The Scale of the Universe

Several hundred years ago, a number of astronomers thought a little more deeply about this seemingly trivial question and concluded that it wasn’t trivial at all. In fact, given certain assumptions about the nature of the universe in which we live, it shouldn't be dark at night—just the opposite, it ought to be quite bright—as bright as what we would see if we were living on the surface of the Sun! They concluded that the night sky ought to be ablaze in glory and the Earth along with it.

This conclusion lies at the end of a logical path down which you and I will proceed. The night sky obviously does not look as bright as the surface of the Sun seen by an observer unfortunate enough to be seated upon it. But that should be the case, so we have a paradox on our hands and its resolution can be found upon a close examination of the premises upon which it is based. Heinrich Olbers popularized the paradox back in 1823 and now it bears his name—Olbers’ Paradox. Kepler seems to have been aware of it back in the early 1600’s and Edmond Halley, of Halley’s Comet fame, discussed it in a lecture he gave to the British Royal Society in 1721. Even Edgar Allen Po was aware of it and it served as the basis of some of his writing. The premises leading to the paradox are as follows—

· First, assume that stars are the objects that mostly light up the night sky. Let’s consider them to be spread more or less uniformly throughout the universe on some suitably large scale.^{^[1]} Clearly, even though stars are concentrated in clumps, like galaxies, clusters and superclusters of galaxies, we can go to a large enough scale where the number of stars we see when looking along any particular direction in space is just what we would see when looking along any other, i.e., the distribution of stars is more or less the same in all directions and at all distances.

· Second, assume that the universe has forever been the way it is now and that it will be the way it is in the future, i.e., it is not changing or evolving with the passage of time. Individual stars are born and eventually they die, but new ones take their place. Stars might move around in galaxies and galaxies might move around in clusters, but overall, the universe as a whole is unchanging with time.

· Finally, assume that the universe is infinite in extent—it has no boundaries—it continues on and on forever in all directions.

Taken together, we are assuming that the universe, on a large enough scale, is isotropic and homogeneous in space and unchanging in time. One place in the universe looks more or less like any other place and one time in the universe looks more or less like any other time. Now, let’s see what these premises imply what we should see when we look around the sky late at night.

Consider any large, imaginary, spherical shell of radius R and of thickness ΔR centered on the Earth (Figure 2). This shell will contain a certain number of stars. We can calculate the light that we see on Earth produced by the stars within this shell. It’s just equal to the number of stars within the shell times the average brightness of a star. Now consider another shell of the same thickness ΔR but twice as far from the Earth, at a radius 2R. Each star in this shell appears to be 4 times dimmer than it would be if it were in the first shell.^{^[2]} But there are 4 times as many stars in this second shell.^{^[3]} Therefore, the stars in this shell contribute the same amount of light to an observer on Earth as do the stars in the first. Uh oh! You can see where this is going to take us. Since there are an infinite number of shells—each contributing the same amount of light, they’re going to make it very bright on Earth—like infinitely bright!

However, we did not allow for the fact that there are a lot of intervening stars that absorb the light emitted by those further away. This effect saves us from burning up in a night sky that we have just concluded is infinitely bright. Instead, we merely burn up in something that is as hot as the surface of an individual star. In essence, the night sky should be as bright as the surface of a star since every direction we look in space ultimately terminates upon the surface of a star in an infinite universe. Olbers tried to resolve this paradox by assuming that the space between stars was filled with intervening gas and dust (he was right). This gas and dust absorb most of the light before it gets to you and me. Olbers thought that this is what saves us from burning up, but he failed to realize that the light gets re-radiated. The gas and dust will heat up until it is in equilibrium with the energy it absorbs from the stars, re-radiating as much energy as it receives. The same thing happens to the Earth, which after all, is just a reasonably big speck of dust. Thus, the night sky should be about as bright per unit area as the Sun's surface. It obviously isn't—hence the paradox. We had better take a closer look at the premises.

Those premises deal with our conception of the nature of the universe in which we live. Clearly, the universe is not burning us up at night and any cosmological theory we concoct had better reflect this obvious fact. In retrospect, a number of astronomical measurements made in the 20th century probably could have been foreseen simply because they provide a way out of Olbers’ Paradox. Let's take a look at some of the recent astronomical observations made of remote objects in the universe and we'll see how they imply that the universe has not been around forever. It began about 13.7 billion years ago in an act of spontaneous generation known as "The Big Bang" and it is Big Bang cosmology that gets us out of Olbers’ Paradox.^{^[4]}

7.2 The “Discovery” of the Universe

Just how big is the Universe—and where is our place in it? That was a question that consumed the attention of astronomers during the early 20^th century. Faint clusters of stars—glowing clouds of hot gasses and giant dust clouds reflecting the light from stars inside them—all look like fuzzy, luminous patches of light when viewed through a telescope such as existed before the early 1900's. Not knowing the true nature of these fuzzy-looking objects, astronomers called them nebulae, which means clouds. Many could be distinguished from all the other luminous patches of light by their unusual spiral shape but no one quite appreciated what that meant so they, too, were called nebulae (Figure 3). No one knew whether these particular objects were clouds or clusters of stars contained within the Milky Way galaxy or whether they were entire galaxies of stars as immense as the Milky Way galaxy itself, but so far removed from it that they simply looked like the other fuzzy patches that did reside inside the Milky Way.

