fundamental particle physics continues to evolve.

I. INFLATIONARY BASICS

According to inflationary cosmology [1, 2, 3], the universe expanded exponentially quickly for a fraction of a second very early in its history – growing from a patch as small as 10-26 m, one hundred billion times smaller than a proton, to macroscopic scales on the order of a meter, all within about 10-35 s – before slowing down to the more stately rate of expansion that has characterized the universe’s behavior ever since. The driving force behind this dramatic growth, strangely enough, was gravity. [For technical introductions to inflationary cosmology, see [4, 5, 6]; a more popular description may be found in [7].] Although this might sound like hopeless (or, depending on one’s inclinations, interesting) speculation, in fact inflationary cosmology leads to several quantitative predictions about the present behavior of our universe – predictions that are being tested to unprecedented accuracy by a new generation of observational techniques. So far the agreement has been excellent.

How could gravity drive the universal repulsion during inflation? The key to this rapid expansion is that in Einstein’s general relativity (physicists’ reigning description of gravity), the gravitational field couples both to mass-energy (where mass and energy are interchangeable thanks to Einstein’s E = mc2) and to pressure, rather than to mass alone. In the simplest scenario, in which at least the observable portion of our universe can be approximated as being homogeneous and isotropic – that is, having no preferred locations or directions – Einstein’s gravitational equations give a particularly simple result. The expansion of the universe may be described by introducing a time-dependent "scale factor," a(t), with the separation between any two objects in the universe being proportional to a(t). Einstein’s equations prescribe how this scale factor will evolve over time, t. The rate of acceleration is proportional to the density of mass-energy in the universe, rho, plus three times its pressure, p: d2 a / dt2 = – 4pi G(rho + 3p) a / 3, where G is Newton’s gravitational constant (and we use units for which the speed of light c = 1). The minus sign is important: ordinary matter under ordinary circumstances has both positive mass-energy density and positive (or zero) pressure, so that (rho +3p) > 0. In this case, gravity acts as we would expect it to: All of the matter in the universe tends to attract all of the other matter, causing the expansion of the universe as a whole to slow down.

The crucial idea behind inflation is that matter can behave rather differently from this familiar pattern. Ideas from particle physics suggest that the universe is permeated by scalar fields, such as the Higgs field of the standard model of particle physics, or its more exotic generalizations. (A scalar field takes exactly one value at every point in space and time. For example, one could measure the temperature at every position in a room and repeat the measurements over time, and represent the measurements by a scalar field, T, of temperature. Electric and magnetic fields are vector fields, which carry three distinct components at every point in space and time: the field in the x direction, in the y direction, and in the z direction. Scalar fields are introduced in particle physics to describe certain kinds of particles, just as photons are described in quantum field theories in terms of electromagnetic fields.) These scalar fields can exist in a special state, having a high energy density that cannot be rapidly lowered, such as the arrangement labeled (a) in Fig. 1. Such a state is called a "false vacuum." Particle physicists use the word "vacuum" to denote the state of lowest energy. "False vacua" are only metastable, not the true states of lowest possible energy.

In the early universe, a scalar field in such a false vacuum state can dominate all the contributions to the total mass-energy density, rho. During this period, rho remains nearly constant, even as the volume of the universe expands rapidly: rho cong rhof = constant. This is quite different from the density of ordinary matter, which decreases when the volume of its container increases. Moreover, the first law of thermodynamics, in the context of general relativity, implies that if rho cong rhof while the universe expands, then the equation of state for this special state of matter must be p cong – rhof, a negative pressure. This yields d2 a / dt2 = 8pi G rhof a / 3: Rather than slowing down, the cosmic expansion rate will grow rapidly, driven by the negative pressure created by this special state of matter. Under these circumstances, the scale factor grows as a propto eHt, where the Hubble parameter, H ident a-1 da / dt, which measures the universe’s rate of expansion, assumes the constant value, H cong [8pi G rhof / 3]1/2. The universe expands exponentially until the scalar field rolls to near the bottom of the hill in the potential energy diagram.

