Lesson 4

4 :: “Filling the Big Bang’s Holes: Inflation and

Quantum Physics”

Why does the universe look the same in all directions? Blame it on inflation. This lesson explains why.

Observational Evidence

Since Timothy Ferris wrote The Whole Shebang, the argument for an accelerating flat universe has only gotten stronger, thanks to new observations of the CMB and supernovae. Vast numbers of dissertations have been devoted to the quest for supernovae, and numerous telescopes have been dedicated to the search for increasingly distant explosions of light. To learn more about the latest searches, you are encouraged to explore the following Web sites:

The High-Z SN Search:

http://cfa-www.harvard.edu/cfa/oir/Research/supernova/HighZ.html

Supernovae Cosmology Tutorial:

http://www.astro.ucla.edu/~wright/sne_cosmology.html

High Redshift Supernova Search Home Page:

http://www-supernova.lbl.gov/

Problems with the Standard Big-Bang Model

Let’s sit back for a moment and consider where we are. The standard big-bang model describes the universe as starting out as a single point of energy that expanded outwards. A few minutes after the big bang started, nucleosynthesis produced the majority of our universe’s helium and — 300,000 years later — protons and electrons combined during the epoch of “recombination.” This act uncoupled photons from electrons and protons, and those photons now make up the CMB. This model successfully describes the density spectrum of objects — galaxies, super clusters, large-scale structures — in the universe. It also explains the abundance of helium and lithium, as well as the CMB.

All good theories have one key attribute in common: They are able to predict future observations. By this definition, the standard big-bang model is a good theory. Like all good theories, it also inspires as many mysteries as it helps to solve. One of these mysteries is the apparent flatness of the universe. Although it is esthetically pleasing, a flat universe is scientifically uncomfortable. The universe could be slightly or highly curved like a hypersphere, or have a minor or major hyperbolic curvature. Given all the curved possibilities, it seems highly unlikely that the universe would choose to be precisely flat.

But the universe looks precisely flat.

Cosmologists are relying on two very separate sets of observations to measure the geometry of space. The first data set measures the expansion rate of the universe using Type 1a supernovae as distance indicators. Astronomers determined that Type 1a supernovae have a characteristic luminosity. This means that like machine-made 100-watt light bulbs, all Type 1a supernovae light up in the same way. The human machine is able to determine roughly how far away a lamp is because the light appears dimmer the further away the human stands. This is because the light is spreading out over an increasingly large area at increasing distances (see Figure 4-1). Mathematically, the area the light (luminosity) must cover increases as the square of the distance, so the brightness we see decreases as the square of the distance. It is possible for astronomers to measure how bright Type 1a supernovae appear. Because the actual luminosity of Type 1a supernovae is known, we can calculate how far away they are located.

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Figure 4-1: The light emitted by an object such as a star or a supernova must cover more and more area when observed at greater and greater distances. The area increases as the square of the distance. At twice the distance (d=2), the light must cover 2×2 = 4 times the area. At three times the distance, the light must cover 3×3 = 9 times the area. As a result, the light appears one-fourth as bright at d=2 and one-ninth as bright at d=3. (Graphic by Pamela L. Gay, copyright 2002)

By measuring the distance to — and recession velocity of — supernovae at a variety of distances, it is possible to determine how the expansion rate of the universe is changing. Cosmologists have intuitively expected the expansion of the universe to slow with time, but this is not what astronomers observe. Astronomers observe an increasing expansion rate.

The second set of data to describe the geometry of the universe comes from the CMB. Astronomers have very carefully measured the number of irregularities in the temperature of the CMB and grouped them according to spatial size. The size of an irregularity corresponds to the distance it could travel at the moment of re-combination. If the universe is flat, this distance will correspond to an angular length of 45 arc minutes (our moon is 30 arc minutes across). If the universe has a spherical geometry, this distance will appear to have a smaller angular size; if it is hyperbolic, it will appear larger. Detailed observations made by Boomerang (http://physicsweb.org/article/world/13/6/3 and http://www.physics.ucsb.edu/~boomerang/) show that the majority of observed irregularities have a size of 45 arc minutes. This evidence proves that the universe, as observed, is just plain flat.

These observations leave cosmologists’ stomachs churning. This universe is unexpectedly expanding and inexplicably flat. Yet again, our image of space and space itself are in discord, and we must find ways to change our models — and our way of thinking — to better match reality. This does not mean that our model is wrong, but rather that, just as Newton’s laws of mechanics were incomplete without Einstein’s theory of relativity, our model of the universe is a good beginning that requires added refinements. The first steps in filling the gaps in the standard big-bang model are laid out in the next sections of this lesson.