One of the earliest catalogues of these nebular objects had been prepared as far back as 1781 by Charles Messier, a French astronomer and comet hunter of some renown. One of the nebulae in his catalog, M31 (Figure 3), would eventually become one of the most famous objects in the sky. Detailed observation of M31 with the large telescopes that would become available in the early 20th century would soon convince astronomers that the boundaries of the universe in which they lived far exceeded those of their own provincial Milky Way. The object in question, M31, is more well-known as the great galaxy in Andromeda and whether or not it should be called a galaxy or a nebula was the key topic in one of the greatest debates of 20th century astronomy.

Harlow Shapley (1885–1972) was one of the great astronomers of that era. Shapley was convinced that the Milky Way Galaxy WAS the universe! Nothing lay outside its boundaries. He developed a technique that allowed him to measure the size of the Milky Way galaxy and the Sun's location in it. The technique involved the use of RR Lyrae stars as distance measuring yardsticks. These stars are Population II, variable stars. The Pop II classification means that they are fairly ancient stars made almost exclusively of hydrogen and helium with very few elements heavier than that. They are typically found in globular clusters which are spherically-shaped groupings of as many as 100,000 Pop II stars, making these the oldest known structures in the galaxy. The clusters are distributed isotropically around the center of the galaxy with more of them found closer to the center and less found further away. The RR Lyraes in them pulsate, expanding and contracting regularly in physical size and intrinsic brightness. Their periods^{^[5]} are typically about 2 days, and their average intrinsic brightness is invariably about 50 solar luminosities. Thus, you can see them at great distances since they're so bright and once you identify them as RR Lyraes by measuring exactly how their brightness varies with time, you can tell how far away they must be by measuring how bright they appear to be to an observer on Earth.

Imagine that you were looking at a light bulb on top of a building and someone told you that it was a 100 Watt light bulb. Now you know how bright a 100 Watt bulb is if it's 1 meter away (you measure it) and if the bulb on the building appears to be 1 million times dimmer (again, you measure it) then you know that the building is 1 km away since the brightness of a light source diminishes as the inverse square of the distance. Thus, RR Lyrae stars can be used as distance measuring yardsticks just like the 100 Watt bulb in this example (Focus Box 1).

Shapley found the RR Lyrae stars in globular clusters and deduced the distance to the cluster using the inverse square law for the dimming of light. He discovered that most of the clusters were centered on a point lying in the direction of the constellation Sagittarius—that the Sun lay within the central plane of the Milky Way that bisected the distribution of the clusters and that its distance to the center of the galaxy was about 2/3 of the way out (Figure 4).

However, he didn't know that interstellar gas and dust dimmed the light from distant stars even more than pure geometry did and he therefore overestimated the distance to the clusters and thus the size of the Milky Way galaxy. He figured that the diameter of the Milky Way was about 300,000 ly—about 3 times larger than it really is and one of the few times that an astronomer erred on the upside in estimating the size of the human species' container. It seemed to Shapley that this was an ungodly large number. He had long been convinced that the Milky Way was it as far as the extent of the matter in the universe was concerned and this measurement further reinforced that belief.

Shapley stood on what he thought was firm ground in his belief that the Milky Way galaxy contained the complete ensemble of matter in the universe. Though it was far larger than any other person had either imagined or measured, it was still finite and therefore offered a way out of Olbers' paradox—the night sky was as dark as it was observed to be since there were no stars or anything else that was luminous beyond the boundaries of the Milky Way. But a number of other astronomers held opposing views concerning the extent of the visible universe and they also stood on what seemed to be equally firm ground. Their position was based on arguments that the spiral nebulae, like Andromeda, which had been found all over the sky were entire “Milky Way” galaxies in their own right, just incredibly distant from our own Milky Way, so that they had the appearance of diffuse, small, spiral-shaped clouds.

In 1924, the decisive blow to the issue was delivered by none other than a young upstart astronomer, Edwin Hubble, whom Shapley absolutely loathed. Hubble had taken over Shapley’s position as kingpin of the astronomers at Mt. Wilson Observatory in California when Shapley left to assume the directorship of Harvard College Observatory. Friends had urged Shapley to stay at Mt. Wilson since, at the time he left, George Ellery Hale had just commissioned a new telescope to be built there—the 100-inch Hale and the new discoveries that would pour out of Mt. Wilson would far surpass anything that Harvard could do. Hubble used the new 100-inch Hale telescope—that Shapley would have used—to obtain photographic plates of Andromeda critical to resolving the issue. To rub more salt into the wound, he even found old photographic plates of the Andromeda Nebula, taken with the 60-inch telescope on Mt. Wilson by Shapley himself, whose critical images he had chosen to ignore. Hubble did not ignore them for, even on these old plates, a certain type of exceptionally bright variable star could be seen amidst the nebular fuzz caused by the remaining billions of unresolved stars that actually make up Andromeda. These variable stars were Cepheid variables and ironically, Shapley had used them, along with the RR Lyrae variables previously mentioned, as yardsticks to accurately pinpoint the distances to many of the more remote globular cluster members of the Milky Way.

