Origins: Fourteen Billion Years of Cosmic Evolution (8 page)

The most striking and significant aspect of this map, as was also true for the balloon-borne observations and for WMAP’s predecessor, the COBE (COsmic Background Explorer) satellite, lies in its near featurelessness. No measurable differences in the intensity of the cosmic background radiation arriving from all different directions appear until we reach a precision of about one part in a thousand in our measurements. Even then, the only discernible differences appear as a slightly greater intensity, centered on one particular direction, that matches a corresponding slightly lesser intensity, centered on the opposite direction. These differences arise from our Milky Way galaxy’s motion among its neighbor galaxies. The Doppler effect causes us to receive slightly stronger radiation from the direction of this motion, not because the radiation actually is stronger, but because our motion toward the cosmic background radiation (CBR) slightly increases the energies of the photons that we detect.

Once we compensate for the Doppler effect, the cosmic background radiation appears perfectly smooth—until we attain an even higher precision of about one part in a hundred thousand. At that level, tiny deviations from total smoothness appear. They track locations from which the CBR arrives with a bit more, or a bit less, intensity. As previously noted, the differences in intensity mark directions in which matter was either a little hotter and denser, or a little cooler and more rarefied, than the average value 380,000 years after the big bang. The COBE satellite first saw these differences; balloon-borne instruments and South Pole observations improved our measurements; and then the WMAP satellite provided still better precision in surveying the entire sky, allowing cosmologists to construct a detailed map of the intensity of the cosmic background radiation, observed with unprecedented angular resolution of about one degree.

The tiny deviations from smoothness revealed by COBE and WMAP have more than passing interest to cosmologists. First of all, they show the seeds of structure in the universe at the time when the cosmic background radiation ceased to interact with matter. The regions revealed as slightly denser than average at that time had a head start toward further contraction, and have won the competition to acquire the most matter by gravity. Thus the primary result from the new map of the CBR’s intensity in different directions is the verification of cosmologists’ theories of how the immense differences in density from place to place throughout the cosmos that we see now owe their existence to tiny differences in density that existed a few hundred thousand years after the big bang.

But cosmologists can use their new observations of the cosmic background radiation to discern another, still more basic fact about the cosmos. The details in the map of the CBR’s intensity from place to place reveal the curvature of space itself. This amazing result rests on the fact that the curvature of space affects how radiation travels through it. If, for example, space has a positive curvature, then when we observe the cosmic background radiation, we are in much the same situation as an observer at the North Pole who looks along Earth’s surface to study radiation produced near the Equator. Because the lines of longitude converge toward the pole, the source of radiation seems to span a smaller angle than it would if space were flat.

To understand how the curvature of space affects the angular size of features in the cosmic background radiation, imagine the time when the radiation finally ceased to interact with matter. At that time, the largest deviations from smoothness that could have existed in the universe had a size that cosmologists can calculate: the age of the universe at that time, multiplied by the speed of light—about 380,000 light-years across. This represents the maximum distance at which particles could have affected one another to produce any irregularities. At greater distances, the “news” from other particles would not yet have arrived, so they cannot be blamed for any deviations from smoothness.

How large an angle would these maximum deviations span on the sky now? That depends on the curvature of space, which we can determine by finding the sum of
Ω
M
and
Ω
Λ
. The more closely that sum approaches 1, the more closely the space curvature will approach zero, and the larger will be the angular size that we observe for the maximum deviations from smoothness in the CBR. This space curvature depends only on the sum of the two Ωs, because both types of density make space curve in the same way. Observations of the cosmic background radiation therefore offer a direct measurement of
Ω
M
+
Ω
Λ
, in contrast to the supernova observations, which measure the difference between
Ω
M
and
Ω
Λ
.

The WMAP data show that the largest deviations from smoothness in the CBR span an angle of about 1 degree, which implies that
Ω
M
+
Ω
Λ
has a value of 1.02, plus or minus 0.02. Thus, within the limits of experimental accuracy, we may conclude that
Ω
M
+
Ω
Λ
=
1, and that space is flat. The result from observations of distant SN Ia’s may be stated as
Ω
Λ
–
Ω
M
=
0.46. If we combine this result with the conclusion that
Ω
M
+
Ω
Λ
=
1, we find that
Ω
M
=
0.27 and
Ω
Λ
=
0.73, with an uncertainty of a few percent in each number. As already noted, these are the astrophysicists’ current best estimates for the values of these two key cosmic parameters, which tell us that matter—both ordinary and dark—provides 27 percent of the total energy density in the universe, and dark energy 73 percent. (If we prefer to think of energy’s mass equivalent, E/c
2
, then dark energy furnishes 73 percent of all the mass.)