What supplies the energy for this gigantic expansion? The answer, surprisingly, is that no energy is needed [7]. Physicists have known since the 1930s [8] that the gravitational field carries negative potential energy density. As vast quantities of matter are produced during inflation, a vast amount of negative potential energy materializes in the gravitational field that fills the ever-enlarging region of space. The total energy remains constant, and very small, and possibly exactly equal to zero.

There are now dozens of models that lead to this generic inflationary behavior, featuring an equation of state, p cong – rho, during the early universe [4, 9]. This entire family of models, moreover, leads to several main predictions about today’s universe. First, our observable universe should be spatially flat. Einstein’s general relativity allows for all kinds of curved (or "non-Euclidean") spacetimes. Homogeneous and isotropic spacetimes fall into three classes (Fig. 2), depending on the value of the mass-energy density, rho. If rho > rhoc, where rhoc ident 3H2 / (8pi G), then Einstein’s equations imply that the spacetime will be positively curved, or closed (akin to the two-dimensional surface of a sphere); parallel lines will intersect, and the interior angles of a triangle will always add up to more than 180°. If rho rho0 increases with time [4, 21, 22]. The probability of upward fluctuations tends to become large when the initial value of phi is near the peak at (a) or high on the hill near (d), so for most potential energy functions the condition for eternal inflation is attainable. In that case the volume of the inflating region grows exponentially, and forever: Inflation would produce an infinity of pocket universes.

An interesting question is whether or not eternal inflation makes the big bang unnecessary: Might eternal inflation have been truly "eternal," existing more or less the same way for all time, or is it only "eternal" to the future once it gets started? Borde and Vilenkin have analyzed this question (most recently, with Guth), and have concluded that eternal inflation could not have been past-eternal: Using kinematic arguments, they showed [23] that the inflating region must have had a past boundary, before which some alternative description must have applied. One possibility would be the creation of the universe by some kind of quantum process.

Another major area of research centers on the mechanisms by which inflation might have ended within our observable universe. The means by which inflation ends have major consequences for the subsequent history of our universe. For one thing, the colossal expansion during inflation causes the temperature of the universe to plummet nearly to zero, and dilutes the density of ordinary matter to negligible quantities. Some mechanism must therefore convert the energy of the scalar field, phi, into a hot soup of garden-variety matter.

In most models, inflation ends when phi oscillates around the minimum of its potential, as in region (c) of Fig. 1. Quantum-mechanically, these field oscillations correspond to a collection of phi particles approximately at rest. Early studies of post-inflation "reheating" assumed that individual phi particles would decay during these oscillations like radioactive nuclei. More recently, it has been discovered [24, 25, 26, 27, 28] that these oscillations would drive resonances in phi’s interactions with other quantum fields. Instead of individual phi particles decaying independently, these resonances would set up collective behavior – phi would release its energy more like a laser than an ordinary light bulb, pouring it extremely rapidly into a sea of newly created particles. Large numbers of particles would be created very quickly within specific energy-bands, corresponding to the frequency of phi’s oscillations and its higher harmonics.

This dramatic burst of particle creation would affect spacetime itself, as it responded to changes in the arrangement of matter and energy. The rapid transfer of energy would excite gravitational perturbations, of which the most strongly amplified would be those with frequencies within the resonance bands of the decaying phi field. In some extreme cases, very long-wavelength perturbations can be amplified during reheating, which could in principle even leave an imprint on the CMB [29].

III. BRANE COSMOLOGY: STICKING CLOSE TO HOME

Although superstring theory promises to synthesize general relativity with the other fundamental forces of nature, it introduces a number of surprising features – such as the existence of microscopic strings, rather than particles, as the fundamental units of matter, along with the existence of several extra spatial dimensions in the universe. Could our observable universe really be built from such a bizarre collection of ingredients?

