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BIG-BANG BUGS

We have seen how, in the 1970s, the big bang became established with virtual certainty. Very often in science, however, a model that may agree beautifully with all the data and have no other viable competitor in sight is still beset with theoretical or philosophical problems. After all, a flat Earth once agreed with all the data available to primitive people. And look how long the geocentric model of the solar system lasted—not just as myth, but as an accurate predictor of the motions of planets.

As of 1980, the following theoretical problems with the big-bang model were common knowledge among cosmologists:

The Flatness Problem

Recall that cosmologists define a density parameter Ω = ρ/ρc, where ρ is the average mass density of some component in the universe and ρc is the critical density at which the universe is exactly balanced on the edge between collapsing from gravity and expanding forever. If ρ refers to the average density of all the components, then Ω = 1 and the geometry of the universe is flat, that is, Euclidean.

Now, here's the problem: According to Friedmann's equations, the density of the universe determines its rate of expansion. Consider the Planck time, t = 10–43 second. If, at that time, Ω had been greater than 1 by just one part in 1060, the universe would have immediately collapsed. If Ω was less than by just one part in 1060, the universe would have expanded so rapidly that the visible universe would have quickly become so dilute that no life would have been possible. In the big-bang model, life can only exist if Ω = 1 to great precision and the universe is extremely flat.

This is one of the parameters that Christian apologists claim had to have been fine-tuned by a creator God in order to make life possible.1 In 2009 book Life after Death: The Evidence,2 Dinesh D’Souza quotes Stephen Hawking from A Brief History of Time: “If the rate of expansion one second after the big bang had been smaller by even one part in a hundred thousand million million, the universe would have recollapsed before it ever reached its present size.”3 William Lane Craig has also referred to this statement in numerous debates.4

The Horizon Problem

When we look in opposite directions in the sky, we see the same temperature and spectrum for the CMB in both regions. This implies that they came from two sources that were in causal contact with one another at some earlier time so that they could interact with one another and achieve equilibrium. Two points in space can only be in causal contact when there is sufficient time for a signal to travel between them. Using the latest numbers, those points are now ninety-three billion light-years apart.

In chapter 10, we saw that the photons in the CMB were emitted when the universe became transparent at an age of 380,000 years. If you apply the standard big-bang model with linear Hubble expansion, you find that the distance between two points on the opposite side of the universe when the age of the universe was 380,000 years would have been about eighty-four million light-years, as shown in figure 12.1. This is much greater than the distance light could have traveled from the big bang, so the sources of the disturbances at A and B could never have been in causal contact so they could reach thermal equilibrium.

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Figure 12.1. Illustration of the horizon problem. Time runs along the horizontal axis, and the distance between two points in the universe is plotted along the vertical axis. Points A and B are on opposite sides of the universe at decoupling, about eighty-four million light-years apart, emitting photons, shown by the dashed lines, that are detected from two opposite directions on the sky by a CMB observer today. Today they are ninety-three billion light-years apart because of the expansion of the universe. The dotted arrows are light rays showing that the regions that can affect A and B were never in causal contact. The drawing is not to scale. Image by the author.

The Structure Problem

We saw in chapter 10 that cosmologists had for many years struggled to try to explain how the complex structures in the visible universe came to be assembled. The problem was bad enough for a static universe. It was even worse for an expanding universe, which dispersed matter over greater distances making it even less likely for isolated clouds to collapse under gravity.

The Monopole Problem

In classical electromagnetic theory, the simplest electric charge is a point particle for which the electric field is visualized as lines of force radiating outward from the center. Two opposite point charges, positive and negative, constitute an electric dipole. So we can call a point charge an electric monopole. There are also quadrupoles, octopoles, and so on. If we take an electric dipole and pull the charges apart, we get two electric monopoles.

A bar magnet is an example of a magnetic dipole, with a north and south pole However, if you cut a magnetic dipole in two, you don't get two magnetic monopoles; you just get two more dipoles. No magnetic monopoles exist in the classical theory, and none have ever been observed empirically.