Scalar Fields

We deal with vector fields every day: fields that have a magnitude and a direction. Magnetic vector fields point north and south and have a strength that depends on the strength of the source magnet and the distance from the magnet. Scalar fields have no direction. They simply interact the same way everywhere. Interactions with the scalar Higgs Field cause the effect of mass. This means that a “massless” photon doesn’t interact with it, although the atomically obese element nobelium (atomic number 102) does. The mass of an atomic particle is just a measurement of how strongly a particle interacts with the Higgs field.

A Vacuum with Potential

To try and understand what we observe, we need to understand why we observe it. In an observationally ideal world, we would be able to “see” the entire universe. This means that the edge of the universe would be close enough that its light would have time to reach us. Put simply, in a 15-billion-year-old universe, nothing would be more than 15 billion light-years away. Even with the standard big-bang model, this is not the case. While no single object is allowed to move faster than the speed of light, the overall expansion of space can — and did — and the result is a universe too big to be completely observed.

Under the standard big bang model, expansion has proceeded at a steady pace, and any changes in the expansion rate have been linear. As a result, we should be able to see 75 to 90 percent of the total universe. Here on earth, on a perfectly clear plain, we can see about three kilometers in all directions. This means that, at most, we can see far less than one percent of the earth’s surface. This is still enough, however, for us to tell that the earth is curved. We can observe ships “disappearing” hull first over the horizon well before they shrink to too small a size to be seen. If we can truly observe 75 to 90 percent of the universe, we should be able to accurately measure the curvature of space.

But what if we don’t see 75 to 90 percent of the universe? A nearsighted individual trying to imagine the shape of the earth but only able to see things no more than a few feet away would always observe the earth as flat. In his observational area, the curvature of the earth would be inappreciable. It is possible that the 10-billion-light-year-deep volume of space that we can observe is, like the nearsighted viewer’s observable region, too small a sample to use to measure the curvature of space. For our observable region to be such a small fraction of the total universe, the expansion rate of the universe would have had to be much greater at some point in the past. The current expansion rate is simply too small to allow for a huge universe.

Cosmologists speculate that during the first second of the universe’s existence it expanded at an exponential rate for 10-34 seconds. This momentary spike in the expansion rate would have an astronomical effect on the size of the universe. To understand why, we need to understand the difference between linear and exponential expansion. Let’s consider a modified version of the parable used by Timothy Ferris in The Whole Shebang. Consider two men who each offer to rescue the king’s daughter. When asked what reward they would ask, the first says to take a chessboard and fill it with money, placing on each square one penny more than was placed in the previous square (one penny on the first square, two pennies on the second, three on the third, etc.). The second, being smarter and greedier, asks the king to fill a chessboard with money, placing twice as many coins on each square as on the previous square (one penny on the first square, two on the second square, four on the third, eight on the fourth, etc.). In the end, the two men rescue the princess together, and the king must reward them both. The first man receives only $20.80 for his efforts, but the second breaks the king’s (and kingdom’s) bank accounts. His reward is more than $184,467 trillion. If at any time the universe has grown exponentially for even the smallest fraction of a second, it could radically change our observation point and reduce our view to that of the nearsighted observer.

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Figure 4-2: The first man, whose money grows linearly, receives only $20.80 for his efforts, but the second, whose money grows exponentially, breaks the king’s (and kingdom’s) bank accounts. His reward is more than $184,467 trillion. (Graphic by Pamela L. Gay, copyright 2002)

This effect could cause us to see space as flat even if it is not, but what would cause the effect of inflation? The expansion rate of the universe is related to the density of mass in the universe. The higher the density, the faster the expansion. Again, we must remember that mass and energy are the same thing. Scientists theorize that space is permeated with scalar fields (see the sidebar). These fields can contain energy, and this energy can increase the mass density of the universe. Physicist Andrei Linde has worked out an inflationary model that uses scalar fields, initially in a high-energy state, to account for inflation. Like a skier at the top of a mountain, these scalar fields contained great potential energy. A skier converts potential energy to kinetic energy as he flies down the mountain slope. Similarly, the scalar fields lost energy as the universe expanded and — just as the skier will come to a stop at the bottom of the mountain — the inflationary epoch ended when the scalar fields reached a minimum energy.

Scalar fields still permeate all of space. Physicists have identified one type of field — the Higgs Field — as the source of mass. (See http://hepwww.ph.qmw.ac.uk/epp/higgs.html for the five best one-page explanations of the Higgs Boson and Field.) This means that even in the deepest vacuum, although there might be no mass — not even a single quark — to be observed, there is a field containing energy that makes up the fabric of space. The child’s question of what fills a vacuum has been answered, and we have found the cause of inflation. Space might still turn out to be flat, but it doesn’t have to be.

