l12body

1. INTRODUCTION

I am Alpha and Omega, the beginning and the ending, saith the Lord, which is, and which was, and which is to come, the Almighty. (King James Bible: Revelations 1:8)

The topic of this lesson is nothing less than the origin and fate of the universe. Some of this material is discussed in Chapters 26 and 27 of your text; but there is more here that you must learn.

Cosmology is a huge and wonderful subject, and we can only touch on some of the high points here. There are also several excellent books on the subject. My favorites are:

The First Three Minutes by Steven Weinberg

A Short History of the Universe by Joseph Silk (Scientific American Books)

Before the Beginning: Our Universe and Others by Martin Rees (Scientific American Books)

The Whole Shebang: A State-of-the-Universe(s) Report by Timothy Ferris (Simon & Schuster)

There are many good web sites on cosmology. I list the best ones I could find here, starting with relatively simple ones and proceeding to higher level. Be sure to read the ones marked with *.

*The Big Bang by Mike Guidry
*Introduction to Cosmology by the Microwave Anisotropy Probe group
Cosmology: a Research Briefing: a report by the National Academy of Sciences
Cosmology tutorial by Ned Wright

2. HISTORY

Here's a historical summary of much of the material covered below. Read it carefully! Be sure you know about the people with biographical links or highlighted in red, and what they did.

NOTES ON THE HISTORY OF COSMOLOGY
1000 BC	According to the Rig Vedas -- ancient Hindu texts -- the universe undergoes an endless cycle of fiery deaths and rebirths. This cycle of creation and destruction is a manifestation of the dance of Shiva. The time for each cycle is a "day of Brahma", which lasts 4.32 billion years. (This number is curiously close to the age of the Earth, 4.6 billion years, as determined from the age of the elements.)
350 BC	According to Aristotle, the universe is eternal and has never changed. The Earth is at the center, and the stars are located at the outer boundary, where all things (including space itself) fade into nothingness. (This idea foreshadows the modern concept of the "event horizon" of the universe.)
1576 AD	Thomas Digges publishes "A Perfect Description of the Celestial Orbes", a variant of the theory of Copernicus (with the Sun at the center of the universe), in which Digges claims that the universe is infinite in spatial extent and filled uniformly with stars. This is one of the first clear statements of the "Cosmological Principle."
1590	The fiery monk Giordano Bruno goes one step further: he says that the Sun is not at the center, but that the universe contains numberless solar systems and is teeming with life. The Church was not amused. He was imprisoned, tortured, and finally burned at the stake in 1600.
1610	The great astronomer Johannes Kepler first pointed out a fundamental problem with an infinite universe populated with stars: the entire sky would be blazing hot. In 1720, Edmund Halley, famous for his prediction of the return of Halley's comet, again draws attention to this problem. In 1823, the German astronomer Olbers once again discusses this problem, and suggests that the solution might be that the universe is filled with dust, which prevents the light from distant stars from reaching us. But 20 years later the great English astronomer John Herschel shows that Olbers' explanation won't work. This problem, now known as "Olbers' paradox" was not resolved until 1920, when Edwin Hubble proved that the universe was expanding.
1750	Thomas Wright published "An Original Theory of the Universe" in which he explained the Milky Way by proposing that the stars were distributed in a thick disk -- the first step in the discovery that the Milky Way is a galaxy.
1755	The great philosopher Immanuel Kant, inspired by Wright's ideas, proposed that the Milky Way was only one of many galaxies, scattered throughout an infinite universe.
1918	From observations of globular clusters and the RR Lyrae variable stars in them, American astronomer Harlow Shapley proved that the globular clusters were distributed in a roughly spherical system, centered, not on the Sun, but at a point at a distance of some 15,000 parsecs. (Shapley overestimated the distance; we now know it is closer to 8,000 parsecs.) This was compelling evidence that the Sun is not at the center of the Milky Way.
1912-1920	American astronomer Vesto Slipher, working at the Lowell Observatory in Flagstaff, Arizona, began to measure the Doppler shifts of spectral lines from spiral galaxies. He found that the vast majority of galaxies were moving away from the Milky Way (except the Andromeda galaxy M31, which was moving toward the Milky Way).
1916	Albert Einstein published his General Theory of Relativity (GTR), which explains how the presence of matter causes space and time itself to be warped, and how the force of gravity can be regarded as the natural trajectories of objects moving in warped space-time.
1917	Einstein realized that the equations of GTR should be able to explain the structure of the entire universe. He assumed that the universe is infinite in extent, has more or less the same average density everywhere (the "Cosmological Principle"), and that the space must be curved because of the matter in the universe. With these assumptions, he found that his equations do not permit a static universe: the universe must be in motion, either expanding or contracting. Einstein couldn't believe his own equations, because they contradicted the "Perfect Cosmological Principle" -- namely, that notion that the universe must be eternal in time as well as uniform in space. To remedy this, Einstein added a new term to his equations of GTR. This term, called the "cosmological constant", acted as a repulsive force of space and time itself; it could counteract the attractive force of gravity and permit an infinite universe that was neither expanding nor contracting.
1917	Dutch astronomer Willem de Sitter solves Einstein's original equations of GTR, without the cosmological constant and with very low density of matter. His solution shows that such a universe must be expanding.
1920	Russian mathematician Alexander Friedmann finds a general set of solutions to Einstein's equations of GTR with no cosmological constant but with any density of matter. His solutions describe a set of model universes, some of which expand forever and some of which collapse again, depending on the mean density of matter in the universe. Nobody paid much attention to Friedmann's solutions.
1920	Harlow Shapley and Heber Curtis held a famous debate about the nature of the "spiral nebulae". Shapley argued that they were gas clouds belonging to the Milky Way; Curtis argued that they were other galaxies, as big as the Milky Way itself and at great distances. The debate did not resolve the controversy, but shortly thereafter, Edwin Hubble and others found novae and Cepheid variable stars in nearby galaxies. In 1930, Shapley conceded that the spiral nebulae must really be other galaxies. Kant's hypothesis of "island universes" was right.
1924	Working at at the great new 2.4-m telescope at Mt. Wilson, California, Edwin Hubble began a systematic survey to measure the distances and Doppler shifts of spiral galaxies, following Slipher's work.
1927	Belgian priest Georges Lemaitre rediscovered Friedmann's solutions to Einstein's equations. But, unlike Friedmann, Lemaitre was interested in observational astronomy as well as mathematics and he was aware of Hubble's observations at Mt. Wilson showing that the distant galaxies were expanding away from the Milky Way -- the more distant the galaxy, the faster the expansion. Lemaitre recognized that this observed expansion law was exactly what Einstein's equations predicted, and he told Hubble. Moreover, it was clear that the cosmic expansion was the solution of Olbers' paradox.
1929	Hubble published his observations showing that the expansion of the universe obeyed the equation V = H₀D, now known as "Hubble's Law". He underestimated the distances of the galaxies, thus derived a value of the "Hubble Constant", H₀ = 500 km/s/Mpc, that is almost ten times the modern value.
1932	By this time, Hubble and Lemaitre had convinced the world that the universe was really expanding, according to the Friedmann solutions. Einstein came to Mt. Wilson to meet Hubble, and said that the invention of the cosmological constant was "the biggest blunder of my life." Here's a photo of Lemaitre (center) and Einstein (right) in Pasadena, California in 1933.
1941	Canadian astronomer Andrew McKellar, observing absorption lines in stellar spectra due to CH+ and CN molecules in interstellar clouds noticed that the molecules were excited, as if they were bathed in a cosmic radiation field at a temperature of about 3 K (-270 C). It was a puzzling result that nobody could understand. Everybody ignored it.
1948	Russian physicist George Gamow, now working at George Washington University in Washington, DC, published a famous paper with R. Alpher and Hans Bethe. He realized that the Friedmann solutions implied that the universe had infinite density when the expansion began, some 10 billion years ago, and that if so, the primordial matter in the early universe (less than a minute old!) would be incredibly dense. Such primordial matter in the universe would naturally undergo fusion reactions, leaving a universe today filled with mostly heavy elements and virtually no hydrogen. That prediction was grossly in conflict with astronomical observations, which showed that the most of the matter in the universe was hydrogen. Gamow realized that this dilemma could be resolved if the universe was filled with gamma rays, and that this radiation would cool down as the universe expanded, such that it would have a temperature of about 25 K today. In fact, Gamow made several errors in his assumptions about the conditions and reactions in the early universe, so the details of his predictions were wrong. Few scientists took Gamow's theory seriously.
1950	Japanese astrophysicist C. Hayashi (the same Hayashi who developed the theory for newly-forming stars) recognized a basic flaw in Gamow's theory for the formation of the elements in the early universe. A gas of pure neutrons could not coexist with such a hot radiation field in the early universe. Hayashi corrected Gamow's theory and published the version that we believe today. But he did not carry out detailed calculations of the radiation temperature.
1962	Russian physicist Yacov B. Zeldovich, working in Moscow, re-derived the theory of the hot big bang (the same theory that was developed by Hayashi). He calculated that the left- over radiation filling the cosmos should have a present-day temperature of about 3 K, not 25 K as Gamow predicted. Zeldovich went on further to suggest that it might be possible to observe this radiation, and he even recognized that the best telescope to use might be the ATT Bell Labs radio telescope at Holmdel, New Jersey. He read a technical report from the Bell Labs, which seemed to say that the radiation "sky temperature" was less than 1 K. Zeldovich concluded that there must be something wrong with his theory.
1964	Robert Dicke, working at Princeton University, knew about the theory of the hot big bang and was building a radio telescope especially designed to observe the radiation.
1964	Arno Penzias and Robert Wilson, working at the Bell Labs radio telescope, were observing "background radiation" that seemed to come from all directions in the sky. It had a temperature of 3.5 +/- 1 K. Penzias and Wilson thought the noise was not real, but due to some flaw in their receiver. Bernard Burke, a radio astronomer from MIT, was visiting Bell Labs immediately after visiting Dicke at Princeton, some 30 miles away. Burke told Penzias and Wilson that Dicke was trying to build a telescope to observe the cosmic background radiation, and that it was predicted to have exactly the temperature of the "noise" that they were observing. They realized that they had discovered the fires of creation!
1989	NASA launches the Cosmic Background Explorer (COBE) satellite, especially designed to measure the spatial distribution and spectrum of the cosmic background radiation (CBR). COBE observations show that the spectrum is exactly as predicted by the Big Bang Theory. Moreover, COBE measures very slight (about 1 part in 100,000) spatial variations in the temperature of the background radiation. These variations show that the distribution of matter and radiation in the early universe is not absolutely smooth. They are a fundamental clue to how matter in the universe developed the structure that we observe today as clustering of galaxies.
1998	Today, we know the Hubble Constant to an accuracy of about +/-15% (H₀ = 65 +/- 8 km/s/Mpc). Only a few years ago, the uncertainty was a factor of two (H₀ = 50 - 100 km s^-1 Mpc^-1). There are more than a dozen experiments underway to measure the fluctuations of the CBR from the ground. Also, NASA plans to launch the Microwave Anisotropy Probe (MAP) satellite shortly after 2000, and the European Space Agency plans to launch a more powerful instrument, called PLANCK, a few years after that. By measuring the fluctuations of the CMB in exquisite detail, these experiments are expected determine the fundamental properties of the universe that we need to know to understand its origin and fate.

