Astronomers search the sky for matter in the form of stars, gas, and dust clouds: all the matter in the universe that emits or scatters light. Assuming that the universe is homogeneous, we can count up all the glowing mass in the general vicinity of our galaxy and measure the average cosmic mass density. The number is remarkably small, only one proton mass per cubic meter: too small by a factor of fifty to close the universe. The obvious implication is that we are living in an infinite open (k = –1) universe with negative curvature and that it will go on expanding forever.
But astronomers and cosmologists have always been wary of jumping to this conclusion. Unlike physics, where being wrong by a factor of fifty is a disgrace, astronomy, until very recently, was a crude science. Estimates could easily be off in either direction by factors of ten or one hundred. Given that the mass density might have had any value, the fact that it came out so close to the critical density filled cosmologists with suspicion. And they were right to be suspicious.
There is another way to determine the mass of a galaxy besides just measuring the light from it, a much more direct and reliable way. And that’s to use Newton’s laws. Let’s return to the asteroid and the stone. Now, instead of moving vertically, the stone is moving in a circular orbit around the asteroid. The gravity of the asteroid keeps the stone in orbit. The key observation, which goes back to Newton, is that by measuring the velocity of the stone and the radius of its orbit, you can determine the mass of the asteroid. In a similar fashion, by measuring the velocity of stars in the outermost parts of a rotating galaxy, astronomers can measure the galaxy’s mass. And what do they find?
The galaxies are all heavier than the astronomers had thought. Roughly speaking, every galaxy is about ten times more massive than all the visible stars and interstellar gas that it contains. The remaining nine-tenths of the mass is a mystery. It is almost certainly not made of the things that comprise ordinary matter: protons, neutrons, and electrons. Cosmologists call it dark matter: dark because it gives off no light.6 Nor does this ghostly matter scatter light or allow itself to be visible in any form, except through its gravity. So strange is modern science. For all these years—since the time of John Dalton—all matter was thought to be the usual stuff of chemistry. But now it seems that 90 percent of all the matter in the universe is something we know nothing about.
As astronomers were in the slow process of convincing themselves that dark matter is really there, theoretical physicists were busy postulating all sorts of new elementary particles for all kinds of reasons. Neutrinos were a very early example, superpartners were another, but they certainly don’t exhaust the imaginative list of hypothetical particles that were postulated for one reason or another. No one knows for sure what dark matter is, but the most likely solution is that there are new, heavy elementary particles that we haven’t discovered yet. Perhaps they are the nonidentical superpartner twins of ordinary particles—the bosonic partners of neutrinos or even the fermion partner of the photon. Perhaps they are a totally unsuspected class of elementary particles that no theorist has dreamed up yet. Whatever they are, they are heavy—they have mass and gravitate—but they have no electric charge to scatter or emit light. That’s all we really know. They must be all around us, constantly passing through the earth and even our bodies, but we can’t see them, feel them, or smell them. Without electric charge, they have no direct way of interacting with our senses. Very sensitive particle detectors are being built so that we may learn more about these mysterious objects, but for now it’s enough to know that they make galaxies ten times heavier than we thought.
The question of whether the universe is open and infinite or closed and finite has haunted astronomy for as long as there have been astronomers. A closed universe with a finite number of galaxies, stars, and planets is intuitively understandable, but an unbounded universe is almost incomprehensible. We have gotten closer to having enough matter to close the universe—tantalizingly close. Originally we were shy of the critical density by a factor of fifty. Now it is only a factor of five, but we are much more confident that we know the amount of mass that is out there. Could it be that the Hubble constant was not measured accurately? If it were smaller by a factor of two or three, then the mass density would be very close to closing the universe. So much hinges on getting this right that we want to close any possible loophole in the reasoning.
Astronomers have been closing in on the value of the Hubble constant for almost eighty years with ever more sophisticated instruments. It now seems very unlikely that it can be small enough to allow the universe to be closed. If this were the end of the story, then we would have to conclude that the cosmic mass density was insufficient to close the universe—but we’re not done yet.
The other way to determine if the universe is open, closed, or flat is very direct. Imagine a very large triangle in space, a triangle of cosmic proportions. To ensure that the sides are straight, we might take them to be the paths of light rays. A cosmic surveyor might measure the angles of the triangle, and if she were a student of Euclidean geometry, she might conclude that the sum of the angles should add up to 180 degrees—two right angles. The ancient Greeks were sure of it; they couldn’t conceive of space being any other way.
But modern geometers know that the answer depends on the geometry of space. If space is flat like Euclid thought, the sum of the three angles would add up to 180 degrees. On the other hand, if space is a sphere, the angles would add up to a total greater than 180 degrees. Less easy to visualize, the angles of a triangle in a negatively curved space will always sum to something less than 180 degrees.