Cepheids are even brighter than the RR Lyrae variables, and like them, they exhibit a well-defined relationship between their period and average luminosity. The brighter Cepheids could be seen at distances far greater than the remotest globular clusters in which Shapley had seen the RR Lyrae. It was several of the extremely bright Cepheids that Hubble was pretty sure appeared as bright spots on the old photographic plates of the Andromeda Nebula that Shapley had looked at and ignored. If that were true, all Hubble had to do was find some Cepheids in Andromeda with the new Hale 100-inch telescope—where they could be identified unmistakably—and measure their period of pulsation. He would then know exactly how bright they were relative to the Sun from their period-luminosity relation. Then, upon measuring their average apparent brightness, he could deduce exactly how far away they were, and by association, the Andromeda “Nebula” as well. In late 1923, he succeeded and on February 19, 1924 he sent Shapley a letter that began with his characteristic dryness—

“Dear Harlow: You will be interested to know that I have found a Cepheid variable in the Andromeda Nebula (M31). I have followed the Nebula this season and in the last nine months have netted nine novae and two variables...”

Cecilia Payne, who was Harvard’s first PhD student in Astronomy, was in Shapley’s office when he received the letter recalled him saying—

“Here is the letter that has destroyed my universe,” he said, holding the letter out.

Needless to say, Harlow must have felt about as low as a snake’s hips. He was the reigning king of using variable stars as distance-measuring yardsticks to far-away places in the sky and now the astronomer he most reviled had used his own tool to completely dismantle the boundary of his Milky Way Universe.

One might wonder how certain Hubble could be of this effect—in other words, how reliable were his velocity measurements? Of all the characteristics of galaxies that Hubble could determine from his measurements—distance, size, brightness—those that allowed a determination of the velocity were the most accurate. They depended on a well-known effect in physics, the Doppler Effect. As mentioned earlier, the spectrum of light from the Sun contains a number of sharp, dark lines, called absorption lines. The Sun is a star, so it should come as no surprise that all stars exhibit the same effect. An example of absorption lines of stars in a remote cluster of galaxies is compared with the absorption spectrum of the Sun in Figure 10. The absorption lines are identical but those of the cluster are shifted towards the red end of the visible spectrum.

Why is this? What happens if, say, the stars that we are observing Text Box: Figure 11 The Doppler shift—the wavelength from a moving light source emitting spherical wave fronts is compressed (blueshifted) in the forward direction and stretched out (redshifted) in the receding direction happen to be moving away from us? The light waves get stretched out so that the wavelength we see is actually longer than the wavelength we would see if the stars were at rest with respect to us. The opposite happens if the stars are moving towards us—the waves get scrunched together so that the wavelength we see looks shorter than it otherwise would. This is the Doppler Effect and it is shown in Figure 11.

Figure 12 Measured distances and redshifts (recessional velocities) of remote galactic clusters.

If the source of light is moving away from the observer, we say that the light has been redshifted—meaning only that the wavelength has been shifted to a longer value. If the source of light is moving towards the observer, we say that the light has been blueshifted—meaning only that the wavelength has been shifted to a shorter value. The amount of the shift is directly proportional to the relative speed between the light source and the observer. The value of the speed can be calculated from the shift in the wavelength of the spectral lines—it is given by the formula v/c = Δλ/λ where v is the relative speed, c is the speed of light, λ is the wavelength of the light when the relative speed is zero and Δλ is the change in the wavelength that occurs when v is whatever it is. Vesto Slipher had known about the redshift anomaly, but he lacked the key piece of information that Hubble had—namely, that the spiral nebulae were not local to the Milky Way but were galaxies far removed from it. Hubble had reasonably accurate measurements of the distances to them. What he saw in his data astonished him—the more distant the galaxy—the greater its redshift—and by extension—the greater its recessional velocity. We show this effect in Figures 12 and 13.^{^[7]} The data show that the redshift, or equivalently the recessional velocity of a galaxy is proportional to its distance from the Earth. This relationship is now known as Hubble’s Law, which can be expressed by the formula v = H₀ r, where H₀ is the slope of the line in Figure 13 and is called the Hubble constant. Its current value is estimated to be 71 km/s per Mpc.