3. THE COSMOLOGICAL PRINCIPLE

In 1917, Einstein realized that his equations of space, time and matter might be used to describe the universe as a whole. To achieve a simple description of the universe, Einstein had to neglect all the detailed structure of the universe, such as the presence of stars and galaxies and relatively empty space in between. Instead, he assumed that the universe could be approximated as a space with uniform density of matter everywhere, where the density of matter would be the average of the density taken over some large dimension, say 100 million light years. We call this assumption of uniformity -- throughout all space, and in every direction -- the cosmological principle. Actually, Edwin Hubble had already obtained evidence in support of the cosmological principle when he observed that the number of distant galaxies was almost the same in every direction.

Is the assumption of a uniform density universe reasonable? Below is a picture of a large part of the sky, about 30 degrees across, showing almost a million galaxies out to a distance of about 2 billion light years. You can see that at this scale, there are more-or-less the same number of galaxies everywhere. You might want to contrast this picture with the all-sky map of The Nearest 15,000 Galaxies, which reached only to about 500 million light years. On that scale, the universe is not smooth at all.

We may conclude from this picture that Einstein's assumption of a uniform universe is OK if we want to describe the behavior of the universe on a large-scale average, where "large-scale" means over distances greater than a few hundred million light years.

4. COSMIC EXPANSION

Einstein's GTR is a theory of space, time, and gravity. In this theory, Einstein regards gravity as a manifestation of curvature of space and time. Think about a spherical surface, such as the Earth. The shortest distance between two points on the Earth's surface is a great circle (provided that you must travel close to the surface of the Earth, such as on an airplane). So, we may regard a great circle on a sphere as the analogue of a straight line on a plane. But great circles intersect. For example, if you travel from the North Pole to the South Pole by plane, the shortest route would be any meridian of longitude. No matter which direction you start out from the North Pole, if you fly straight ahead, you will eventually arrive at the South Pole. If two planes start out along two different meridians, they will get further and further apart; but after passing the equator they will converge again, finally meeting at the South Pole. If you didn't know that the Earth was round, you might think that there is some invisible force causing the planes to come together again. You might call it gravity.

It turns out that three-dimensional space can be curved too. If two light waves (or photons) travel out from a quasar in different directions, they may first get further apart, but then converge again. We may regard this convergence of light waves as resulting from gravity, perhaps the gravity due to the mass of an intervening cluster of galaxies (see gravitational lenses). But Einstein regarded this gravity not as a force, but as a curvature of space and time. To be sure, the curvature is caused by the presence of matter. Here are the key ideas of the GTR: (1) the force of gravity should be regarded as a curvature of space and time; (2) objects (and light) move along the analogues of great circles in this curved space time; and (3) the curvature of space and time results from the presence of matter.

To express these ideas exactly (for example, exactly how we describe a great circle in 4-dimensional space-time, and exactly what is the shape of curved space-time that results from the presence of matter) requires some fairly serious mathematics, which we won't go into here.

