I knew the idea was very good, but I didn’t know how good. My guess is that even Alan didn’t know how good it was. Certainly no one could guess that within twenty-five years Inflation would be the centerpiece for a new Standard Model of cosmology.
To understand the mechanism behind Inflation, we have to understand how a universe with a positive cosmological constant behaves. Remember that a positive cosmological constant gives rise to a universal repulsive force proportional to distance. The effect is to force the distance between galaxies to grow. This can happen only if the balloon that they are drawn on—space itself—expands.
Vacuum energy or mass has an unusual property. Ordinary mass density, like that due to the galaxies, dilutes when the universe grows. The mass density in the form of ordinary matter is about one proton per cubic meter. Suppose the radius of the universe doubled over some billions of years but the number of protons in the universe remained fixed. Then the mass density would obviously decrease. In fact it would decrease by a factor of eight. Double the radius again, and the number of protons per cubic meter decreases to one sixty-fourth of its present value. The same is true of the dark-matter component.
But vacuum energy is very different. It’s a property of empty space. When empty space expands it’s still just empty space, and the energy density is exactly what it was originally. No matter how many times you double the size of the universe, the vacuum energy density stays the same, and its repulsive effect never diminishes!
By contrast, ordinary matter thins out and eventually becomes ineffective at slowing down the expansion. After a sufficient amount of expansion, all forms of energy will be diluted away except for vacuum energy. Once this happens there is nothing to counteract the repulsive effects of the vacuum energy, and the universe expands exponentially. If the cosmological constant were large enough to double the size of the universe in one second (it’s not), then it would become four times as big in two seconds, eight times as big in three seconds, sixteen times, thirty-two times, and so on. Things that are close to us now would soon be rocketing away faster than the speed of light.
The real universe is in the early stages of this kind of exponential expansion. It won’t bother us very much since the cosmological constant is only strong enough to double the size of the universe over a period of tens of billions of years. But imagine that for some unknown reason, in the very early universe, the cosmological constant were much bigger, perhaps a hundred orders of magnitude bigger. This may sound like a strange thought experiment, but remember that the hard thing to understand is why today’s cosmological constant is so ridiculously small. Make it one hundred orders of magnitude larger, and it becomes ordinary, at least from the theoretical physicists’ point of view.
If the cosmological constant were that big early on, it would cause the universe to double in a tiny fraction of a second. In one second the universe would grow from the size of a proton to something vastly larger than the known universe. This is real Inflation of the kind envisioned by Starobinsky and Guth.
The reader may wonder what kind of double-talk allows me to speak of different cosmological constants in the early and late universe, i.e., during Inflation and now. After all, aren’t constants constant? Stop now and think Landscape. The cosmological constant in a given region of the Landscape is nothing but the local altitude. A picture of a bit of Landscape is worth a thousand words.9 The picture below is a very simplified version of a Landscape that might resemble our neighborhood. The little ball represents the universe, rolling along, seeking a valley where the vacuum energy is minimum.
Some unknown history of the universe placed it on a relatively broad, high shelf overlooking a deep valley of almost zero altitude (here is where Guth’s Inflation begins). How the universe arrived on the shelf is a question for another day. Because the shelf is so flat, the universe rolled very slowly at first. While it was on the shelf, the vacuum energy (altitude) was practically unchanging. To state it differently, the altitude of the plateau served as a cosmological constant while the universe was resting on the shelf.
And, as I’m sure you guessed, as it slowly rolled, it inflated because the vacuum energy was large and positive. If the shelf was flat enough and the rolling slow enough, the universe would double many times before coming to the steep descent down to the valley. This was the inflationary era, although in a more modern form than Starobinsky and Guth first proposed. If the universe doubled one hundred times or more during this period, it would have grown to such large proportions that it would be as flat and homogeneous as the CMB requires.
Eventually the rolling brought the universe to the edge of the shelf and then down into the valley, where it came to rest. If the altitude at that point is not quite zero, then the long-term future of the universe will have a small cosmological constant. If by chance the cosmological constant is small enough in the valley, and other conditions are right, galaxies, stars, planets, and life could form. If not, that particular pocket would be sterile. All of known cosmology took place during a roll from one value of the cosmological constant to a much smaller one. Can anyone seriously doubt that there was more to the history and geography of the universe than this brief episode and this tiny pocket?
But wait! Something is wrong with this picture. If the universe inflates to such a large degree, it can be expected to be incredibly homogeneous. All the wrinkles would have been ironed out so completely that there would be no variations at all in the CMB. But we know that without some small wrinkles to seed the galaxies, the universe would have remained smooth indefinitely. We seem to have overdone the homogenizing.
The solution to this puzzle involves an idea so radical and surprising that at first you might be tempted to dismiss it as pie-in-the-sky speculation. But it has withstood the test of time and is currently one of the cornerstones of modern cosmology. Once again its initial discovery took place in Russia, by a young cosmologist named Slava Mukhanov, who was studying Starobinsky’s work. History repeats itself: Mukhanov’s work was unknown outside the USSR until several groups working in the United States independently rediscovered it.