In 1929, Hubble stunned the astronomical world with the publication of this result—rather prosaically entitled—“A Relation Between Distance and Recessional Velocity Among Extra-Galactic Nebulae.” Hubble, of course, immediately realized the implication of this result, but it is notable that, like Newton before, he “framed no hypotheses.” He had been burned once before by putting forth publicly in an earlier publication what proved to be an errant hypothesis about the implications of one of his observations. He was adamant that he would never repeat that mistake again.

bd06210_ What Do You Think About This? The Hubble Constant, H₀

Think about what the Hubble Law implies—if we let time run backwards, then all the galaxies would be moving towards us and after a time τ, all galaxies would be piled on top of one another—that is—assuming they don’t slow down and stop. We can estimate τ from Hubble’s Law. H₀ has the dimensions of time^-1 and must be equal to 1/ τ. Thus, τ = 1/ H₀. Let’s do the math—we’ll convert all distance units to km and seconds into years—

That’s 13.8 gigayears (13.8 billion years).

7.5 A One Dimensional Bug World

Figure 14 Three bugs on a 1-dimensional (circular) expanding 'Bugworld.'

We’re going to digress for a second—bear with me. In 1884, the English schoolmaster, Edwin Abbott published a novella that was intended to be a satire of Victorian culture. It was—but the concept of dimensionality that it presented had a far more lasting influence. It conjured up a two dimensional world and what it would look like from the point of view of inhabitants confined to such a world. We’re going to simplify Abbott’s picture. Let’s imagine a one dimensional world inhabited by ladybugs, which are mere dots in that world. Think of a hula hoop of a given radius R, populated by bugs. It takes only a single number to represent the “address” of a bug—it could be an angle, for example, relative to some arbitrary reference line—rather like we define longitude relative to the Greenwich meridian on the essentially two dimensional surface we call home. The bugs can move only in one dimension—clockwise or counter-clockwise around the hoop. They have no concept of any dimension, or space that lies perpendicular to any point on the hoop. Take a look at Figure 14—we’ve shown three bugs in Bug World—blue, green and red. Let’s also suppose that these three bugs are just sitting there—not moving along the hoop—happy as little bugs in Bug World. They each measure the distance to each other along the hoop and they get a value of S. Now, suppose that the radius of the hoop is increasing with time—that in a given time T, the radius of the hoop doubles from R to 2R. What might these bugs think is happening in their world? No bug thinks she is moving! Remember, they have absolutely no concept of any space that is not ON their hoop. They might not even know that their world is finite, circular, because they might not have circumnavigated it. However, they now measure the distance to each other again. Miraculously, blue bug discovers that she is now 2S away from green bug and 4S from red bug—but at time T earlier, she was only S and 2S away from these two neighbors respectively. Furthermore, green bug and red bug will conclude the same thing regarding any two neighbors to their left or right. In other words, each bug thinks that the others are moving away—the speed of recession of the nearest neighbor would be v₁ = (2S – S)/T = S/T and the speed of recession of the second neighbor would be v₂ = (4S – 2S)/T = 2S/T. Each bug thinks that they are at rest—it is their neighbors that are moving and the further away they are—the faster they are moving. Each bug might conclude that they are located at the center of their one dimensional universe, when in fact there is no center. Each point on the hula hoop is indistinguishable from any other.

One more point—suppose a smart bug plotted a graph of the recessional velocity of the other bugs vs. their distance—here’s what they would get—the recessional velocity of any bug is directly proportional to their distance away from the reference bug (Figure 15). This “law” is a direct consequence of the expansion of the one-dimensional space that constitutes the Bug World universe. No bug is really moving. The space between them is increasing with time and that is causing the apparent recessional velocity. This kind of law is exactly what Hubble found for the galaxies in our universe—our three-space dimensional world. The implication—obvious to Hubble and quickly recognized by everyone who read his momentous publication—we live in an expanding universe. Hubble had made not only the first, but also the second of the three most spectacular discoveries in 20^th century astronomy.

At the time, Albert Einstein, like many others, believed in a steady-state, essentially static model of the universe—one with no beginning and no end. However, his famous general theory of relativity led to a universe that could not be static. So he artificially inserted a cosmological constant—a fudge factor, if you will—into his theory in order to provide a repulsive force that would counteract gravity on a large scale—leading to a static universe. As soon as Einstein heard of Hubble’s discovery, he realized that he needed no such cosmological constant since the unadulterated equations of his general relativity theory led to a universe should either be either expanding or contracting. Einstein had missed out on an incredible prediction. This, as mentioned earlier, was what Einstein called “one of the greatest blunders of his life.”

7.6 The Big Bang

penzias&wilson.gif Arno Penzias and Bob Wilson were trying to find the source of excess noise in their antenna, where pigeons were roosting. They spent hours searching for and removing the pigeon dung—still the noise remained, "Either we’ve seen a pile of pigeon *&%&# or the creation of the universe.”

"Thus, they looked for dung but found gold, which is just opposite of the experience of most of us."