As French physicist Pierre Curie remarked in 1894, the absence of magnetic monopoles is the only difference between electricity and magnetism. In 1931, Paul Dirac showed that magnetic monopoles are consistent with quantum mechanics and restore the symmetry between electricity and magnetism.5

In 1974, Dutch physicist Gerard ’t Hooft6 and Russian physicist Alexander Polyakov7 independently proved that unified gauge theories that include electromagnetism will contain magnetic monopoles. In 1976, British physicist Thomas Kibble (one of the six authors who proposed the Higgs mechanism in 1964, see chapter 11) showed that in a gauge symmetry–breaking phase transition, the new phase need not be uniform but could exhibit so-called topological defects such as appear in a ferromagnet. These defects include domain walls, strings, and monopoles.8

In 1979, Harvard graduate student John Preskill calculated that monopoles 1016 times as massive as a proton should have been produced during the GUT phase transition in numbers comparable to that of protons.9 If that had been the case, the mass of the universe at the time would have been so great that it would have collapsed in less than 1,200 years.10

During the 1980s, numerous searches for magnetic monopoles were conducted and none found.11 In 1987, I spent a six-month sabbatical in Italy working on MACRO (Monopole, Astrophysics, and Cosmic Ray Observatory) in the Grand Sasso Underground Laboratory. The lab is in a highway tunnel through the mountains near L’Aquila, scene of a 2009 earthquake (which did not affect the lab). MACRO was built primarily to search for magnetic monopoles and was the most sensitive monopole search ever performed. It detected none and by 2002 had set a very stringent upper limit on the monopole flux, well below what had been estimated should exist based on the effects they should have had on galactic magnetic fields.12

Nevertheless, at the worst, the failure to detect magnetic monopoles was a problem for GUTs, not for the big bang. I mention it mainly for historical reasons, since monopoles provided a major impetus for elementary particle physicists to become involved in early-universe cosmology.

INFLATION, OLD AND NEW

In 1980, several physicists and astrophysicists independently began to develop a scenario for an early universe that would ultimately provide viable solutions to the problems with the conventional big bang. On January 11, Russian physicist Alexsei Starobinsky, working with Stephen Hawking at Cambridge, submitted a paper to Physics Letters showing that quantum effects in the early universe could lead to a de Sitter universe and thus an exponential expansion we now call inflation.

In 1970, Hawking and Roger Penrose had used general relativity to prove that our universe began as a singularity, an infinitesimal point of infinite density.13 Since then this result has been used by theologians to argue that our universe must have had a beginning and, although it doesn't follow, that there had to have been a personal Creator.14 Starobinsky showed, and both Hawking and Penrose agreed, that quantum effects in the early universe eliminate the singularity. Not being a quantum theory, general relativity breaks down at distances less than the Planck length, 10–35 meter.15

On May 5, 1980, an acquaintance of mine at the time, astrophysicist Demosthenes Kazanas of the NASA Goddard Space Flight Center, submitted a paper to the Astrophysical Journal with the title “Dynamics of the Universe and Spontaneous Symmetry Breaking.”16 There he argued that a phase transition in the early universe associated with spontaneous symmetry breaking would result in an exponential expansion that could account for the observed isotropy of the universe. I believe this was the first published paper explicitly recognizing exponential expansion as the solution to one of the major problems with the conventional big bang, namely the horizon problem.

On September 9, 1980, Japanese physicist Katsuhiko Sato submitted a paper to the Monthly Notices of the Royal Astronomical Society also showing that a first-order phase transition can lead to an exponentially expanding universe.17 He suggested that fluctuations could account for the origin of galaxies but did not mention the other big-bang problems.

The seminal paper on inflation, however, was submitted to Physical Review D on August 1, 1980, by physicist Alan Guth, then working as a postdoctoral researcher at the Stanford Linear Accelerator.18 Guth grasped the full significance of an early period of exponential inflation, emphasizing how it solves both the flatness and horizon problems and also suggested a possible solution to the monopole problem.

The flatness and horizon problems are by far the most significant, as Guth soon realized. Either was capable of falsifying the big-bang scenario had no solution proved possible. On the other hand, the magnetic-monopole problem was not critical. No magnetic monopoles exist in either classical or quantum electrodynamics, and none have been seen in nature. At best they add some symmetry to electromagnetism, but they appear to be required only in GUTs.

In Guth's 1997 excellent popular book The Inflationary Universe,19 he relates how he was drawn to the notion of inflation by the monopole problem and admits he knew little about cosmology at the time. He had never heard of the horizon problem until December 1979. But he learned fast, and by the time he wrote the paper he fully appreciated the deep significance of both the flatness and horizon problems.

Guth nicely explains his original model in his book, but he and others soon realized it had to be modified. Rather than reviewing that history, which is highly technical, I will argue that exponential inflation is a natural consequence of general relativity.