Cosmologists have long known that if the universe has a non-zero cosmological constant, the relative influence of matter and dark energy must change significantly as time passes. On the other hand, a flat universe remains flat forever, from its origin in the big bang to the infinite future that awaits us. In a flat universe, the sum of
Ω
M
and
Ω
Λ
always equals 1, so if one of these changes, the other must also vary in compensation.

During the cosmic epochs that followed soon after the big bang, the dark energy produced hardly any effect on the universe. So little space existed then, in comparison to the eras that would follow, that
Ω
Λ
had a value just a bit above zero, while
Ω
M
was only a tiny bit less than 1. In those bygone ages, the universe behaved in much the same way as a cosmos without a cosmological constant. As time passed, however,
Ω
M
steadily decreased and
Ω
Λ
just as steadily increased, keeping their sum constant at 1. Eventually, hundreds of billions of years from now,
Ω
M
will fall almost all the way to zero and
Ω
Λ
will rise nearly to unity. Thus, the history of flat space with a non-zero cosmological constant involves a transition from its early years, when the dark energy barely mattered, through the “present” period, when
Ω
M
and
Ω
Λ
have roughly equal values, and on into an infinitely long future, when matter will spread so diffusely through space that
Ω
M
must pursue an infinitely long slide toward zero, even as the sum of the two
Ω
s remains equal to 1.

Observational deduction of how much mass exists in galaxy clusters now gives
Ω
M
a value of about 0.25, while the observations of the CBR and distant supernovae imply a value close to 0.27. Within the limits of experimental accuracy, these two values coincide. If the universe in which we live does have a non-zero cosmological constant, and if that constant is responsible (along with the matter) for producing the flat universe that the inflationary model predicts, then the cosmological constant must have a value that makes
Ω
Λ
equal to a bit more than 0.7, two and a half times the value of
Ω
M
. In other words,
Ω
Λ
must now do most of the work in making (
Ω
M
+
Ω
Λ
) equal to 1. This means that we have already passed through the cosmic era when matter and the cosmological constant contributed the same amount (with each of them equal to 0.5) toward maintaining the flatness of space.

Within less than a decade, the double-barreled blast from the Type Ia supernovae and the cosmic background radiation has changed the status of dark energy from a far-out idea that Einstein once toyed with to a cosmic fact of life. Unless a host of observations eventually prove to be misinterpreted, inaccurate, or just plain wrong, we must accept the result that the universe will never contract or recycle itself. Instead, the future seems bleak: a hundred billion years from now, when most stars will have burnt themselves out, all but the closest galaxies will have vanished across our horizon of visibility.

By then, the Milky Way will have coalesced with its nearest neighbors, creating one giant galaxy in the literal middle of nowhere. Our night sky will contain orbiting stars, (dead and alive) and nothing else, leaving future astrophysicists a cruel universe. With no galaxies to track the cosmic expansion, they will erroneously conclude, as did Einstein, that we live in a static universe. The cosmological constant and its dark energy will have evolved the universe to a point where they cannot be measured or even dreamt of.

Enjoy cosmology while you can.

CHAPTER 6

One Universe or Many?

T
he discovery that we live in an accelerating universe, with an ever-increasing rate of expansion, rocked the world of cosmology early in 1998, with the first announcement of the supernova observations that point to this acceleration. Now that the accelerating universe has received confirmation from detailed observations of the cosmic background radiation, and now that cosmologists have had several years to wrestle with the implications of an accelerating cosmic expansion, two great questions have emerged to bedevil their days and brighten their dreams: What makes the universe accelerate? And why does that acceleration have the particular value that now characterizes the cosmos?

The simple answer to the first question assigns all responsibility for the acceleration to the existence of dark energy, or, equivalently, to a non-zero cosmological constant. The amount of acceleration depends directly on the amount of dark energy per cubic centimeter: More energy implies greater acceleration. Thus, if cosmologists could only explain where the dark energy comes from, and why it exists in the amount that they find today, they could claim to have uncovered a fundamental secret of the universe—the explanation for the cosmic “free lunch,” the energy in empty space that continuously drives the cosmos toward an eternal, ever more rapid expansion and a far future of enormous amounts of space, correspondingly enormous amounts of dark energy, and almost no matter per cubic light-year.

What makes dark energy? From the deep realms of particle physics, cosmologists can produce an answer: The dark energy arises from events that must occur in empty space, if we trust what we have learned from the quantum theory of matter and energy. All of particle physics rests on this theory, which has been verified so often and so exactly in the submicroscopic realm that almost all physicists accept it as correct. An integral part of quantum theory implies that what we call empty space in fact buzzes with “virtual particles,” which wink into and out of existence so rapidly that we can never pin them down directly, but can only observe their effects. The continual appearance and disappearance of these virtual particles, called the “quantum fluctuations of the vacuum” by those who like a good physics phrase, gives energy to empty space. Furthermore, particle physicists can, without much difficulty, calculate the amount of energy that resides in every cubic centimeter of the vacuum. The straightforward application of quantum theory to what we call a vacuum predicts that quantum fluctuations must create dark energy. When we tell the story from this perspective, the great question about dark energy seems to be, Why did cosmologists take so long to recognize that this energy must exist?