Comments of Ivan Kaminow, one of Penzias’ and Wilson’s colleagues at Bell Labs, Holmdel, N.J. See, for example—http://www1.bell-labs.com/project/feature/archives/cosmology/

Subsequent astronomical observations showed that the distribution and numbers of clusters and superclusters of galaxies was indeed spread throughout the universe rather uniformly. This led astronomers to adopt the idea, called the cosmological principle, whereby the universe, when viewed on sufficiently large distance scales, had no preferred directions or preferred places. This principle, coupled with the observation that the universe was expanding, allowed for two opposing possibilities—one was a theory that called for a universe with a beginning—put forth in 1931 by the Belgian Catholic priest, Georges Lemaître, which eventually became known as the Big Bang. It was strongly supported and developed in more detail by the Russian physicist, George Gamow. Gamow showed how nuclear reactions during the early stages of the Big Bang could generate all the hydrogen and helium we see in the universe—but not any elements heavier than that. Fred Hoyle, the British astrophysicist figured out where these heavier elements came from. Gamow later joked that he had got 99% of it right since these heavier elements constitute only about 1% of all the matter. A universe that had a beginning would be expected to have different characteristics at different locations and at different times—we would not expect that it was always in the state that we see it in now—it would change and evolve.

The other possible theory of the universe was Fred Hoyle’s Steady State Theory—new matter would be created continuously throughout the universe causing existing matter to move away and make room for it. In this model, the universe is roughly the same at any point in space and time—it does not change or evolve on the whole. It was actually Hoyle who coined a name for Lemaître’s theory, sarcastically calling it "this 'Big Bang' idea" during a radio broadcast on March 28, 1949, on BBC. The term, to Hoyle’s great surprise, actually stuck and, unfortunately for him, evidence mounted in support of the Big Bang. Hoyle, albeit somewhat reluctantly, was forced to admitted that the Big Bang Theory was “more or less” correct.

The Big Bang was the ultimate free lunch—something apparently sprung from nothing! How did it work its magic and how have physicists pieced together the significant events that have taken place in the universe after its flashy beginning? Essentially, we examine the details of the universe that we see around us today—run the clock backwards—and then use the laws of physics to calculate what the universe was like in the past. To some extent, we can actually compare the results of the calculations with actual observation—for when we look at things very remote from us, say, 10 billion ly away, we are seeing those things as they were 10 billion years in the past. That’s how long it took light that originated there—to get here to us. We can then construct a timeline depicting the conditions that must have existed in the universe back to its very beginning—almost. We describe the results of such an analysis below.

7.7 The Two Majors Eras of the Big Bang

The history of the universe following the Big Bang can be divided into two major eras—the radiation era^{^[8]} and the matter era. Stars are made of matter and they form when particles are pulled together because of their mutual gravitational attraction. During the radiation era, the pressure generated by photons impinging upon particles overwhelms any mechanism such as gravitation—preventing them from being pulled together to form structures. At temperatures > 10,000 K the various materials that make up the universe are on the whole distributed uniformly throughout space, forming no complicated structures. In such an environment, neutral atoms do not exist. Hence, the radiation era in its latter stage consists predominantly of a plasma, or hot gas of electrically charged matter—electrons, protons, simple atomic nuclei—and radiation, or photons.

The term, matter means anything that is made out of the fundamental particle building blocks, quarks and electrons. All matter has a rest mass, m. This means that we can slow it down, stop it and “hold it in our hands”—so to speak. It can never be made to travel faster than the speed of light. Light, or radiation, has no rest mass. If you stop it from moving, you "destroy" it, i.e., it gets absorbed by the matter that is used to stop it from moving. If a light photon exists—it moves—and it does so at the speed of light. Right after the Big Bang, the universe was filled mostly with pure energy in the form of light photons. The energy density of this radiation was enormous and photons could interact with other photons to produce matter and it did just that. This process in which photon collisions produce real particles with a rest mass is called pair production. Two photons collide—they disappear and their energy is directly converted into matter and anti-matter such as an electron–positron or quark–anti-quark pair (Figure 17) .

As the number of particles increased, the real particles and anti-particles could annihilate, creating two photons in the process. Eventually, the matter and radiation formed a hot primordial soup filled with particles, anti-particles and photons almost in equilibrium in an on-going process of creation and destruction of matter. But mostly, the universe was filled with radiation and not much matter. As the universe expanded and cooled, both matter and radiation were losing energy but radiation was losing it faster since its wavelength λ was being stretched by the expansion of space. Both radiation density and the matter density were decreasing as the universe cooled and expanded, but the radiation density was dropping faster. Eventually, about 24,000 years after the Big Bang, the radiation density dropped below that of the matter density at Text Box: Figure 18 Density of radiation and matter decrease as universe ages, but radiation density decreases faster and matter eventually dominates. a temperature of about 10,000 K and from this time on had less and less of an effect on the dynamics of the universe (Figure 18). We now live in the matter era, or an era in which matter dominates the structures that are now emerging in our universe.

The two major eras discussed above have been subdivided into nine epochs whose names have been selected to best represent the characteristics of the universe during their respective time intervals. We show these characteristics in a graph of the Big Bang timeline in Figure 19 and soon we will discuss the processes that characterize each of these epochs but first, we define two terms which we will encounter in the discussion—freezeout and decoupling.