If you write down Friedmann's equations for a de Sitter universe with a positive cosmological constant, it takes only college freshman math to prove that the solution is an exponential expansion. Regardless of the specific model, inflation solves the flatness, horizon, and monopole problems and sets the stage for solving the structure problem.

The Flatness Problem Solved

Recall that in chapter 8 I described expanding three-dimensional space in terms of the common analogy of the expanding two-dimensional surface of an inflating (!) balloon. Imagine a balloon starts out small and then expands by many orders of magnitude. A small patch on the surface will become very flat. The universe within our light horizon is like that small patch, which inflation has made very flat indeed.

Now this is usually interpreted to mean that the universe has Ω = 1, that is, the density ρ is exactly equal to the critical value ρc for which the geometry of the universe is Euclidean. Recall that in this case the cosmological curvature parameter k = 0. The current empirical value is Ω = 1.002 ± 0.011. If it should turn out that ρ is just ever so slightly less than ρc, say by one part in 10100, then we have a universe with slightly negative curvature, k = –1, which will also expand indefinitely.

On the other hand, if ρ is just ever so slightly greater than ρc, say by one part in 10100, then we have a universe with slightly positive curvature, k = +1. In classical cosmology, when the cosmological constant was assumed to be zero, k = +1 referred to a “closed universe” that would someday collapse in a “big crunch.” However, as we will see, even a “closed universe” dominated by a positive cosmological constant will continue to expand.

Later we will see that a universe with k = +1 provides a plausible mechanism for the origin of our universe that is completely consistent with existing knowledge and has been worked out fully mathematically.

Earlier in this chapter I mentioned that Christian apologists Dinesh D’Souza, William Lane Craig, and others have quoted Stephen Hawking that the expansion rate is fined-tuned to “one part in a hundred thousand million million.” That was taken from pages 121–122 of A Brief History of Time. However, they conveniently ignored Hawking's explanation a few pages later, on page 128:

The rate of expansion of the universe would automatically become very close to the critical rate determined by the energy density of the universe. This could then explain why the rate of expansion is still so close to the critical rate, without having to assume that the initial rate of expansion of the universe was very carefully chosen.20

In other words, inflation accounts for the fact that the expansion of the universe is equal to the critical rate out to sixty decimal places.

The Horizon Problem Solved

The horizon problem results from the observed fact that the CMB is highly uniform across the sky, with the same blackbody spectrum and temperature. As seen in figure 12.1, photons observed from opposite sides of the sky would never have been in causal contact according the big-bang model in which the Hubble expansion extrapolated back to the origin of the universe.

Inflation solves the problem, as illustrated in figure 12.2. In the time after the origin of the universe, but before inflation, the points A and B were close together and so came to quasi-thermal equilibrium with one another. Inflation stretched the distance between them by many orders of magnitude so that photons from them appear today as correlated signals from the opposite sides of the sky.

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Figure 12.2. How inflation solves the horizon problem. A fluctuation in a small region of space sends photons in opposite directions. Inflation stretches the distance between them so that they provide correlated signals from opposite sides of the sky. Image by the author.

The Monopole Problem Solved

As mentioned, Guth was led to inflation while trying to solve the monopole problem in GUTs. However, since monopoles have never been seen anyway, this is only a theoretical problem for grand unified theories. The failure to see any monopoles might have falsified GUTs if no solution had been found but would not have killed the big bang.

Guth did not claim to solve the monopole problem in his original paper but suggested a solution. He and collaborator Henry Tye had come up with the idea that supercooling occurred, delaying the completion of the GUT phase transition and the nucleation of monopoles. Supercooling and superheating are familiar phenomena in thermodynamics as well as everyday life, and actually constitute the most common types of phase transitions, called first-order phase transitions. In a familiar example, when you boil water, it does not instantaneously convert into steam but forms bubbles. It takes a long time for all the water to convert to steam. If you put a cup of very pure water in your microwave, you will be able to heat it to above the boiling point without it boiling; it is superheated. Then, when perturbed, as by someone touching the cup, the water will all simultaneously turn to steam (be careful, people have been scalded by this phenomenon). Similarly, if you cool water below its freezing point, ice crystals will nucleate if some seed is present. But if the water is very pure, homogeneous nucleation takes place and the ice formed is uniform like glass.