Quantum mechanics and its jittery consequences are normally thought to apply to the world of the very small, not galaxies and other cosmic-scale phenomena. But it now appears all but certain that galaxies and other large-scale structures are remnants of original minute quantum fluctuations that were expanded and enhanced by the unrelenting effect of gravity.
The idea that the universe is at an exact point in the Landscape is a little too simple. Like everything else, quantum fields such as the Higgs field have the jitters. Quantum mechanics is enough to ensure that the fields do fluctuate from point to point in space. No amount of Inflation can iron out the random quantum fluctuations that every field must have. This is true in our vacuum today, and it was true during the rapid exponential expansion of Inflation. But rapid Inflation does something to these fluctuations that doesn’t happen to any appreciable degree in our very slowly expanding universe. It stretches out the old wrinkles but keeps replacing them with new ones. New wrinkles on top of old wrinkles, all expanding as the universe expands. By the time Inflation ended and the universe tipped over the edge of the ledge, the accumulated quantum wrinkles had built up and formed the minute density contrasts that eventually grew to become galaxies.
These frozen-in quantum wrinkles also imprinted themselves on the surface of last scattering, and we can see them as the tiny variations of brightness in the cosmic microwave vacuum. The connection between the quantum theory of the microscopic world and the large-scale structure of the astronomical and cosmological world is one of the greatest achievements of cosmology.
Let me finish this chapter by summarizing the two most important things we have learned from cosmological observations during the last decade. First, we have found a real shocker: there really is a cosmological constant. The first 119 decimal places cancel, but astonishingly, in the 120th the result is not zero!
The second point o
f enormous interest is that the theory of Inflation has strong support from the study of cosmic background radiation. The universe apparently grew exponentially for some period of time. It is all but certain that the entire universe is many, many orders of magnitude bigger than the part we can see.
These are both great discoveries, but they are also disturbing. If we reached into a bag of random numbers and pulled out generic values for the constants of nature, neither a small cosmological constant nor a suitable period of Inflation would be likely outcomes. Both require an enormous degree of fine-tuning. As we’ve seen before, the universe appears to have been specially designed. More about this specialness in the next chapter.
CHAPTER SIX
On Frozen Fish and Boiled Fish
For explaining physics to an audience of nonphysicists, analogies and metaphors are obviously invaluable. But for me they are also tools for thought, my own idiosyncratic tools. Often I convince myself of the truth of some difficult point by inventing an analogy that applies similar questions to a more ordinary context.
The Anthropic Principle has created more confusion and irrelevant philosophical claptrap than anything that has come out of science for quite some time. Incessant argument occurs over its meaning, how it should be used to explain and predict, when it is legal, when it is not, when it is sensible, and when it is nonsense. The surest guide for me is to build an analogy about the more familiar world, where good old common sense can clear the air. More than a decade ago, I made up a parable to convince myself that the Anthropic Principle can make some sense.
A Birthday Present for Tini
It’s an old tradition for well-known physicists to celebrate their sixtieth birthdays with parties, but these birthday parties usually consist of a couple of long days of continuous physics seminars—without music. I had to give a lecture at one such party for an old friend, Martinus Veltman. Tini—a bristly, bearded, colorful ogre of a Dutchman—looked like a cross between Orson Welles playing Macbeth and Saddam Hussein when he came out of his spider hole. Tini recently won the Nobel Prize for his work with Gerard ’t Hooft that developed the mathematics of the Standard Model.
Because Tini was one of the first people to recognize the problem of vacuum energy, I thought I would give a birthday talk called “Tini and the Cosmological Constant.” What I wanted to speak about was the Anthropic Principle and Steve Weinberg’s calculation of galaxy formation. But I also wanted to explain how the Anthropic Principle could make good scientific sense. So as usual I made up an analogy.
Instead of asking why the cosmological constant is so precisely fine-tuned, I substituted a similar question: why is the temperature of the earth finely tuned to be in the narrow range in which liquid water can exist? Both questions ask how it happens that we live in a very unlikely environment that seems perfectly tailored to our own existence. To answer my question I proposed the following parable about intelligent fish.1
A Fish Story
Once upon a time, on a planet completely covered by water, lived a race of big-brained fish. These fish could survive only at a certain depth, and none had ever seen either the surface above or the bottom below. But their big brains made them very smart and also very curious. In time their questions about the nature of water and other things became very sophisticated. The most brilliant among them were called fyshicists. The fyshicists were wonderfully clever, and in a few generations they came to understand a great deal about natural phenomena, including fluid dynamics, chemistry, atomic physics, and even the nuclei of atoms.
Eventually some of the fyshicists began to question why the laws of nature are what they are. Their sophisticated technology allowed them to study water in all its forms, especially ice, steam, and of course, the liquid state. But with all their efforts still one thing stumped them. With all the possible values from zero to infinity, how could they account for the fact that the background temperature, T, was fine-tuned to be in the very narrow range that allowed H2O to exist in its liquid form? They tried many things, including symmetries of various kinds, dynamical relaxation mechanisms, and many other ideas, but nothing could explain it.