Imagine a container full of gas made of a mixture of methane, ammonia and water. Now suppose we start lowering the temperature of this mixture. Water freezes at 273 K, ammonia at 195 K and methane at 91 K. As soon as the temperature of the gas drops below 273 K, the water will freezeout—it will turn into ice crystals which precipitate out of the remaining gas mixture, i.e., it will decouple or no longer interact with it. The same thing will happen to ammonia as the temperature is lowered below 195 K and finally to methane upon dropping below 91 K. A similar thing happens to both particles and forces as the universe expands and cools. These freezeouts and decouplings have left a residue or visible imprints on our universe, whose discovery has provided strong support for the Big Bang theory.

7.8 The Radiation Era of the Big Bang (from age 0 to 24,000 years)

· The Big Bang — Age : zero

Perhaps, the most frequently asked question when anyone brings up the issue is—what happened before the Big Bang and how did it start? It’s a little bit like asking what’s north of the North Pole. Time and space, as we know it in our universe, began with the Big Bang. The Big Bang is not an explosion that sent stuff flying outward through existing space—it is an explosion of spacetime, itself—space and time started with the Big Bang and space begin to expand in time, much like what was going on in Bug World. Current thinking is that the Big Bang was a quantum fluctuation in the vacuum of a multiverse—the home of many disconnected universes—each one with its own set of physical laws and characteristics that are quite different than ours. Most people think of the vacuum as empty space. It is not! A quantum fluctuation of the vacuum is a process in which particle–anti-particle pairs are continually created and destroyed. Indeed, such fluctuations have a measurable effect on the behavior of atoms in our own universe! Is this hypothesis—creating our universe in a multiverse—a testable one, i.e., amenable to some experimental verification? A number of scientists think so and it is an area of theoretical investigation at the very forefront of physics, but as things stand now, we do not have an answer.

· The Planck Epoch

Age : < 10^-43 s Radius : <10 ^-52m Temperature : >10³² K

Moreover, we cannot say what happened within the first 10^-43 seconds following the Big Bang. We believe that the four known forces (gravitation, weak, electromagnetic and strong) that describe the behavior of all particles in our current epoch were completely indistinguishable from one another during these first fleeting moments of the early universe. In other words, there existed only one fundamental, unified force that described the behavior of everything that existed. The conditions of the universe were so bizarre that gravitation was a part of this unified force and it behaved in a way that could only be described by quantum mechanics, but at the current time, we do not know how to do that. Thus, our current theory of physics fails us here. We simply cannot intelligently discuss what went on during the first 10^-43 seconds! We call this epoch—the Planck epoch, after Max Planck, one of the founding fathers of the theory of quantum mechanics.

· The GUT Epoch

Age : 10 ^-43 – 10 ^-35s Radius : <10 ^-52 – 10^-50 m Temperature : 10³² – 10²⁸K

We do know, however, that when the Planck epoch ended—the force of gravity “split off” or “froze out” from the remaining unified “strong-electroweak” force and from that point on each of these separate forces could be described with great accuracy by Einstein's general theory of relativity and by a Grand Unified Field Theory—or GUT, for short. At this time, the temperature of the universe and the corresponding energies of its constituents were so great that the process of pair production was generating all sorts of particle—anti-particle pairs. Many of the pairs were the extremely massive grand unified x particles and their corresponding anti-particles, denoted here as . The number of these particles grew to the point where as many were being created by radiation as were being destroyed by annihilation, converting back to radiation in the process. The amount of radiation and numbers of x, pairs were in thermal equilibrium. As the universe expanded, cooled and aged from 10^-43 to about 10^-35 s, these x, pairs would mostly annihilate, but a number of them would remain and eventually decay into quarks and anti-quarks as the end of the GUT epoch approached.

· The Electroweak Epoch

Age: 10 ^-35 – 10 ^-12s Radius : 10 ^-50 m – 12 light s Temperature : 10 ²⁸ – 10 ¹⁶ K

At around 10^-35 seconds, though, something incredible happened in the universe. It cooled to a temperature of about 10²⁸ K where it underwent a phase transition—analogous to the phase change that occurs when liquid water cools to ice at 273 K. There is no alignment of the molecules that make up water when it is at a temperature higher than the freezing point. Any direction looks the same as any other. The water thus exhibits symmetry. This perfect symmetry of water is broken, however, when it freezes into ice. Ice has a crystalline structure with well defined x, y, z directions in space that line up along the crystalline axes (Figure 20). All directions do not look the same! You can tell directions. The state of frozen water is not perfectly symmetrical. It has a natural (x, y, z) coordinate system aligned with the principle axes of the crystal. Liquid water has no such natural coordinate system.