Unfortunately, the details of the actual situation turn this question into, How did particle physicists go so far wrong? Calculations of the amount of dark energy that lurks in every cubic centimeter produce a value about 120 powers of ten greater than the value that cosmologists have found from observations of supernovae and the cosmic background radiation. In far-out astronomical situations, calculations that prove correct to within a single factor of 10 are often judged at least temporarily acceptable, but a factor of 10
120
cannot be swept under the rug, even by physics Pollyannas. If real empty space contained dark energy in anything like the amounts proposed by particle physics, the universe would have long since puffed itself into so large a volume that our heads could never have begun to spin, since a tiny fraction of a second would have sufficed to spread matter out to unimaginable rarefaction. Theory and observation agree that empty space ought to contain dark energy, but they disagree by a trillion to the tenth power about the amount of that energy. No earthly analogy, nor even a cosmic one, can illustrate this discrepancy accurately. The distance to the farthest galaxy that we know exceeds the size of a proton by a factor of 10
40
. Even this enormous number is only the cube root of the factor by which theory and observation currently diverge concerning the value of the cosmological constant.

Particle physicists and cosmologists have long known that quantum theory predicts an unacceptably large value for the dark energy, but in the days when the cosmological constant was thought to be zero, they hoped to discover some explanation that would, in effect, cancel positive with negative terms in the theory and thereby finesse the problem out of existence. A similar cancellation once solved the problem of how much energy virtual particles contribute to the particles that we do observe. Now that the cosmological constant turns out to be non-zero, the hopes of finding such a cancellation seem dimmer. If the cancellation does exist, it must somehow remove almost all of the mammoth theoretical value we have today. For now, lacking any good explanation for the size of the cosmological constant, cosmologists must continue to collaborate with particle physicists as they seek to reconcile theories of how the cosmos generates dark energy with the value observed for the amount of dark energy per cubic centimeter.

Some of the finest minds engaged in cosmology and particle physics have directed much of their energy toward explaining this observational value, with no success at all. This provokes fire, and sometimes ire, among theorists, in part because they know that a Nobel Prize—not to mention the immense joy of discovery—awaits those who can explain what nature has done to make space as we find it. But another issue stokes intense controversy as it cries out for explanation: Why does the amount of dark energy, as measured by its mass equivalent, roughly equal the amount of energy provided by all the matter in the universe?

We can recast this question in terms of the two Ωs that we use to measure the density of matter and the density equivalent of dark energy: Why do Ω
M
and Ω
Λ
roughly equal one another, rather than one being enormously larger than the other? During the first billion years after the big bang, Ω
M
was almost precisely equal to 1, while Ω
Λ
was essentially zero. In those years, Ω
M
was first millions, then thousands, and afterward hundreds of times greater than Ω
Λ
. Today, with
Ω
M
=
0.27 and
Ω
Λ
=
0.73, the two values are roughly equal, though Ω
Λ
is already notably larger than Ω
M
. In the far future, more than 50 billion years from now, Ω
Λ
will be first hundreds, then thousands, after that millions, and still later billions of times greater than Ω
M
. Only during the cosmic era from about 3 billion to 50 billion years after the big bang do the two quantities match one other even approximately.

To the easygoing mind, the interval between 3 billion and 50 billion years embraces quite a long period of time. So what’s the problem? From an astronomical viewpoint, this stretch of time amounts to nearly nothing. Astronomers often take a logarithmic approach to time, dividing it into intervals that increase by factors of 10. First the cosmos had some age; then it grew ten times older; then ten times older than that; and so on toward infinite time, which requires an infinite number of ten-times jumps. Suppose that we start counting time at the earliest moment after the big bang that has any significance in quantum theory, 10
-43
second after the big bang. Since each year contains about 30 million (3 x 10
7
) seconds, we need about 60 factors of 10 to pass from 10
-43
second to 3 billion years after the big bang. In contrast, we require only a bit more than a single factor of 10 to stroll from 3 billion to 50 billion years, the only period when Ω
M
and Ω
Λ
are roughly equal. After that, an infinite number of ten-times factors opens the way to the infinite future. From this logarithmic perspective, only a vanishingly small probability exists that we should find ourselves living in a cosmic situation for which Ω
M
and Ω
Λ
have even vaguely similar values. Michael Turner, a leading American cosmologist, has termed this conundrum—the question of why we find ourselves alive at a time when Ω
M
and Ω
Λ
are approximately equal—the “Nancy Kerrigan problem” in honor of the Olympic figure skater, who asked, after enduring an assault by her rival’s boyfriend, “Why me? Why now?”