Actually, the easiest problem to solve using the GTR is that of the uniform universe. Einstein recognized immediately that if the universe contains matter, it must be curved. But if the universe is curved, all the matter must be in motion. In fact, according to Einstein's theory, the matter is not moving through space, the space itself is in motion. The universe must be either expanding or contracting. I demonstrated the idea of a moving space by representing galaxies as knots on a stretching rubber band, or dots on an inflating balloon. The knots or dots are moving apart from each other. But they are not moving through the space (they are fixed on the rubber band, or on the balloon). The apparent motion is due to the expansion of the space itself.

When Einstein realized that universe containing matter must be in motion, he couldn't believe his own theory! He thought that the universe must be unchanging in time, i.e., -- a universe with no motion, no beginning, and no end. This idea, that the universe is not only the same everywhere in space, but also in all time, is called the perfect cosmological principle. It wasn't based on any observation; it was just Einstein's preconception, or prejudice. And in fact, it's not right!

Therefore, instead of taking his solutions for the universe at face value, Einstein modified his general theory of relativity (GTR) by introducing a new term into his equations, which he called the cosmological constant. It was represented by the symbol L (Greek Lambda). It had the effect of a long-range repulsive force of space and time that could counteract the attractive force of gravity. With the right choice of L, the solutions of Einstein's modified equations would permit a universe consistent with the perfect cosmological principle.

But meanwhile, Alexander Friedmann, a mathematician in St. Petersburg, Russia, had solved Einstein's equations for the universe without the cosmological constant. These solutions are called Friedmann solutions, which are illustrated above. You can see that there are actually two distinct types of solutions for the universe. All solutions start with a singularity, in which the distance between any two galaxies in the universe is compressed into a single point (which implies that the entire universe is compressed to a single point!). One type of solution, called the closed universe, first expands, slows down, and then collapses again to a singularity. Then it might begin expanding again, in an endless succession of reincarnations, called the oscillating universe. (We're not actually sure that the universe will oscillate in this case. It may simply cease to exist after it collapses.) The other type of solution, called the open universe, expands forever. It has a definite beginning but no end. Actually, the diagram distinguishes between two types of open universes, a "very open universe", which expands forever, finally coasting at constant velocity, and an "open universe" which expands forever but is always decelerating.

Today, we believe that the Friedmann solutions accurately represent the past and future history of the universe. But we don't know yet whether the universe is open, very open, or closed. According to Friedmann's solutions of Einstein's equations, the answer to that question is determined by a quantity called W₀, which obeys the equation W₀ = r/r_cr, where r is the actual average density of matter in the universe and r_cr is the critical density of the universe, which is given by the equation

r_cr = 3H₀²/(8pG),

where H₀ is Hubble's constant and G is Newton's constant of gravity. Taking H₀ = 65 km s^-1 Mpc^-1 (the best estimate today), we find that the critical density corresponds to the mass equivalent of about 5 atoms per cubic meter. If W₀> 1 (if the actual density of the universe is greater than the critical density), the universe is closed (and will collapse again). But if W₀< 1 (the actual density of the universe is less than the critical density) or W₀= 1 (the actual density of the universe is exactly equal to the critical density), the universe is open (and will expand forever).

Actually, the question of whether the universe will expand forever or collapse again can be answered by a very simple argument that is familiar to anybody who has taken a course in physics. The key concept is called escape velocity. Escape velocity is the minimum velocity that an object must have in order to escape the force of gravity. For example, the escape velocity from Earth is about 11.2 km/s (see text, p. 49). If a rocket is launched straight upwards from Earth with velocity less than 11.2 km/s, it will fall back; but if it is launched with velocity greater than 11.2 km/s, it will escape the Earth's influence entirely and coast out into interplanetary space. Whether or not an object will escape from the influence of gravity is determined by two quantities: the amount of mass that attracts it back; and the speed of the object.

The escape velocity of any part of the universe is the minimum expansion velocity that it must have to escape the gravitational attraction of all the matter in that part of the universe. The speed of the universe is given by the Hubble constant (H₀). The amount of mass is given by the average density of matter (r). Those two quantities are all we need know to determine W₀ and, hence, whether the universe will expand forever or collapse again. The calculation is simple. You aren't required to know it, but you can find it here if you are interested: critical density.

We'll come back to the issue of whether the universe is open or closed in Section 6 of this lesson.

5. COSMIC HORIZON: THE END OF SPACE

Does the universe have a limit or is it infinite? People have been asking this question ever since they began to think about the universe. Amazingly, this question can be answered.

The key concept here is that of an event horizon. We already encountered this concept when we discussed black holes (see Lesson 8). The universe itself has an event horizon: it's the surface beyond which the galaxies (if they exist) are moving away from us faster than light. According to Einstein's theory of relativity, time (as measured by any kind of clock on a moving object) runs more slowly as perceived by us. The faster the object is moving away from us, the more time slows down. If an object moves away from us with the speed of light, time stops! But if there is no passage of time, there is no way to transmit any kind of information. We observe such an object in any conceivable way. We cannot know whether it exists.

The resolution of Olbers' paradox comes from a combination of the concepts of cosmic expansion, the horizon, and look-back time. The sky is not infinitely bright because the starlight from distant galaxies is redshifted so much that it is cool and invisible. In fact, we can see so far that we see radiation coming from a time before stars and galaxies even existed.

It's easy to estimate the distance of the event horizon of the universe. A galaxy at distance D is moving away from us with a velocity given by Hubble's Law:

V = H₀D.

If we set V = c = 300,000 km/s (the speed of light) and take H₀ = 65 km/s/Mpc, we find D = 4615 Mpc, or 15 billion light years. Hubble's Law says that galaxies beyond that distance are moving away from us at speeds greater than the speed of light, so we can't know whether or not they exist.

But I have oversimplified, in two ways. First, I have neglected the fact that the light we see from galaxies near the horizon left those galaxies a long time ago. We can't see galaxies at the horizon as they are today; we can only see them as they were when the light left them, billions of years ago. So, when we look toward the horizon of the universe, we are looking toward the very distant past. In fact, my above estimate of 15 billion light years is roughly equal to the age of the universe itself. So, when we look toward the edge of space we are also looking toward the beginning of time!

My second oversimplification was to neglect the fact that the expansion of the universe has slowed down. According to Friedmann's solutions, galaxies that are moving away from us at a given speed today were moving faster when the universe was younger.


Decelerating Universe	Coasting Universe

To understand the horizon of the universe better, consider the two figures above, which represent the motions of distant galaxies. In each case, the horizontal axis represents the position of the Milky Way. Distances are in light years and times in years. Therefore, something moving away from the Milky Way at the speed of light will be represented by a line with a positive (upward to the right) 45^o slope, while a light signal moving toward the Milky Way is represented by a yellow line with a negative 45^o slope.

The figure on the left represents a decelerating universe (W₀= 1). At the present time (= 1 on the horizontal axis), we can look back (along the yellow light-line) as far as the galaxy that moves according to the blue curve. But the galaxy represented by the red curve is moving away from us faster than light (its slope is greater than 45^o) at the time we might see it.* Therefore, it is beyond our event horizon today.

(*Be careful not to over-interpret these figures, which are schematic. For example, the figures suggest that you will see a galaxy near the event horizon as it was when the universe was roughly half its present age. But that is not correct. Because we perceive time running slower for a rapidly receding galaxy, that galaxy will actually be much younger than half the age of the universe. You can find a more accurate discussion and graphs of the properties of the cosmic horizon in Ned Wright's Cosmology Tutorial.)