Closely allied with the fyshicists were another group, the codmologists, who were also studying their watery world. The codmologists were less interested in the ordinary depths, where the big-brained fish lived, than they were in discovering if an upper boundary to their water-world existed. The codmologists were well aware that much of the water-world was not habitable, the pressure being wrong for their big brains. Journeying by fin to the upper reaches was by no means possible. Their big brains would explode if exposed to the very low water pressure in these regions. So instead, they speculated.
It happened that one school of thought among the codmologists held a very radical (some said ridiculous) idea about the fine-tuning of T. And they had a name for the idea—the Ickthropic Principle. The I.P. maintained that the temperature was in the liquid water range because only in this case could fish exist to observe it!
“Garbage!” said the fyshicists. “That’s not science. It’s religion. It’s just giving up. And besides, if we agree with you, everyone will laugh at us and take away our funding.”
Now not all of the codmologists meant the same thing by the Ickthropic Principle. In fact it was hard to find any two who agreed. One thought that it meant that the Head Angel Fish had made the world just for the purpose of accommodating big-brained fish. Another thought that the quantum-wave function of the waterverse was a superposition of all values of T and only by observing it did some ancestral fish “collapse the wave function.”
A small number of codmologists, led by Andrei-the-Very-Big-Brained and Alexander-Who-Swims-Deep, held a very extraordinary idea. They believed that a stupendously big space existed beyond the upper water boundary. In this very big space, many other bodies similar in some ways to their water-world but different in other ways might exist. Some worlds would be unimaginably hot, so hot that the hydrogen nuclei might even fuse to form helium and then perhaps grow even hotter. Other worlds would be so cold that frozen methane would exist. Only a tiny fraction of the bodies would be at temperatures conducive to the formation of fish. Then it would be no mystery why T was fine-tuned. As every angler knows, most places are fishless, but here and there conditions are just right. And that’s where the fish are.
But the fyshicists sighed and said, “Oh Lord, there they go again with their fishy ideas. Just ignore them.” The end.
The story was a complete flop. Loud sighs and moans from the audience were audible during the seminar. Afterward people avoided me. Tini himself was less than impressed. The Anthropic Principle affects most theoretical physicists the same way that a truckload of tourists in the African bush affects an angry bull elephant.
Anthropic Landscapes
No one, knowing what we do about astronomy, would doubt that the codmologists got it right. The story suggests that there are situations where an anthropic (or “ickthropic”) explanation makes sense. But what are the rules? When is anthropic reasoning appropriate? When is it inappropriate? We need some guiding principles.
First, there is the obvious: an anthropic explanation of proposition X can make sense only if there is a strong reason to believe that the existence of intelligent life would be impossible unless X is true. For the big-brained fish, it’s clear: too hot, and we get fish soup; too cold, and we get frozen fish. In the case of the cosmological constant, Weinberg provided the reasoning.
When you start to think about what it takes for life to be possible, the Landscape becomes a nightmarish minefield. I’ve already explained how a large cosmological constant would have been fatal, but there are many other dangers. The requirements for a universe fall into three main categories: the Laws of Physics must lead to organic chemistry; the essential chemicals must exist in sufficient abundance; and finally, the universe must evolve to create a large, smooth, long-lived, gentle environment.
Life is of course a chemical process. Something about th
e way atoms are constructed makes them stick together in the most bizarre combinations: the giant crazy Tinkertoy molecules of life—DNA, RNA, hundreds of proteins, and all the rest. Although chemistry is usually regarded as a separate branch of science—it has its own university departments and its own journals—it is really a branch of physics: that branch which deals with the outermost electrons in the atom. These valence electrons, hopping back and forth or being shared between atoms, give the atoms their amazing abilities to combine into a diverse array of molecules.
How is it that the Laws of Physics allow marvelously intricate structures like DNA that hold themselves together without collapsing, flying apart, or destructing in some other way? To some degree it is luck.
As we saw in chapter 1, the Laws of Physics begin with a list of elementary particles like electrons, quarks, photons, neutrinos, and more, each with special properties such as mass and electric charge. No one knows why the list is what it is or why the properties are exactly what they are. An infinite number of other lists is possible. But a universe filled with life is by no means what one would expect from a random choice of the list. Eliminating any of these particles (electrons, quarks, and photons) or even changing their properties a modest amount would destroy conventional chemistry. This is obviously so for electrons and quarks, which make up the atom and its nucleus, but it may be less obvious for the photon. Photons are of course the little “bullets” that make up light. True enough, without them we couldn’t see, but we could still hear, feel, and smell, so maybe the photon isn’t so important. Thinking that, however, is a big mistake: the photon happens to be the glue that holds the atom together.
What keeps the valence electrons in orbit around the central core of the atom? Why don’t they just fly off and say adios to the protons and neutrons? The answer is the electrical attraction between the oppositely charged electrons and atomic nucleus. Electrical attraction is different from the attraction between a fly and a strip of flypaper. The flypaper may be very sticky and hold on fiercely, but once you separate the fly even a little, the flypaper immediately lets go. The fly flies off, and unless it is stupid enough to come back, it is completely free. In physics jargon the flypaper force is strong but short range—it doesn’t reach out over large distances.
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