It already had been established that the GUT phase transition was strongly first order. The bubbles of GUT phase that are formed in the phase transition will not immediately form monopoles since the fields remain scrambled until the temperature drops sufficiently. Guth and Tye proposed that the bubbles will expand sufficiently during the supercooled phase so that when the monopoles finally form they will be highly diluted.

Guth at first conjectured that our universe formed when the bubbles collided and their energies, concentrated in the bubble walls, were converted into particles. But calculations by Guth and Erik Weinberg showed that because of the continued expansion of the space between bubbles, they would never collect into a uniform mass but form finite clusters.21 They considered the possibility that the universe was within a single bubble but concluded (prematurely) that it would be too empty to resemble any real universe.22

But that was for the Guth-Weinberg model. Without any empirical data, choosing a model is a matter of educated guesswork. At the same time, Russian physicist Andrei Linde23 and American physicists Andreas Albrecht and Paul Steinhardt24 had come up with their own models. These showed that it was possible for our universe to have been formed from just one of the bubbles. These models were termed new inflation. I will not discuss these either, since Linde soon came up with a better idea.

CHAOTIC INFLATION

Andrei Linde is one of the most original and productive of the many original and productive inflationary cosmologists who quickly became noticed after Guth's paper appeared. Guth graciously acknowledges that Linde independently invented much of the inflationary universe theory in the late 1970s, although Linde admitted that he did not immediately realize its significance.25

In 1983, Linde conceived another model called chaotic inflation that is so simple and natural that, while it is probably not exactly correct in detail, it is probably not far wrong and enables us to understand the process with minimal assumptions and a minimum of technical details. It is standing up well with the most recent observations.

Unlike other inflation models, chaotic inflation does not rely on trying to guess the shape of the inflating potential from GUTs or some other dynamical theory for which we have no observational guidance and no fundamental principle on which to base it. It simply starts out with almost nothing and lets quantum mechanics and statistics do their jobs.

I will follow recent convention and refer to the field responsible for inflation as the inflaton field, so we are not tied to GUTs or any other unnecessarily specific model. We just assume that any field that arises is simply a scalar field, equivalent to a cosmological constant in de Sitter space, which we have seen will produce an exponential expansion.

Once again, let us go back to the Planck time, 10–43 second and worry later what might have gone on before. Let me assume that the universe at that time was as small as it can be operationally defined, which is a sphere whose radius was equal to the Planck length, 10–35 meter (orders of magnitude are good enough at this level). The sphere would be empty except for a vacuum energy that would have a random value following a normal (Gaussian or bell-curve) distribution with a statistical standard deviation equal to the Planck energy, 1028 electron-volts. Note this is not a small number; it is equivalent to a temperature of 1032 degrees and a rest energy about thirty times that of a particle of dust.

A positive energy fluctuation equivalent to a positive cosmological constant would produce a de Sitter universe that expands exponentially. A negative fluctuation would result in exponential collapse, which we need not consider. Because of the constant energy density of the de Sitter vacuum, the universe gains internal energy as it expands. This is equivalent to a mass that we can call the “seed” of inflation. Energy is conserved and the internal energy or mass comes from the loss of gravitational energy as the universe “falls up” because of the negative pressure of the vacuum. The mass of the seed must exceed a certain limit sufficient to sustain inflation, or else the normal attractive gravity of the mass will cause it to quickly collapse.

In both classical and quantum field theory, fields have the mathematical properties of a one-dimensional simple harmonic oscillator such as a simple pendulum. The field value ø is analogous to the displacement of a pendulum from its equilibrium position. Because of the uncertainty principle, the quantum harmonic oscillator is never at rest but oscillates around its equilibrium point with a minimum energy called the zero-point energy. Thus any variation in ø can properly be called a “quantum fluctuation.”

As illustrated in figure 12.3, we can visualize the oscillator metaphorically as a ball rolling up and down the side of a bowl. In this case, if the shape of the bowl is parabolic, the ball will exhibit simple harmonic motion, so this serves as a good model for the behavior of ø. The mathematics will be the same.

Normally the ball will roll quickly back down. However, the equation of motion for the oscillator in an expanding universe predicts that, because of the expansion of space, the return to equilibrium will be slowed by friction. This is analogous to the jar being filled with molasses. Actually, the contents of the bowl are more like molasses riding on water riding on air.26 So, for small displacements, the ball just oscillates back and forth near the bottom of the bowl. However, Linde noted that occasionally, when the displacement is large, the molasses will slow the ball and it will stay for a while with a large displacement from equilibrium.