But if we wait another 6 billion years or so, until the universe is 1.5 times its present age, the galaxy on the red curve would have slowed down enough that we could see it. Therefore, in a decelerating universe, the horizon of the universe encompasses more and more galaxies as cosmic time progresses.

The situation is different in the coasting universe (W₀< 1), represented by the graph on the right. In this case, the galaxies coast with constant velocity after an initial deceleration phase. The galaxy represented by the green curve will always moving away from us slower than light, so it will always remain within the horizon. The galaxy represented by the blue curve is just at the horizon at the present time, and will remain so in the future. The galaxy represented by the red curve is beyond the horizon now and will remain so in the future. Therefore, in a coasting universe, galaxies beyond the horizon will remain unknowable forever.

If a galaxy is unknowable now but knowable in some future time, can it be said to exist today? If it is unknowable forever, can it be said to exist at all? What is the meaning of the word exist? I'm only an astronomer and I'm getting out of my league here. These are questions of epistemology -- better ask your philosophy professor.

6. THE AGE OF THE UNIVERSE

There are two main ways to estimate the age of the universe.

Cosmic expansion age: Hubble's Law says that all galaxies are moving away from each other and it follows that they were closer together at early times. In fact, one can estimate the age of the universe from Hubble's Law as follows:

Hubble's Law, V = H₀D, says that the velocity, V, of a galaxy is proportional to its distance, D, from us. But the distance of a galaxy from us is its velocity times the time it has been moving: D = Vt. Putting this into Hubble's Law, we find V = H₀Vt, or t = 1/H₀. Taking a Hubble constant H₀ = 65 km/s/Mpc, we find t = 15 billion years. If H₀ is smaller, t will be larger, and conversely.

But this argument is oversimplified, because it is based on the assumption that the universe has always been expanding at the same rate. In fact, the universe certainly has slowed down since its early days, and it may still be slowing down. The formula D = Vt is true only if the velocity has always been constant. If the velocity of a distant galaxy was once greater than it is today, the distance will be greater than implied by the above formula. In fact, for a decelerating universe with density exactly equal to the critical density (W₀= 1), the distance of a given galaxy is given by D = (3/2)Vt, in which case we find t = 2/3H₀. This formula gives t = 10 billion years if H₀ = 65 km/s/Mpc.

Globular cluster ages: Certainly, the universe can't be any older than the stars in it. As far as we know, the globular clusters are the oldest star systems in the universe; we think they were formed when the universe was less than 1/10 its present age. Therefore, the age of the universe ought to be roughly equal to the age of the globular clusters. We have already described how to determine the ages of globular clusters from the main sequence turnoff (see Lesson 6). The best estimate today is 11.5 +/- 1.3 billion years, as you can see in Ages of Globular Clusters.

These constraints on the age of the universe are summarized in the above graph. The black horizontal line represents the best estimate of the age of the universe from globular clusters and the red horizontal lines represent the upper and lower bounds of uncertainty of the globular cluster ages. Similarly, the black curve represents the age as determined from the Hubble expansion (with H₀ = 65 km/s/Mpc), while the red curves represent the upper and lower bounds of the expansion ages. These two measurements of the age of the universe are consistent if W ₀ and H₀ are in the green range. Thus, we can see that in a relatively low density universe (W ₀ = 0.1), the only permissible age is about 13 billion years; while in a relatively high density universe (W ₀ = 1), the permissible range of age is between 10 and 11 billion years.

7. THE BIG BANG

George Gamow's original theory: Shortly after World War II, Russian physicist George Gamow, now working at George Washington University in Washington, DC, began to think about what the universe might be like during its earliest moments. He realized that the Friedmann solutions implied that the universe had infinite density when the expansion began, some 10 billion years ago, and that if so, the primordial matter in the early universe (less than a minute old!) would be as dense as the matter in the interiors of stars.

Gamow was one of the pioneers in understanding the theory of nuclear fusion, and so he was interested in the nuclear reactions that might occur under such circumstances. He assumed that the primordial matter in the universe, which he called "Ylem", was composed of pure neutrons.

The network of reactions begins with the decay of a neutron into a proton, an electron, and a neutrino*:

n ® p + e + u , (1)

*Strictly speaking, the reaction produces an antineutrino, but I will ignore the distinction between neutrinos and antineutrinos, which is not critical to the arguments that follow.

which takes place with a half-life of 10.2 minutes (half of the original neutrons will decay in that time). It is shortly followed the combination of a proton and a neutron to form a deuterium nucleus (a form of heavy hydrogen composed of a neutron and proton bonded together) and a gamma ray photon:

p + n ® d + g. (2)

Both of these reactions release energy and will heat the gas to hundreds of millions of degrees. At such temperatures, the deuterium nuclei will undergo further nuclear reactions with neutrons and protons such as:

d + p ® ³He + g (3), ³He + n ® ⁴He + g (4),

d + n ® ³H + g (5), and ³H + p ® ⁴He + g (6).

The net result of these reactions will be a universe of pure helium. This result is grossly in conflict with astronomical observations, which show that the matter in the universe is 90% hydrogen.

Then Gamow had a brilliant insight: he realized that if the universe was already filled with gamma rays, the radiation could prevent the buildup of heavy elements by driving reaction (2) in the reverse direction:

d + g ® p + n. (7)

If the density of gamma rays in the early universe is sufficiently high, reaction (7) will destroy the deuterium nuclei before they hit a proton and undergo reaction (3). Gamow could calculate that a sufficiently high density of gamma rays meant that the universe must be filled with blackbody radiation that had temperature greater than 10⁹ K until 20 minutes A.B.E. (after the beginning of the expansion). After 20 minutes, 3/4 of the neutrons would have decayed into protons. If all the remaining neutrons formed helium according to reactions (2 - 4), the resulting mass fraction of helium in the universe would be about 25%, which is roughly the observed value.

As the universe expands, the radiation cools off. (You can regard this cooling as a consequence of the redshift of the gamma ray photons due to the cosmic expansion.) Gamow calculated that if the radiation had a temperature of 10⁹ K when it was 20 minutes old, it would have a temperature of about 25 K now.

The modern theory of the hot big bang: In 1950, a Japanese astrophysicist, Chushiro Hayashi, pointed out that one of Gamow's basic assumptions, that the universe was originally filled with neutrons and gamma rays, could not be correct. If the radiation had a temperature of 10⁹ K when the universe was 20 minutes old, it would have to be much hotter when the universe was much younger, say 1 second A.B.E. But if the radiation is hotter than 10¹⁰ K, the gamma rays will be sufficiently energetic to produce electrons and positrons (anti-electrons) by the reaction:

g + g ® e⁺ + e^-. (8)

Thus, such a universe must be filled, not only with neutrons and gamma rays, but also with electrons and positrons. But then, the positrons will react with the neutrons to produce protons and neutrinos:

e⁺ + n ® p + u (9)

and the electrons will react with the protons to produce neutrons and neutrinos:

e^- + p ® n + u. (10)

Because reactions (8 - 10) must occur, it's impossible for the early universe to be filled with only neutrons and gamma rays. There will certainly be plenty of electrons, positrons, and neutrinos as well, and these reactions (as well as the reverse reactions) will cause the neutrons to switch back and forth rapidly to protons.