Sending a team of cosmic surveyors billions of light-years to the corners of an immense triangle is not feasible, and even if it were, it would take billions of years to get there and billions of years more to get the result back to earth. But the ingenuity of astrophysicists is unbounded, and believe it or not, they devised a way to do the job without ever leaving the earth. I will return to how they did it after I explain the cosmic microwave background, or CMB. But the result is easy to state: space appears to be flat! The angles add up just as Euclid assumed. Or at least they add up to 180 degrees to within the accuracy of the experiment.
By now, dear reader, you must realize something is terribly wrong. We have two ways to determine if the universe is open, closed, or flat and two incompatible answers. The amount of mass in the universe appears to be five times too small to either close the universe or even to make it flat. But surveying cosmic triangles seems to leave little doubt that the geometry of the universe is flat.
The Age of the Universe and the Oldest Stars
Imagine a cosmic movie, a biography that follows the universe from its birth in fire to its present old age. But instead of viewing the movie in the ordinary way—from birth to old age—we run it backward, on rewind, so to speak. Instead of expanding, we see it contracting. The galaxies appear to move according to a reverse version of the Hubble Law—their velocity being proportional to their distance but approaching us instead of receding. Let’s follow one of those distant galaxies as it approaches us. Using Hubble’s Law (run backward), we can determine its velocity. Let’s say the galaxy is one megaparsec away. Hubble’s Law tells us that it is approaching with a velocity of seventy-five kilometers a second. Knowing how far away it is and how fast it is moving, it’s an easy exercise to determine how long it will be until the galaxy is on top of us. I will do it for you. The answer is about fifteen billion years. That’s the answer if we assume that the galaxy moves with a steady constant speed.
What if we started with a galaxy two megaparsecs away instead of one? Hubble’s Law tells us that it is moving twice as fast as the previous galaxy: twice as far but twice as fast. It too will arrive in our lap in fifteen billion years. In fact the same is true for any distant galaxy. According to this reckoning all the galaxies will merge into an undifferentiated mass in about fifteen billion years in the reverse movie.
But galaxies don’t move with uniform
speed as they approach. In the forward version of the movie, gravity slows them as they recede. Thus, in the backward version, gravity speeds them up as they fall toward one another. This means that it should take less time for them to collide. When cosmologists carry out the correct calculation (in the forward version), they find that the galaxies were crowded together in a dense mass about ten billion years ago. This would mean that it has been only ten billion years since the hydrogen and helium gases began to differentiate themselves into the clumps that eventually became galaxies. To say it concisely, the universe, according to this reckoning, is ten billion years old.
Determining the age of the universe has been a bumpy ride. Originally Hubble underestimated the distances to the galaxies by about a factor of ten. This led him to conclude that the universe started its expansion a mere one billion years ago. But by Hubble’s time, rocks two billion years old had already been dated by their radioactivity. Obviously there was an error, and it was soon found. But a modern version of the problem still exists. Astronomers and astrophysicists, who study the detailed properties of stars in our galaxy, find that the oldest stars are older than the universe. They are about thirteen billion years old. The child is older than the parent!
In short, three big problems affect our thinking about the universe. First, there is the contradictory evidence concerning the geometry of space, whether it is open, closed, or flat. Second, is it really younger than the oldest stars? And third, the mother of all problems: is there a cosmological constant as Einstein originally believed, and if not, why not? Are these problems connected? Of course they are.
The Solution
Perhaps the resolution is that our theory of gravity—the General Theory of Relativity—is just plain wrong. In fact some physicists have jumped to this conclusion. These physicists usually try to make modifications in the theory that will only affect the gravitational force at very great distances. Personally, I don’t find much merit in these schemes. They are usually very contrived, often violate fundamental principles, and in my opinion, are quite unnecessary.
Another possible way out is to suppose that astronomers are taking the precision of their data too seriously. You can make a good living betting against experimental data that contradict the prevailing expectations. Such data are almost always wrong, and further experimentation usually proves it. In this case I would have bet against the astronomical data, not the theory. But it seems I would have lost my bet. As the data have improved over the last few years, they reinforce the fact that observation and theory are at odds with each other. There really is something wrong.
But one possibility lurks just beneath the surface that cannot be easily dismissed. What if there is a small cosmological constant after all? What if Einstein’s greatest blunder was really one of his greatest discoveries? Could that resolve the conflicts?
When we considered whether the observable mass in the universe would be enough to render it flat or closed, we completely ignored the possibility of vacuum energy. That would be a mistake in a world with a cosmological constant. Einstein’s equations say that all forms of energy affect the curvature of space. Energy and mass are the same thing, so vacuum energy must be counted as part of the mass density of the universe. The ordinary and dark matter together add up to about 30 percent of the mass needed to flatten or close the universe. The obvious way out of the dilemma is to make up the missing 70 percent in the form of a cosmological constant. This would mean that the vacuum-energy density was a little more than twice the mass of ordinary and dark matter combined, about thirty proton masses per cubic meter.