This so-called “slow roll” is a necessary feature of most inflation models and is artificially built into the “new inflation” models mentioned earlier. Here it is natural. Slow roll allows time for the original seed to expand by many orders of magnitude before the ball finally reaches bottom. Once at the bottom, it oscillates back and forth with ever-decreasing amplitude, never coming completely to rest. The energy lost to friction creates the elementary particles that then form our universe.

We can make this all quantitative, at least for illustration. For the inflaton field ø, we can write the potential energy density in harmonic oscillator form, u(ø) = m2ø2/2, where m is the mass of the quantum of the field, which we can think of as the inflaton particle. The value of m is unknown and so is treated as an adjustable parameter, the only one in the model. If we now put u into the equation of motion, we can use numerical methods to calculate ø, H, and the cosmological scale factor a as a function of time. You can find this all worked out in The Comprehensible Cosmos, including derivations of all the equations used at an undergraduate mathematics level.27 Here I will just show the results.

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Figure 12.3. An illustration of chaotic inflation. The potential energy density is given by u(ø) = m2ø2/2, where ø is the scalar field and m is the mass of the inflaton. It is assumed to start at ø = 10 Planck units. The evolution of the inflaton field is equivalent to a unit mass ball rolling down a parabolic well such as that of a damped, simple pendulum. Image by the author.

Let us work in “Planck units” where ħ =h/2π = c = G (Newton's gravitational constant) = 1. For illustration, I have chosen an initial fluctuation in ø of 10 Planck units and m = 10–7 in Planck units (1011 GeV). The motion of the ball as it rolls down the hill from there is shown in figure 12.3. As the ball slowly descends, the volume of the universe increases exponentially. Its motion is damped by the expansion of space so the ball loses energy as it rolls down and then oscillates back and forth around the bottom of the potential with decreasing amplitude.

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Figure 12.4. The evolution of the inflaton field ø(t) with time for chaotic inflation. The time scale is approximately seconds × 10–34. The region t < 0.5 is suppressed. Image by the author.

Figure 12.4 illustrates how the field evolves with time t in units of the Planck time. The region t < 0.5 is not shown in order to illustrate the damped oscillation of the field. During the time t < 0.6, the field drops from 10 units (off scale) to zero and then oscillates about zero with ever-decreasing amplitude.

Figure 12.5 shows the evolution of the scale factor of the universe, a, which for our purposes we can think of as the universe's radius. Exponential inflation of 214 orders of magnitude is followed by a smooth transfer to the conventional Hubble expansion. This is illustrative only and not meant to exactly model our universe.

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Figure 12.5. The evolution of the scale factor of the universe with time for chaotic inflation with m = 10–7 an initial inflaton field of 10 Planck units. The time scale is approximately seconds × 1034. The zero of the time axis is suppressed for illustrative purposes. The part of the curve labeled “Big Bang” refers to the normal Hubble expansion. Image by the author.

LARGE-SCALE STRUCTURE

While particle astrophysicists in the eighties were toying with the incredible idea that the universe expanded by many orders of magnitude during its first tiny fraction of a second, observational astronomers were discovering that the cosmos revealed with their latest telescopes was incredible in its own right.

In the 1970s, the general picture of the universe had been one of a more-or-less homogeneous distribution of clusters of galaxies moving away from each other uniformly with the Hubble flow. But by the 1980s, evidence began to accumulate that thousands of galaxies over a region of space millions of light-years across show small but measurable deviations from the purely radial recessional velocities they were expected to have from of the universe's expansion. The motions of the galaxies in our local cluster seemed to be directed toward a region of the sky that was about two hundred million light-years away at the center of the Hydra-Centaurus supercluster. This was termed the Great Attractor.28

Within a few years, other unexpected structures in the distributions of clusters, superclusters (clusters of clusters), and complexes (clusters of superclusters) would make their presence known. In 1987, my University of Hawaii colleague Brent Tully observed a filamentary structure one billion light-years long and 150 million light-years wide he called the Pisces-Cetus Supercluster Complex. It consists of five superclusters with a total mass of 1018 solar masses, including the Virgo supercluster of 1015 solar masses of which we are a part.