Despite their inability to calculate a cosmological constant whose value comes anywhere close to the measure one, cosmologists do have an answer to the Kerrigan problem, but they differ sharply on its significance and implications. Some embrace it; some accept it only reluctantly; some dance around it; and some despise it. This explanation links the value of the cosmological constant to the fact that we are here, alive on a planet that orbits an average star in an average galaxy. Because we exist, this argument runs, the parameters that describe the cosmos, and in particular the value of the cosmological constant, must have values that allow us to exist.

Consider, for example, what would happen in a universe with a cosmological constant much larger than its actual value. A much greater amount of dark energy would make Ω
Λ
rise far above Ω
M,
not after about 50 billion years but after only a few million years. By this time, in a cosmos dominated by the accelerating effects of dark energy, matter would spread so rapidly apart that no galaxies, stars, or planets could form. If we assume that the stretch of time from the first formation of clumps of matter to the origin and development of life covers at least 1 billion years, we can conclude that our existence limits the cosmological constant to a value between zero and a few times its actual value, while ruling out of play the infinite range of higher values.

This argument gains more traction if we assume, as do many cosmologists, that everything we call the universe belongs to a much larger “multiverse,” which contains an infinite number of universes, none of which interact with any other: in the multiverse concept, the entire state of affairs embeds in higher dimensions, so space in our universe remains completely inaccessible to any other universe, and vice versa. This lack of even theoretically possible interactions puts the multiverse theory into the category of apparently nontestable, and therefore nonverifiable, hypotheses—at least until wiser minds find ways to test the multiverse model. In the multiverse, new universes are born at completely random times, capable of swelling up by inflation into enormous volumes of space, and of doing so without interfering in the least with the infinite number of other universes.

In the multiverse, each new universe springs into existence with its own physical laws and its own set of cosmic parameters, including the rules that determine the size of the cosmological constant. Many of these other universes have cosmological constants enormously larger than ours, and quickly accelerate themselves into situations of near-zero density, no good for life. Only a tiny, perhaps an infinitesimal fraction of all the universes in the multiverse offer conditions that allow life to exist, because only this fraction have parameters that permit matter to organize itself into galaxies, stars, and planets, and for those objects to last for billions of years.

Cosmologists call this approach to explaining the value of the cosmological constant the anthropic principle, though the anthropic approach probably offers a better name. This approach toward explaining a crucial question in cosmology has one great appeal: people love it or hate it, but rarely feel neutral about it. Like many intriguing ideas, the anthropic approach can be bent to favor, or at least seem to favor, various theological and teleological mental edifices. Some religious fundamentalists find that the anthropic approach supports their beliefs because it implies a central role for humanity: without someone to observe it, the cosmos—at least the cosmos that we know—would not, could not, be here; hence a higher power must have made things just right for us. An opponent of this conclusion would note this is not really what the anthropic approach implies; on a theological level, this argument for the existence of God implies surely the most wasteful creator one might imagine, who makes countless universes in order that in a tiny sector of just one of these, life might arise. Why not skip the middleman and follow older creation myths that center on humanity?

On the other hand, if you choose to see God in everything, as Spinoza did, you cannot help but admire a multiverse that effloresces universes without end. Like most news from the frontier of science, the concept of a multiverse, and the anthropic approach, can be easily bent in different directions to serve the needs of particular belief systems. As things stand, many cosmologists find the multiverse quite enough to swallow without connecting it to any system of beliefs. Stephen Hawking, who (like Isaac Newton before him) holds the Lucasian chair in astronomy at Cambridge University, judges the anthropic approach an excellent resolution of the Kerrigan problem. Stephen Weinberg, who won the Nobel Prize for his insights into particle physics, dislikes this approach but pronounces himself in favor, at least for the time being, because no other reasonable solution has appeared.

History may eventually show that for now, cosmologists are concentrating on the wrong problem—wrong in the sense that we don’t yet understand enough to attack it properly. Weinberg likes the analogy with Johannes Kepler’s attempt to explain why the Sun has six planets (as astronomers then believed), and why they move in the orbits that they do. Four hundred years after Kepler, astronomers still know far too little about the origin of planets to explain the precise number and orbits of the Sun’s family. We do know that Kepler’s hypothesis, which proposed that the spacing of the planets’ orbits around the Sun allows one of the five perfect solids to fit exactly between each pair of adjoining orbits, has no validity whatsoever, because the solids do not fit particularly well, and (even more important) because we have no good reason to explain why the planets’ orbits should obey such a rule. Later generations may regard today’s cosmologists as latter-day Keplers, struggling valiantly to explain what remains inexplicable by today’s understanding of the universe.