Because the cosmological constant represents a repulsive force, it would have an effect on the way that the universe expands. The early phase of the expansion would not be much affected, but as the distance grows between galaxies, so too does the repulsive force. Eventually the cosmological constant can accelerate the outward motion of the galaxies, causing the Hubble expansion to pick up speed.
Let’s run it backward. The galaxies are falling inward, but now the extra repulsion slows them down. The initial estimate of their inward velocity (the one we make today) overestimates how fast they will be moving as they grow closer. Failure to account for the vacuum energy will lead us to underestimate the length of time until the galaxies all merge. In other words, if there were a cosmological constant but we didn’t know it, we would find the universe appearing younger than it really is. Indeed, if we include the effects of a vacuum energy equal to about thirty proton masses per cubic meter, the ten-billion-year lifetime of the universe gets stretched to about fourteen billion years. That’s perfect because it makes the universe just a little older than the oldest stars.
These conclusions concerning the existence of a cosmological constant are so important that I want to repeat them. The existence of a small cosmological constant, representing 70 percent of the energy in the universe, solves the two biggest puzzles of cosmology. First, the additional energy is just enough to make the universe flat. This fact removes the awkward discrepancy between the observed flatness of space and the fact that the mass in the universe was insufficient to render it flat.
The second paradox that is eliminated by the cosmological constant is the equally awkward discrepancy that the oldest stars appear older than the universe. In fact, the same vacuum energy—70 percent of the total—remarkably, is exactly what is needed to make the universe a little older than these ancient stars.
Type I Supernovae
Over the last decade the historical accuracy of the universe’s biography has been greatly improved. We now know the history of the expansion in much greater detail. The trick involves a class of distant events called Type I supernovae. A supernova is a cataclysmic event in which a dying star collapses under its own weight and becomes a neutron star. The supernova is so unimaginably violent that when it occurs in a galaxy it can outshine the billions of stars that galaxy comprises. Supernovae are easy to spot even in very distant galaxies.
All supernovae are interesting, but something is very special about Type I supernovae. They originate from double star systems in which an ordinary star and a white dwarf are orbiting each other at a relatively close distance. The white dwarf star is a dead star that didn’t have quite enough mass to collapse to a neutron star.
As the two stars revolve around each other, the gravity of the white dwarf gradually sucks matter away from the ordinary star and, in this way, slowly increases its own mass. At some very precise point, when the mass is just right, the white dwarf can no longer support its own weight, and it implodes, creating a Type I supernova. The behavior of the final collapse doesn’t depend on the original mass of the white dwarf, or for that matter, its companion. In fact these events are believed to occur in a unique way and always give the same amount of light. An astronomer would say they all have the same luminosity.7 Astronomers can tell, with a good degree of certainty, how far away they are by how bright they appear.
The velocity of the galaxy in which the supernova is embedded can also be easily determined using the Doppler method. And once we know both the distance and the velocity of the distant galaxy, the Hubble constant is easy to determine. But the special thing about very distant galaxies is that their light was given off long in the past. A galaxy five billion light-years away radiated the light that we now see five billion years ago. When we measure the Hubble parameter on earth today, we are really measuring the value that it had five billion years ago.
By concentrating on galaxies at a variety of different distances, we effectively measure the history of the Hubble parameter. In other words, Type I supernovae allow us to know a great deal about the history of the universe during the various stages of its evolution. And most important, they allow us to compare our real universe with mathematical models, with and without cosmological constants. The results are unambiguous. The expansion of the universe is accelerating under the influence of a cosmological constant, or something very much like it. To theoretical physicists like mysel
f, this is a stunning reversal of fortune that cannot help but change our entire outlook. For so long we were trying to explain why the vacuum energy is exactly zero. Well, it seems that it is not zero. The first 119 decimal places of the cosmological constant cancel, but then, in the 120th, incredibly, a nonzero value results. To make matters even more interesting, its value is just about what Weinberg predicted it would be based on the Anthropic Principle!
Light from Creation
Because light travels with a finite velocity, great telescopes that look to tremendous distances are also looking far back into the past. We see the sun as it was eight minutes ago, the nearest star as it was four years ago. Early humans were first beginning to stand straight when the light started its two-million-year journey from the nearest galaxy, Andromeda.
Oldest of all is the light that has been traveling to us for about fourteen billion years. This light started before the earth or even the oldest stars were formed. Indeed, the hydrogen and helium had not yet begun the process of differentiation into galaxies. So hot and dense were these gases that the atoms were all ionized. It was as close to creation as nature will ever allow us to see, at least if the messenger is electromagnetic radiation.
Think of the universe as a series of concentric shells with us at the center. There are, of course, no real shells out there, but nothing prevents us from dividing space up in that way. Each successive shell is farther away than the last. Each shell also represents an earlier (time) epoch than the previous. By looking deeper and deeper, we are, in effect, running the movie of the universe backward.
The Cosmic Landscape Page 16