Naïvely, one might expect the extra dimensions to conflict with the observed behavior of gravity. To be successful, string theory, like general relativity, must reduce to Newton’s law of gravity in the appropriate limit. In Newton’s formulation, gravity can be described by force lines that always begin and end on masses. If the force lines could spread in n spatial dimensions, then at a radius r from the center, they would intersect a hypersphere with surface area proportional to rn-1. An equal number of force lines would cross the hypersphere at each radius, which means that the density of force lines would be proportional to 1 / rn-1. For n = 3, this reproduces the familiar Newtonian force law, F propto 1 / r2, which has been tested (along with its Einsteinian generalization) to remarkable accuracy over a huge range of distances, from astronomical scales down to less than a millimeter [30, 31].

An early response to this difficulty was to assume that the extra spatial dimensions are curled up into tiny closed circles rather than extending to macroscopic distances. Because gravity has a natural scale, known as the Planck length, lP ident [hbar G / c3]1/2 cong 10-35 m [where hbar is Planck’s constant divided by 2pi], physicists assumed that lP sets the scale for these extra dimensions. Just as the surface of a soda straw would appear one-dimensional when viewed from a large distance – even though it is really two-dimensional – our space would appear three-dimensional if the extra dimensions were "compactified" in this way. On scales much larger than the radii of the extra dimensions, rc, we would fail to notice them: The strength of gravity would fall off in its usual 1 / r2 manner for distances r >> rc, but would fall off as 1 / rn-1 for scales r << rc [32]. The question remained, however, what caused this compactification, and why this special behavior affected only some but not all dimensions.

Recently Arkani-Hamed, Dimopoulos, and Dvali [33] realized that there is no necessary relation between lP and rc, and that experiments only require rc leq 1 mm. Shortly afterward, Randall and Sundrum [34, 35] discovered that the extra dimensions could even be infinite in extent! In the Randall-Sundrum model, our observable universe lies on a membrane, or "brane" for short, of three spatial dimensions, embedded within some larger multidimensional space. The key insight is that the energy carried by the brane will sharply affect the way the gravitational field behaves. For certain spacetime configurations, the behavior of gravity along the brane can appear four-dimensional (three space and one time), even in the presence of extra dimensions. Gravitational force lines would tend to "hug" the brane, rather than spill out into the "bulk" – the spatial volume in which our brane is embedded. Along the brane, therefore, the dominant behavior of the gravitational force would still be 1 / r2.

In simple models, in which the spacetime geometry along our brane is highly symmetric, such as the Minkowski spacetime of special relativity, the effective gravitational field along our brane is found to mimic the usual Einsteinian results to high accuracy [36, 37]. At very short distances there are calculable (and testable) deviations from standard gravity, and there may also be deviations for very strong gravitational fields, such as those near black holes. There are also modifications to the cosmological predictions of gravity. In the usual case, when Einstein’s equations are applied to a homogeneous and isotropic spacetime, one finds H2 propto rho – k / a2, where k is a constant connected to the curvature of the universe. If instead we lived on a brane embedded within one large extra dimension, then H2 propto rho + alpha rho2 – k / a2, where alpha is a constant [38].

Under ordinary conditions, rho decreases as the universe expands, and so the new term in the effective Einstein equations should have minimal effects at late times in our observable universe. But we saw above that during an inflationary epoch, rho cong constant, and in these early moments the departures from the ordinary Einsteinian case can be dramatic. In particular, the rho2 term would allow inflation to occur at lower energies than are usually assumed in ordinary (nonembedded) models, with potential energy functions that are less flat than are ordinarily needed to sustain inflation. Moreover, the spectrum of primordial perturbations would get driven even closer to the scale-invariant shape, with ns = 1.00 [39, 40]. Brane cosmology thus leads to some interesting effects during the early universe, making inflation even more robust than in ordinary scenarios.

Posted by tom sakurai on 2017-03-12 20:23:37

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