It is reactions (9) and (10) and their reverse reactions, not the decay of neutrons (reaction 1), that determine the helium abundance of the universe. At about 1 second A.B.E., the radiation temperature drops below 10 billion degrees and reactions (9) and (10) become too slow to change neutrons back and forth into protons. At this time, there are about three times as many protons as neutrons. As the universe continues to expand, the radiation cools below a billion degrees and these neutrons can combine with protons to form deuterium and helium according to reactions (2 - 6). By three minutes A.B.E., these reactions have run to completion and the universe consists of about 75% hydrogen and 25% helium by mass.

After Hayashi pointed out the flaw in Gamow's theory, several other astrophysicists independently revised the theory of the hot big bang to include these reactions. (It seems that they were mostly unaware of each other's work.) The most important consequence was that the revised theory predicted that the left-over radiation from the cosmic fireball would now have a temperature of about 3 K, almost 10 times lower than Gamow's original prediction of 25 K.

You can find a very nice summary of these reactions, including graphics, here: Formation of the elements in the early universe.

Cosmic deuterium: As we described, by 3 minutes A.B.E., the nuclear reactions (3 - 6) have run almost to completion and the universe consists of about 75% hydrogen and 25% helium. But traces of deuterium (and other light elements) should remain, and this fact provides an extremely important test of the theory of the hot big bang universe. The fraction of deuterium that remains is sensitive to the density of neutrons and protons in the universe before 3 minutes A.B.E. If the density is high, reactions (3 - 6) are more complete and there is less residual deuterium; if the density is low, there is more deuterium. The ratio of deuterium/hydrogen atoms observed in the universe today is between 10^-4 and 10^-5. We believe that these deuterium atoms were produced in the big bang. The observed ratio is consistent with the theory of the hot big bang universe if the average density of ordinary matter (hydrogen, helium, and other elements -- we call this baryonic matter) is between 1 and 1.6% of the critical density. See Big Bang Nucleosynthesis.

The main difference between the big bang and a supernova explosion: as in the big bang, fusion reactions occur in stars when they burn and finally explode as a supernova. But a supernova produces many heavy elements, such as oxygen, iron, and uranium, while the big bang produces only hydrogen and helium, plus traces of deuterium and lithium. Why are the results of these explosions so different?

The reason is that the physical conditions are very different during the two explosions. When the temperature of an exploding star is a billion degrees, the density is roughly 10⁸ g/cm³. At such densities and temperatures, nuclear reactions can create all the known elements. But when the temperature of the universe is a billion degrees, the density is only about ten times that of air. At such low densities, the triple-alpha reaction that is required to convert helium into carbon and other heavy elements is too slow to be effective. The buildup of heavy elements stops at helium.

8. THE COSMIC MICROWAVE BACKGROUND (CMB)

Gamow's triumph: In Section 2 of this lesson you can find a chronicle of the discovery of the cosmic fireball radiation. It is surely one of the most fascinating stories in the history of science. Be sure to review it.

As we have described, George Gamow's theory of the hot big bang was wrong. Gamow overlooked the most important reactions that determine the formation of elements in the early universe and his prediction of the temperature of the cosmic fireball radiation was off by a factor of almost 10. Yet we attribute the theory of the big bang universe to Gamow, and rightly so. He was the first scientist who dared to try to explain what the universe was like when it was only minutes old, and he realized that it must be filled with gamma rays in order to prevent nuclear reactions from turning all the matter into heavy elements. Gamow led the way by asking the right questions. After that, it was inevitable that other scientists would check his theory and correct the errors. And several did, apparently without knowing of each other's work.

George Gamow came to the University of Colorado from Washington University in 1956. He was a great popularizer of science as well as a great scientist. During the 1950s he wrote many books about astronomy, mathematics, and other branches of science intended for students at every level, from elementary to college. I was inspired by Gamow's books to study astronomy, and his example is one of the reasons that I am taking the trouble to write this on-line textbook.

I had the privilege of meeting Gamow only once. It was in 1966, at a famous conference in New York, where Penzias and Wilson described their discovery of the CMB. Gamow was asked to comment on their presentation. He said that he had thought a long time ago that the universe must have had a temperature of billions of degrees during its first few minutes in order to prevent all the hydrogen from being consumed, and that it followed that the universe must be filled with microwave radiation now. Then, and I can almost remember his exact words: "Now these guys, Penzias and Wilson, have found the radiation. So I guess I was right. Great! They are bright young fellows. I like these guys!"

Thermal history of the universe: According to the big bang theory, the universe at an age of 1 second A.B.E. is filled with radiation at a temperature of about 10¹⁰ (10 billion) K. As the universe expands, this radiation (and the matter) will cool down. By 300,000 years A.B.E., the cosmic temperature will be 3700 K, roughly the temperature of the photosphere of a red giant star.

A very important transition in the history of the universe occurs at this time, which we call the recombination epoch. Before this time, almost all the hydrogen atoms in the universe are ionized, so that the cosmic gas consists of bare protons and electrons, plus helium atoms. In such a gas, just as in the Sun's interior, a photon cannot travel far before it scatters off a free electron in the gas. The result of this diffusion is that the universe is opaque: we cannot tell where the photons were originally produced. But after the recombination epoch, the temperature is low enough that the electrons can attach to protons and remain bound to form neutral hydrogen atoms.

The photons of the cosmic background radiation, now consisting mainly of red and infrared photons, do not interact with the neutral hydrogen and helium atoms. At the recombination epoch, the universe becomes transparent. The photons that we detect in the microwave background today have traveled freely through cosmic space since the universe was only 300,000 years old.

In a very real sense, the universe before the recombination epoch was like the interior of the Sun: hot and opaque. The universe after the recombination epoch is more like interstellar space: cool and transparent. Because of this analogy, we speak of the place where the radiation last interacted with matter as the cosmic photosphere.

Spectrum: In 1965, Penzias and Wilson measured a background radiation temperature of 3.5 +/- 1.0 K. At that time many scientists were not convinced that they were really seeing the radiation from the big bang. A crucial test would be to see whether the background radiation actually had the spectrum of blackbody radiation that was predicted by the theory. That test required observations of the radiation at wavelengths shorter than 2 millimeters, which could only be done from space. (The Earth's atmosphere is too bright to make such measurements from the ground.)

The issue was settled by observations with the Cosmic Background Explorer (COBE) satellite, launched in 1989. COBE observations showed that the background radiation spectrum at wavelengths less than 3 mm fit the theoretical blackbody curve to an accuracy of better than one part in 1000.

Actually, the temperature of the microwave background had already been measured in 1941 by Andrew McKellar indirectly through observations of optical absorption lines due to the cyanogen (CN) molecule in interstellar clouds. Each CN molecule acts as a tiny antenna that is tuned to absorb radiation at wavelengths of 2.64 and 1.32 mm. One can infer the intensity of this radiation by measuring the relative intensities of optical absorption lines due to these CN molecules. But in 1941 there was no theory of the big bang radiation, so few people paid any attention to the observation, and nobody recognized its significance until 25 years later.