As we have seen, measuring distances have always provided a major challenge to astronomers. Over the years they have developed what they call the cosmic distance ladder, a series of methods where each applies out to a specific distance, at which point a new method then takes over with sufficient overlap so that each method can help calibrate the neighboring method.

I need not go into all the methods used. I have already discussed parallax, which works for nearby stars out to about one hundred light-years, and Cepheids, which works for galaxies out to thirteen million light-years. In 1977, Tully and his collaborator Richard Fisher had published a new method for determining distances to spiral galaxies that related their intrinsic luminosities to their rotational speeds.29 As with other methods, you determine the distance by measuring the observed luminosity at Earth and assume it falls off as distance squared to give the observed value. Tully and Fisher used this method and others to provide an atlas of what they called “nearby” galaxies.30

But basically, redshift remains the most precise measurement that astronomers can perform, and Hubble's law can still give an approximate distance. The latest period in astronomical history has been marked by extensive redshift surveys of galaxies that have revealed a remarkable weblike structure to the visible universe.

The first extensive redshift survey was started in 1977 by the Harvard-Smithsonian Center for Astrophysics (CfA), which was completed in 1982. It was followed by another CfA survey from 1985 to 1995. Using these data, in 1989, Margaret Geller and John Huchra discovered a filament of galaxies whose redshifts implied it was roughly two hundred million light-years away with a length of five hundred million light-years, a width of three hundred million light-years, and a thickness of sixteen million light-years. It was dubbed the Great Wall.31 As we will see in the next chapter, a large number of extensive redshift surveys have been conducted since 2000.

Basically, the visible universe is composed of one hundred billion to perhaps as much as a trillion galaxies that astronomers organize into groups, clusters, superclusters, sheets, filaments, and walls. These are separated by voids with diameters from thirty to five hundred million light-years that contain few galaxies. In 2013, Tully and collaborators produced a remarkable video that dramatically illustrates this structure.32

Nevertheless, the vastness, beauty, and complexity we see with our eyes and telescopes give us a false impression that the cosmos is highly complex and therefore intricately designed. In fact, the universe on the whole is simple and almost random. The invisible 99.5 percent of the mass of the universe has hardly any structure. The 69 percent that is dark energy has none while the structure of the 26 percent that is dark matter is not as finely detailed as the visible matter that is clumped around it. Furthermore, by a factor of a billion the universe is numerically composed mostly of photons and neutrinos in motion that is random to one part in 100,000. Far from looking as if it were designed by a supreme being of infinite intelligence, our universe looks as if it were the product of chance alone.

STRUCTURE AND INFLATION

At first, it was thought that inflation made the structure problem even worse. After all, one of the triumphs of inflation was to explain the extraordinary smoothness of the cosmic microwave background. So how could it be expected to explain the obvious lack of smoothness of all the visible matter around us—galaxies, stars, planets, the Rocky Mountains?

I have noted that prior to the introduction of inflationary cosmology several authors had proposed that structure formation in the universe was the result of primordial density fluctuations in the early universe. But without any knowledge of the nature of the primordial matter, they could do little more than speculate.

Inflationary cosmologists got the idea that small density perturbations caused by quantum mechanical zero-point fluctuations in the inflaton field were multiplied by many orders of magnitude during inflation and could have provided the variations in density needed for gravitational clumping and the formation of galaxies.

Applying their different models of inflation, cosmologists in the 1980s tried to calculate the density variation resulting from quantum fluctuations in the inflaton field. Guth describes the three-week workshop on the early universe held in Cambridge June 21 to July 9, 1982, organized by Stephen Hawking and Gary Gibbons, and how everyone was coming up with different estimates, most orders of magnitude too small to produce galaxies.33 However, shortly after, a 1983 paper by James Bardeen using a novel calculational technique that was model-independent argued that a density fluctuation on the order of 10–3 to 10–4 from inflation was not implausible.34

Despite the uncertainty in magnitude, inflation was expected to give, at least approximately, the scale-invariant fluctuations that, as we saw in chapter 11, are deemed to be necessary for structure formation. In the simplest model where the inflaton field is the uniform scalar field in a de Sitter universe, scale invariance follows from the time translation invariance of the exponential solution. Specific models of inflation are more complicated, but they all give something very close to scale invariance. Actually, we will see that they, including chaotic inflation, predict a slight but significant variation from scale invariance that serves as yet another risky test for the inflationary model.