The loss of symmetry that occurred when the universe cooled below 10²⁸ K manifested itself by a splitting of the grand unified force into two distinct forces—the strong force and a unified electro-weak force. x and particles could no longer be created by radiation interacting via the grand unified force because the temperature was too low. Those x and particles that remained then decayed into combinations of quarks, anti-quarks, electrons and positrons but the decay was asymmetric—that is, the x and decayed at different rates leaving a slight excess of quarks over anti-quarks. This decay rate asymmetry was the one of the discernible differences in behavior between the strong force and the electro-weak force. At the high temperatures that exist during the GUT epoch, x and behave the same way—at the lower temperatures that occur following this epoch, they do not. The decays are mediated by the electro-weak force and this force acts differently on anti-particles than it does on real ones. It is this effect that ultimately led to our universe being constructed of matter and not anti-matter since matter is made from those quarks that did not annihilate with the slightly less abundant anti-quarks.

Inflation :

Age: 10^-35 – 10^-32 s Radius : 10 ^-50 m – 1 m

This phase transition had another huge effect on the structure of the universe, beginning at 10^-35 seconds— the opening salvo that ushered in the electroweak epoch—it led to a period of incredibly rapid expansion driven by the release of an enormous amount of energy. This phenomenon is akin to the energy that is released when water freezes into ice. As water freezes, the water molecules change from a state of random, disordered motion into one where they are highly ordered and relatively fixed in position. The molecules thus go to a lower state of energy and heat energy is released in the process. Ask any fish in a lake about this phenomenon. If energy were not released as the top surface of the lake froze, the water underneath would not remain liquid and it would freeze, too. This energy release in the early universe maintained a constant energy density during its subsequent period of expansion which in turn generated an outward pressure that drove the expansion at an exponential rate. This process has been given the name inflation. Between 10^-35 sec and 10^-32 sec the universe grew some 50 orders of magnitude—from an infinitesimally small spec to about the size of a basketball (Figure 21). The space between particles actually stretched out faster than the light travel time between them.^{^[9]} Any gross inhomogeneities that existed in the universe as a whole would no longer be visible to us. Thus, our observable universe now consisted of a highly inflated region of smoothed out, relatively flat space that had once been extremely small.

Figure 21 Radius of universe vs time since the 'Big Bang.'

During this time, the temperature was no longer hot enough for the radiation to produce the x and particles, which by now had all decayed into quarks and leptons and their antiparticle counterparts. The universe now consisted of a soup of photons, quarks, leptons, and gluons.^{^[10]} At 10^-12 seconds, the temperature had cooled off to about 10¹⁶ degrees or so—too low to create intermediate vector bosons.^{^[11]} The freezeout, or splitting, of the electroweak force now occurred and the weak and electromagnetic force separated. From now on, there were four separate forces in nature (strong, electromagnetic, weak and gravitational) and the future course of the universe would be determined by their characteristics.

· The Quark Epoch

Age : 10 ^-12 – 10 ^-6s Radius : 12 light s – 3.3 light hr Temperature : 10¹⁶ – 10 ¹³ K

This time frame is characterized by free quarks, leptons and photons all in thermal equilibrium. It was too hot and particle collisions still too energetic for quarks to be confined as hadrons.

· The Hadron Epoch

Age : 10 ^-6 – 1s Radius : 3.3 light hr– 137 light da Temperature : 10 ¹³– 10 ¹⁰ K

Between 10^-6 - 1 seconds, the universe cooled enough that all of our known hadrons (most prominently protons and neutrons) “condensed” out of this soup—three quarks came together to form protons and neutrons, two quarks came together to form mesons and anti-quarks (those that had not yet annihilated) formed anti-protons, neutrons and mesons. Free quarks disappeared from the universe. From this point on, the only free, fairly stable particles in the universe were photons, leptons, protons and neutrons. These would form the building blocks of any subsequent structures.

· The Lepton Epoch

Age : 1 – 100s Radius : 137 light da – 1.2 ly Temperature : 10¹⁰ – 10⁹ K

The temperature of the universe had now fallen to the point where radiation could create only lepton pairs (electrons and positrons) via the pair production process. By the end of the epoch, collisions were too weak to even do that. Leptons and anti-leptons (which were slightly outnumbered by the leptons) annihilated leaving only a small amount of leptons. Most of the protons and neutrons were also annihilating with their corresponding anti-particles leaving only a very small amount of matter—about one proton, neutron and electron for every billion photons. At 0.1 seconds, neutrinos completely decoupled from everything in the universe. These weakly interacting, electrically neutral neutrinos rarely interacted with any other form of radiation or matter. They were left to fly around through the universe—ghost particles—virtually unimpeded by anything in their path.

· The Nuclear Epoch

Age : 10 ² s – 24,000 yr Radius : 1.2 ly – 38,000 ly Temperature : 10⁹– 60,000 K

Figure 22 Nuclear fusion reactions during the Big Bang that produced helium from hydrogen.