The figure below summarizes the observations of the microwave background radiation. You can see that the temperature of the background radiation, originally measured to be 3.5 +/- 1.0 K, is now known to be 2.728 K, with an accuracy better than one part in 1000.

Spectrum of the cosmic microwave background. The various modern observations fit exactly on the violet curve, which represents the radiation from a perfect blackbody with a temperature of 2.728 K. The blue bar represents the original 1965 measurement by Penzias and Wilson. The green dots represent the 1941 measurement by McKellar.

Isotropy: the big bang theory not only predicts that the microwave background radiation should have a blackbody spectrum, it also predicts that the radiation should be isotropic -- i.e., that it should have the same intensity in every direction. We shall see that measurements of the angular distribution of the microwave background have become powerful tools for understanding the origin of structure in the universe. The figure below shows the results from COBE.

	Top: light blue to red represents an increase in radiation temperature of a few parts in 1000. The radiation is slightly warmer toward the upper right because the solar system is moving in that direction with a velocity of about 600 km/s. This variation is called the "dipole asymmetry."
	Middle: the dipole asymmetry has been subtracted and the scale has been changed so that light blue to red now represents an increase in radiation temperature of only a few parts in 100,000. The dominant feature is the glow of dust from the Milky Way.
	Bottom: The radiation from the Milky Way has been subtracted. The residual fluctuations represent the temperature fluctuations of the "cosmic photosphere" when the universe was about 300,000 years old.
The cosmic microwave background as observed by the COBE satellite

We can draw two basic conclusions from these observations:

The temperature of the cosmic photosphere is extremely smooth. (Unlike the Sun's photosphere, where the temperature ranges from about 6000 K to 4800 K in sunspots.)
The temperature is not perfectly smooth: it varies by about 1 part in 100,000.

Both of these conclusions have profound implications, as we shall now discuss.

9. COSMIC INFLATION: THE THEORY OF EVERYTHING

The fact that the temperature of the universe is almost perfectly uniform presents a most important puzzle that has its origins in the concept of the event horizon of the universe. As we described above in Section 5 of this lesson, more and more galaxies come within the cosmic event horizon as the universe expands and decelerates. That result implies that the number of galaxies within the cosmic horizon of any part of the early universe was much smaller than the number of galaxies within the observable universe today. An observer sitting on a galaxy in the early universe would have no way of knowing the existence of a galaxy beyond his horizon. (To be sure, those galaxies existed, because we can see them today.)

We can calculate the distance to the horizon of any piece of the universe at the recombination epoch, when it was 300,000 years old. Likewise, we can calculate how big such a piece should appear to us today. The answer is: the angular diameter should be about 1 - 1.6^o-- about 2 - 3 times the angular diameter of the Sun.

Here's the puzzle: since there is no way that any part of the universe can know about the existence of any other part of the universe beyond its horizon, why does the cosmic photosphere have nearly uniform temperature? Scientists like to think they can explain the universe by physical mechanisms that obey the laws of nature. But one of the most important laws of nature is that no signal can travel faster than light. That means that there is no possible physical mechanism that can cause parts of the universe beyond each other's horizons to have the same temperature. That means that there is no reason for the temperature of the cosmic photosphere to be uniform over angles greater than 1.6^o.

One explanation might be that the Creator just made the universe that way. But scientists are never satisfied with such an explanation. Rather than regard a natural phenomenon as the whim of the Creator, we prefer to regard it as a consequence of the laws of nature. If you like, we prefer to regard the Creator as the giver of the laws, so that our job is to understand those laws and all their natural consequences. So, rather than just regard the smoothness of the microwave background as God-given, we would prefer to find a mechanism that would account for the smoothness of the microwave background.

Today, the most popular hypothesis to account for this smoothness is called the theory of cosmic inflation. The idea is illustrated in the graphs below. The graph on the left is identical to the one we used above in section 5 to illustrate how the event horizon can expand to include more and more galaxies in a decelerating universe. But now we are considering times before the galaxies formed, so we'll talk about atoms in the cosmic gas rather than galaxies. The graph on the right illustrates how the situation changes if the expansion of the universe accelerates. Here you see that when the age of the universe is 0.5 (we'll talk about the units of time in a moment), we can see a light beam (the diagonal yellow line) coming from either the green, blue, or red atoms, because all of these atoms are expanding at less than the speed of light (their slopes are less than 45^o). But when the age of the universe is 1, we can't see the red atom because it is now travelling faster than the speed of light with respect to us; and when the age is 1.5, the green atom is also just at the horizon.


Decelerating Universe	Accelerating Universe

So, the situation is exactly the opposite of that in the decelerating universe: in an accelerating universe, atoms that were once all within each others' horizons pick up so much speed that they move out of sight of each other.

That's the trick of inflation: if, at some early time, the universe was accelerating, not decelerating, all the atoms could have been within sight of each other. If so, information (such as photons) could propagate from one atom to another and back, and all parts of the universe would tend to come to the same temperature.

But what kind of force could make the universe accelerate? It would have to push things apart, unlike gravity, which always attracts. The strongest repulsive force we know is the nuclear force, which becomes repulsive when neutrons and protons get too close and helps to prevent atomic nuclei (and neutron stars) from collapsing. There is only one way (without violating the laws of nature) that we can imagine the universe to be controlled by a repulsive force strong enough to counter gravity. We must think about the universe when it was so young and that it had density greater than that of an atomic nucleus. Then, repulsive forces such as the nuclear force might be strong enough to counter gravity.

In fact, the most popular theory of inflation suggests that the repulsive force did its main work even earlier than that, at a time of about 10^-34 seconds A.B.E. At that time the energy density of the universe was so high that three of the four known forces of nature (electromagnetism, the weak nuclear force, and the strong nuclear force) should all merge into one primitive unified force, according to a theory of matter called the Grand Unified Theory (GUT).

So, the time scale on the graph above illustrating the accelerating universe should be in units of about 10^-34 seconds! Before that time, all atoms (more precisely, subatomic particles) in the present and future universe were in contact, so the universe could reach a more-or-less uniform temperature. After that time, the universe had accelerated to such a speed that the horizon of any piece of the universe had a size far smaller than an atomic nucleus. Then, the universe began to decelerate and all these little horizons began to grow, so that more and more pieces of the universe came into contact with each other. But now there is a reason that these disconnected pieces of the universe would all find themselves having the same temperature when they come into contact: they all were in contact before the epoch of inflation.

Is this theory correct? We don't have a shred of evidence to prove it -- unless you regard as evidence the fact that the cosmic microwave background is almost uniform. Elementary particle physicists think that the GUT theory will provide the necessary repulsive force, but they do not yet have atom smasher machines that are energetic enough to test these theories. But it's fun to think about the theory of inflation, and even more fun to think that such a theory might someday be tested experimentally.

To summarize the theory of inflation: at a time earlier than 10^-34 seconds A.B.E., the entire universe was far smaller than a proton. It wasn't expanding and it contained everything, which was almost nothing. Cosmologists call this early state the false vacuum. In the false vacuum, space-time itself was like some kind of super-dynamite. When it exploded, the sudden release of energy created all the radiation and the matter in the universe and also gave it a kick that set the whole shebang into expansion. The ultimate free lunch!