During the inflationary period, tiny quantum fluctuations in the density of the inflaton field expanded by many orders of magnitude. When inflation ceased, the universe was a hot, highly dense gas of elementary particles, which then followed the more sedate Hubble expansion. The fluctuations caused the expanding sphere of gas to vibrate and produce sound waves that propagated in all directions with the speed of sound. Since the medium vibrating was mostly photons, the sound speed was essentially the speed of light divided by √3. In the sophisticated models we will discuss later, the speed of sound is allowed to vary as the baryon-to-photon ratio varies, thus providing a tool to measure their relative contributions.

As the universe continued to expand and cool, the various processes described in chapter 10 took place. During all this time, the particles remained tightly coupled in quasi equilibrium, with a well-defined temperature that grew less as the universe expanded, from 1027 degrees at the end of inflation following the straight line on the log-log plot shown in figure 10.2.

Recall the artificial distinction made by astronomers and cosmologists between radiation and matter. They are both composed of material particles, but radiation is extreme relativistic (v >> c) while matter is nonrelativistic (v << c). Radiation composed of photons remained the dominant ingredient of the universe for fifty-seven thousand years, so that period is called radiation dominance. However, because of the redshift caused by the universe's expansion, the energy density of radiation falls off faster than the energy density of matter, and the universe passed from radiation dominance to matter dominance. As we will see, matter dominance ended about five billion years ago. Since then, the universe has been increasingly dominated by what is called dark energy that behaves very much like a cosmological constant with an accelerating expansion of the universe.

Now we are talking here about mass/energy density, not number density. Zero-mass photons and low-mass neutrinos continued to outnumber everything else during matter domination. Then, at 380,000 years, the temperature dropped to the point where atoms could form. This is referred to as “recombination.”35 Recombination cleared the universe of most of its charged particles as positively charged nuclei and negatively charged electrons neutralized each other in atoms. And, most significantly, because photons no longer had charged particles with which to collide, they “decoupled” from the rest of the universe, which then became transparent. Over the next 13.8 billion years, these photons would cool to 2.725 K and become the cosmic microwave background we observe today.

At present, photons still outnumber atoms by a billion to one. Neutrinos decoupled much earlier, at two seconds, to form a relic background of their own at 1.95 K. Although there are hundreds in every cubic centimeter, these neutrinos produce no measurable effects, at least with current technology, and are generally ignored. As we will see, they are unlikely to be the ingredient of dark matter.

Decoupling also meant that the photon pressure in matter that served to counteract gravity and prevent it from collapsing was released and the process of structure formation by gravity infall could begin. This was aided by dark matter, which was there all along but had not participated in the electromagnetic interactions that had previously kept the photons and charged particles in equilibrium. And so whatever pattern of vibration the sphere of photons had at decoupling was frozen for all time. The regions of higher density were also hotter and the less dense regions colder, so temperature fluctuations in the gas traced its density fluctuations, and that pattern appears today in a CMB temperature variation across the sky.

LOOKING BACK TO THE BEGINNING

By the 1980s, the realization that the CMB carried information on the earliest moments of the universe spurred many efforts to make more-precise measurements of any possible deviations from the smooth distribution over the entire sky that had so far been observed. Inflation explained that smoothness but also suggested that variations or “wrinkles” should appear at about the one-in-a-hundred-thousand level. These anisotropies would prove to be a crucial test that would make or break the theory.

One of the leaders of this observational effort was a University of California at Berkeley particle physicist George Smoot. Working with Nobel laureate Luis Alvarez and others at the Lawrence Berkeley National Laboratory, which I frequently visited on other projects at the time, Smoot and colleagues had developed a differential microwave radiometer that measured temperature differences of the CMB from two directions in the sky.

In 1976, the Berkeley instrument made a series of flights aboard the Lockheed U-2 “spy plane.” It detected the difference in temperature caused by the motion of the Milky Way, which includes our sun and Earth, at six hundred kilometers per second through the background radiation field. This is the so-called dipole anisotropy with the frequency of the CMB being blueshifted on the side we are moving toward and redshifted on the side we are moving away from because of the Doppler effect.36

In the mid-1970s, Smoot and colleagues proposed to NASA that they develop a satellite to be named COBE, the Cosmic Microwave Background Explorer. The spacecraft was to carry three instruments:

After considerable delay caused by the Challenger disaster and other problems, COBE was launched on November 18, 1989, on the back of a Delta rocket. And thus began the next amazing chapter in humanity's comprehension of the cosmos.