Headline: Earth Scientists Destroy Universe

Humans are a fatalistic bunch, and even physicists are not immune to a tendency to look for the worst. If you want to read essays on possible human destruction of the space-time continuum, check out this Web site:

Will Brookhaven Destroy the Universe? Probably Not:

http://rhip.phys.utk.edu/rhip/RHICNews/Essay%20Will%20Brookhaven%20Destroy%20the%20Universe%20Probably%20Not.htm

Making Molehills Out of Mountains

The inflation of the universe goes some way toward abating cosmologists’ stomach ailments. An inflationary epoch also explains why the universe is homogeneous and isotropic. Cosmologists have always assumed these things to be true, but they couldn’t explain why they should be true. Suppose we look at a volume of space 10 billion light-years north of the North Pole and another region 10 billion light-years south of the South Pole. We would be looking at two regions that have never seen each other because the light has not had time to travel from one region to the other. Why should these two regions be made of the same distribution of objects and have the same characteristics?

Think of it this way: Two people go to the same grocery store and buy groceries. Although it is possible for both of them to buy exactly the same items, it is highly unlikely that this will happen. If the two people communicate with each other and share a recipe before buying groceries to cook the same meal, they will purchase the same things. Communication is the key — communication allows the conditions between systems to reach equilibrium.

When we look skyward, we observe hundreds of chunks of sky that have never been in contact with one another, and they all look the same. From a probabilistic view, this isn’t possible. This means that something other than random chance is causing the universe to be homogeneous and isotropic.

Inflation explains these observations in two ways. First, the epoch of inflation didn’t have to start at time zero. The universe might have had a brief period during which its contents could mix. Second, the expansion of the universe might have smoothed out the inherent lumpiness. Consider a child’s chunk of Silly Putty. If you press a pancake of it onto a newspaper cartoon, it picks up the ink and you easily see patterns from the newsprint. If you then stretch the Silly Putty, the once clear markings fade as the ink is spread over a larger and larger area (see Figure 4-3). In effect, the expansion of the Silly Putty, just like the expansion of the universe, distributed the material over such a large area that the whole surface looks smooth. The mountains of the early universe have been flattened into minor molehills in the fabric of space.

Our now inflationary big-bang model of the universe helps to explain the apparent flatness of space and gives us a reason to postulate that the universe is homogeneous and isotropic. We are left with the observation from supernovae that the expansion rate of the universe is still increasing. This implies that the energy of the vacuum of space continues to push mass outwards. It also means that the universe might yet go through another inflationary period of radical evolution.

This possibility was of great concern to the physicists who first developed nuclear weapons and collided atoms in particle accelerators. They feared that the sudden release of energy could provoke the universe to tumble from its current energy level to a lower state — the same way that a hard shove would cause our skier to fall from a resting point on a mountain ledge to the base of the mountain. Such a radical change in the state of the universe would destroy everything as we know it.

Like the chicken that cried that the sky is falling, the fearful few physicists who were concerned weren’t listened to. Science has continued to experiment, smashing atoms and blowing up Pacific atolls. After all, if stars can explode and black holes can collapse into existence, mankind’s more mundane creations shouldn’t have too large an effect on the universe as a whole. Physicists hope that if the universe can exist for 15 billion years without too many catastrophic events, it will continue to exist — even with mankind’s destructive habits — for another 15 billion years and longer. Although we might be capable of destroying our own world, it appears that our experiments will not destroy the universe. I discuss these experiments and the nature of the universe before the age of inflation in the next section. Having explored the largest scales of the universe, it is time to dive into the smallest dimensions of the subatomic world.

Moving Forward

In our next lesson, we’ll undertake a hunt for a unified Theory of Everything that unites all forces during the first moments of the universe. Be sure to do the assignment and quiz, and check in with your fellow students and instructors on the Message Board to raise any questions you have or discuss the course progress thus far.

Assignment: Making Matter

Read Chapter 9 of The Whole Shebang: A State-of-the-Universe(s) Report by Timothy Ferris. Ferris comments:

[T]he fact that the geometry of cosmic space is anywhere near flat was inexplicable in the classical big bang model. To make cosmic geometry come out that way would have required extraordinary fine-tuning of the initial conditions. . . . God might have been up to it, but why should he have gone to the trouble?

In Lesson 1, you learned that early philosophers believed that the earth (and humankind) are at a very special location — the center of the universe. Originally, humans believed that God placed man in the center — now we worry that he might not have bothered to place us in a uniquely flat universe. What does this say about how our view of mankind’s place in the universe has changed? Do you think it is better for society for humans to see themselves as special, or to view humanity as just one small part of a much greater whole?

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