This whole scenario reminds me of an old song:

Freedom's just another word for nothin left to lose
Nothin ain't worth nothin, but it's free.
(From Me and Bobbie McGee, by Kris Kristofferson).

10. THE FORMATION OF STRUCTURE

We now turn to the second major conclusion of the COBE observations: the Cosmic Microwave Background (CMB) is not absolutely smooth; its temperature varies ever so slightly (by about 1 part in 100,000). What does this variation imply?

The issue here is the evolution of structure in the universe. We see that the CMB is very smooth, and that implies that the matter and radiation in the universe had almost exactly the same density and temperature everywhere at the epoch of recombination (300,000 years A.B.E.). But we see that the universe today is highly structured, with superclusters of galaxies defining the surfaces of giant voids, typically a few hundred million light years in diameter (see Galaxy Clusters and Large Scale Structure). How did the distribution of matter in the universe change from almost perfectly smooth to highly structured?

Astrophysicists believe that the variations in the CMB are manifestations of very slight fluctuations in density of matter in the early universe. After recombination, gravity attracts the matter toward the regions of slightly elevated density, and this process becomes amplified as these regions become denser. We call this process gravitational instability. (In 1684AD, Isaac Newton pointed out that this would happen.) We suspect that this instability will amplify the almost imperceptible fluctuations that we see in the early universe into the giant structures (voids and superclusters) that we see in the universe today.

Because the universe has expanded by a factor of roughly 1,300 since the epoch of recombination, the giant voids seen in today's universe would have been roughly 1,300 times smaller at recombination than they are today. In fact, if we could see such voids in the CMB, they would have typical angular diameters of about 1^o. Note that this angular diameter is nearly the same as the angular diameter of the cosmic horizon at the recombination epoch (see above). That means: the mass within the cosmic horizon at the epoch of recombination is roughly equal to the mass of a supercluster of galaxies today. Cosmologists think that this coincidence is no accident, because that the density fluctuations at the epoch of recombination will naturally have their greatest amplitude at a scale size corresponding to the cosmic horizon.

The trick is to show that gravitational instability can cause these tiny initial fluctuations to develop into clusters and superclusters of galaxies with a spatial and size distribution similar to that seen in the universe today. To demonstrate that, cosmologists simulate the development of these instabilities with supercomputers. You can find several spectacular MPEG movies illustrating the results of such simulations at LANL simulations of galaxy formation and the Grand Challenge Cosmology Consortium. The short answer is: they do!

Left: Results of a simulation of the distribution of matter in a block of the universe 500 million light years on a side. The calculation starts from very slight initial density fluctuations such as those seen in the CMB. As the universe expands, the fluctuations grow in amplitude until they resemble the density structure seen in the universe today. For further details and movies, see Computing the Universe from the National Center for Supercomputing Applications.

But these calculations would not agree with the observations unless the universe was filled with dark matter. The gravity due to the visible matter alone would be far too weak to cause the initial density fluctuations to condense into the galaxies and clusters that we see today.

According to these simulations, galaxies and clusters of galaxies began forming at redshifts in the range 3 - 4, when the universe was 2 - 3 billion years old. Observations appear to support this result. If galaxies and quasars were common at earlier times (say, with redshifts greater than 4), we should have been able to find many of them with the Hubble Space telescope and large ground-based telescopes; but we have not. We think that we are now looking deep enough that we can see the universe as it was before most galaxies were born. Moreover, the galaxies that we do see with redshifts in the range 2 - 4 have different shapes than the ones we see today. They may be newborn galaxies -- see Galaxies: snapshots in time.

The cosmic microwave background revisited: Thanks to such calculations, this story for the origin of structure in the universe is beginning to look very plausible. But the theory makes one crucial assumption that has yet to be confirmed. Do the density fluctuations at the epoch of recombination really have their greatest amplitude at angular sizes 1 - 2^o (the horizon size)? The COBE satellite saw fluctuations in the CMB, but its telescope was too small to resolve angular sizes less than about 7^o. (Why? See Lesson 2.)

In late 2000, NASA will launch the Microwave Anisotropy Probe (MAP) satellite. MAP will make an all-sky map of the sky with angular resolution of 0.3^o, sufficiently fine to measure precisely the distribution of scale sizes of fluctuations of the CMB radiation. (Click here to see a comparison of what we expect to see with MAP and what we have seen with COBE.)

In fact, cosmologists think that the results from MAP will tell us all the fundamental numbers that determine the evolution of the universe: the closure parameter, W₀; the densities of ordinary (baryonic) and dark matter; and the cosmological constant, L*. (*You might say: "Wait a minute! I thought you said that the cosmological constant was Einstein's biggest blunder. Why bring it back into the picture?" Well, we may have no choice. See below.)

Here are two excellent sites where you can review the key concepts of the expanding universe and especially the significance of observations of the CMB:

Microwave Anisotropy Probe; and

An Introduction to the Cosmic Microwave Background by Wayne Hu.

If you want to go deeper into the subject of the CMB, try some of the other buttons on the bottom bar of Wayne Hu's page.

11. SUMMARY

The above picture gives a quick overview of the history of the universe as we perceive it today. We believe that the entire universe all started with a big bang. The bang may have been launched by a process called cosmic inflation, a theory that was invented to explain the cosmological principle, which states the observed fact that the universe is almost the same everywhere, on average.

In 1917, Einstein used this cosmological principle and his theory of general relativity to make a mathematical theory for the universe. His equations said that the universe must be in motion. Since Einstein couldn't believe that, he introduced a new term, the cosmological constant, into his equations. This term acted as a repulsive force and could be set to balance the attractive force of gravity so that the universe was static and eternal.

A decade later, Edwin Hubble discovered that the more distant a galaxy is from us, the faster it is moving away from us. Hubble's Law was consistent with Alexandre Friedmann's solutions of Einstein's original equations without the cosmological constant. Hubble's Law implies that the universe all started with an explosion.

The behavior of Friedmann's solutions of Einstein's equations is determined by a quantity called the closure parameter W₀ = r/r_cr, where r is the average density of matter in the universe and r_cr is the critical density, which has a value equivalent to the mass of about 5 hydrogen atoms per cubic meter. If W₀ > 1 (i.e., r > r _cr), the universe will collapse again. But if W₀ < 1, the universe will expand forever. Most of the matter in the universe is dark matter.

According to Friedmann's solutions, the present age of the universe depends on the Hubble constant, H₀, and also on the value of W₀. Taking our best estimates of these numbers today, H₀ = 65 +/- 8 km/s/Mpc and W₀ = 0.2, we find that the universe has an age of about 12 - 13 billion years. This estimate is consistent with the ages of the oldest known star clusters (the globular clusters).

In 1948, George Gamow published a theory (with Alpher and Bethe) to describe the universe as it was during its first few minutes. Gamow realized that the universe at that time must be filled with radiation at temperature of billions of degrees; otherwise nuclear reactions would convert all the hydrogen in the universe to helium and other heavy elements, in contradiction with observations. Gamow also realized that this radiation would cool as the universe expanded. He estimated that the temperature of the radiation today would be about 25 K.

C. Hayashi pointed out that Gamow's original theory was flawed. Several other scientists corrected these flaws and showed that the temperature of the radiation today should be about 2.5 K in order to account for the observed abundance ratio of helium to hydrogen.

In 1965, Penzias and Wilson discovered the Cosmic Microwave Background (CMB) radiation. They found that it had a temperature of 3.5 +/- 1 K everywhere in the sky. 25 years later, observations with the Cosmic Background Explorer (COBE) satellite showed that this radiation had a blackbody spectrum (temperature = 2.728 K) and was almost perfectly isotropic. But not quite: COBE found very slight fluctuations in the CMB temperature.

When the universe was about 300,000 years old (the recombination epoch), the cosmic gas became neutral. Then gravitational instability caused the very slight density fluctuations to begin to collapse. By the time the universe was 2 - 3 billion years old, the collapse had proceeded to the point that galaxies and clusters of galaxies were forming. With modern telescopes, we can see galaxies and clusters in the process of formation. The distribution of galaxies and clusters in the universe today is consistent with supercomputer calculations of the development of structure in the universe that start with tiny density fluctuation as indicated by the microwave background.

Here's a good summary: The Hot Big Bang Model from Cambridge University.

12. MYSTERIES

I have summarized the standard thinking about the universe today. But I don't want to leave you with the impression that I am confident that this story is all told, or even that it will hold up. If we end our discussion with questions rather than answers, you will leave this course with a more realistic impression of the actual state of cosmology today. Here are some of the big ones:

What will be the fate of the universe?
What is the dark matter?
Is there a cosmological constant?
Is the theory of inflation correct?
What, if any, of this should we believe?

The Fate of the Universe

Fire And Ice

Some say the world will end in fire,
Some say in ice.
From what I've tasted of desire
I hold with those who favor fire.
But if I had to perish twice,
I think I know enough of hate
To say that for destruction ice
Is also great
And would suffice.

Robert Frost (1916)

The Friedmann models say that if the closure parameter W₀ > 1, the universe will collapse again: it will end in fire. If this happens, it will be a long time from now -- perhaps 50 - 100 billion years. Our descendants, if they exist then, will first see the nearby clusters of galaxies stop expanding from us and begin to fall back. The microwave background will begin to warm up. Later, they will see the more distant galaxies turn around. When the final collapse occurs, all the galaxies will crash together and the microwave background will heat up to billions of degrees again: the big crunch.

Shiva, the creator and destroyer: will his dance go on forever? Will the universe rebound into another cycle of expansion? If so, will its next reincarnation be similar to this one, or perhaps something entirely different? Or will it just collapse out of existence: no space, no time, no nothing? We can't answer these questions. As with the very early universe, we don't know how space, time, matter, and energy behave at such high densities.

But today, we think that the closure parameter W₀ = 0.2 +/- 0.1, which implies that the universe will expand forever -- if the Friedmann models are correct. If so, we can describe the fate of the universe with some confidence: it will end in ice. As it continues to expand, the clusters of galaxies will get further and further apart. The universe is much less active today than it was several billion years ago, and this fading will continue. The galaxies will slowly deplete their interstellar gas and will collide less often. Star formation will slow down and eventually cease. After hundreds of billions of years, most galaxies will contain only faint red dwarf stars.

But do we really know the value of W₀ that accurately? It depends on the density of dark matter. We can infer the density of dark matter around galaxies and clusters of galaxies by analyzing motions and gravitational lensing. It's not enough to stop the expansion. But how much dark matter exists in the giant voids between the clusters of galaxies? Could there be enough there? Today, most cosmologists think not. But just a few years ago, most thought that W₀ = 1. When things are changing this fast, perhaps it's a good idea to regard today's most popular idea with a bit of skepticism.

In a few years, the MAP satellite should measure the value of W₀ very accurately -- if you can believe the current models for the fluctuations of the CMB.

What is the dark matter?

It should also give you pause that the fate of the universe depends on stuff we have never seen. The only reason we know it's there is that we can see the effects of its gravity. People have spent a lot of money and effort to build ultra-sensitive detectors that might detect the dark matter, but no luck so far. Better review dark matter. Here's a good place: Dark matter.

Is there a cosmological constant?

Einstein called the cosmological constant his greatest blunder. Why bring it up again? Mainly, because sometimes we encounter observations that appear utterly inconsistent with the big bang model of the universe. But if the cosmological constant is included in Einstein's equations, the solutions allow a much greater variety of possible models for the cosmic expansion than the Friedmann solutions.

Just a few years ago, it seemed that there was a fundamental contradiction between different measures of the age of the universe. At that time, the Hubble constant seemed to be in the range 75 - 100 km/s/Mpc, implying a universe with age less than 10 billion years today. Moreover, the best estimate of the ages of the globular clusters was about 16 billion years. But you can't have a universe younger than the stars in it! That would be a scientific crisis. But with a cosmological constant, you could have a universe older than 1/H₀, and the crisis would be resolved.

Cosmologists are loath to include a cosmological constant in their equations. It converts a simple set of solutions (the Friedmann models) into a much messier set. They would like the universe to be simple. But if forced to choose between including a cosmological constant or giving up the theory of the expanding universe, they'll include it.

Recently, that crisis seems to have abated. The value of the Hubble constant has come down, and so have the estimates of the ages of globular clusters. Now, it seems that there is no fundamental contradiction if the universe has an age of 12 - 13 billion years. So we can do without a cosmological constant. Right?

Maybe not! Now there's new trouble. Recent observations of distant supernovae by two different groups seem to suggest that the expansion of the universe is accelerating, not decelerating. (See To Infinity and Beyond.) The only way to have an accelerating universe today is to have some kind of long-range repulsion in the universe that overcomes gravity. That's exactly what a cosmological constant represents.

Is the theory of inflation correct?

I don't know. What's worse, I don't know of any experiments or observations that can be done to test the theory. It's an interesting idea. Perhaps someday somebody will find a way.

What, if any, of this should we believe?

You can believe anything you like! If you remember only one lesson from this course, I hope it is this: Science is not about belief; it's about exploration. We guess where we are, and then we make observations to confirm our guesses. If all measurements are consistent, we proceed further into the unknown. If not, we try harder to figure out where we are. One thing that scientists do believe is that we will eventually arrive at some reasonable approximation to the truth about nature if we simply keep trying. But as soon as we understand something, it will be a path to a new and deeper puzzle.

I'll end this course by giving you my own perspective on cosmology today: I think the evidence that the universe started from a hot big bang is pretty convincing. I am also impressed by the chain of logic that takes us from the observed fluctuations of the microwave background to the large-scale distribution of galaxies and clusters today. There's still a lot of uncertainty in these observations, though.

Mainly, I'm impressed by what we stand to learn within the next few years. The MAP satellite will produce much more precise measurements of the fluctuations of the CMB than we have today; and ground-based programs such as the Sloan Digital Sky Survey will provide much more detailed and extensive maps of the distribution of galaxies in the universe. Likewise, the Hubble Space Telescope and several new 8- to 10-meter telescopes will give us a much better view of the very distant universe, at a time when the galaxies and clusters first formed; and powerful new X-ray telescopes such as AXAF and XMM will give us a much better picture of the distribution of the hot gas between the galaxies.

Taken together, these new observations will provide much more rigorous tests of our present picture of the universe. Will the present picture hold up under such scrutiny? I don't know. If history is any guide, there will be some surprises. We'll have a bit of a mess on our hands. That's what makes science fun!

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