Temperatures were now low enough that simple nuclear fusion reactions could occur between protons and neutrons, which synthesized some helium-4 (₂He⁴) as well as small amounts of deuterium (₁H² or D), Helium-3 (₂He³) and lithium-7 (₃Li⁷). This process is called primordial nucleosynthesis and it took place primarily in the time interval 3 – 20 minutes after the Big Bang. An example of the fusion reactions that produce D, He³ and He⁴ is shown in the Figure 22. Nuclear species heavier than these were not created during the Big Bang for two essential reasons: (1) free neutrons were quickly disappearing from the universe, i.e., those not bound up inside some nucleus—decay into a proton, electron and anti-neutrino with a half-life of about 10 minutes. (2) The production of ever heavier nuclear species requires a fusion reaction of helium and ever heavier nuclei just created. But such nuclei are made in part of more than one proton and thus any two such heavier nuclei will experience ever greater electrical repulsion forces between their larger positive charges. Such fusion reactions require increasingly higher temperatures, but the universe was expanding rapidly and the temperature and nuclei density were dropping precipitously. Thus, subsequent fusion reactions that could create heavier nuclei had neither the fuel (free neutrons), nor the necessary energy (higher temperatures) required to initiate the fusion.

Thus, from about 20 minutes on, free “light” nuclei and electrons make up all of the matter in the universe. Eventually, at 24,000 years, the energy density of this matter exceeded the energy density of the much more numerous photons and began to shape the future course of events in the universe.

7.9 The Matter Era (from 24000 years to Now)

· The Atomic Epoch
Age : 24000 – 3.8x10⁵ yr Radius : 38,000 – 1.5x10⁶ ly Temperature : 60,000 – 3000 K

Prior to this time the radiation was so intense and energetic that it broke apart any atoms that momentarily formed in the hot plasma of photons and electrically charged particles that made up the universe. But as the universe continued to expand and its temperature continued to drop, neutral atoms began to form, or “condense” out of this hot soup. Radiation does not interact easily with neutral atoms—it streams through a gas of neutral atoms rather easily. It does not do so in a gas consisting of charged particles. Thus, as the neutral atoms formed, the universe suddenly became “transparent”—you could now see through it—as though a great fog had lifted. The radiation born in the Big Bang decoupled forever from the matter it had given birth to. This time has been called the time of recombination—a misnomer since electrons and nuclei were never combined as atoms in the first place. From this point on, radiation would not provide much pressure to keep material structures from beginning to form. The formation of neutral atoms was essentially complete when the temperature of the universe had fallen to about 3000 K at an age of about 380,000 years.

· The Galactic or Stellar Epoch
Age : 3.8x10⁵ – 13.7 x10⁹ yr Radius : 1.5x10⁶ – 13.7 x10⁹ ly Temperature : 3000 – 2.73 K

When radiation pressure ceased to be the dominant force in the universe, gravity began to assert itself. The matter in the universe was distributed in a way that was smooth—but not completely smooth. The more dense regions of matter were pulled together by gravitational forces that led to the formation of very massive stars and concentrations of matter that ultimately turned into galaxies and clusters of galaxies. Evidence of such inhomogeneities is provided for us by measurements by COBE (COsmic Background Explorer) and WMAP (Wilkinson Microwave Anisotropy Probe) of the radiation left over from the Big Bang. This radiation was once strongly coupled to the matter it had produced and so any inhomogeneities in this radiation distribution generated matter inhomogeneities that eventually coalesced into large structures as the universe continued to expand and cool.

Stars are one of the major components of galaxies nowadays. The collapse of matter into stars halts only when nuclear fusion starts in their cores, which generate enough heat that the resulting pressure stabilizes the star against additional gravitational collapse. It is these nuclear fusion reactions in the cores of stars that generate all the elements in the universe from carbon-12 (₆C¹²) up to iron-56 (₂₆Fe⁵⁶). Additional amounts of these elements as well as elements heavier than iron are formed via the process of explosive nucleosynthesis that occurs in a supernova explosion triggered by the catastrophic collapse of a massive star after all the energy generating fusion reactions in its core has been exhausted. Some extremely large stars formed independent of galaxies about 100 million years after the Big Bang. These massive early-forming stars were very short-lived and quickly exploded infusing the nascent universe with the heavy elements that the Big Bang failed to create.

The universe itself has now expanded to a visible radius of about 13.7 billion ly and has cooled to a temperature of 2.726 K. The CMBR (Cosmic Microwave Background Radiation) is the relic radiation left over from the Big Bang after radiation decoupled from matter at age 380,000 years and temperature 3000 K.

7.10 Evidence for the Big Bang

There are three main pieces of evidence that support the theory that our universe began with the Big Bang. We have already alluded to three of them—

1. Finite age and expansion explains— Olbers’ paradox—why the night sky is dark

The Big Bang theory resolves the paradox in two ways:

· First—the universe had a beginning 13.7 billion years ago and its visible extent is 13.7 billion ly. There can be no stars or any luminous objects, which we can see further away than that. If we try to look beyond that distance we would be looking at something older than 13.7 billion years since it would have taken the light from such objects longer than 13.7 billion years to get to us—and the universe did not exist more than 13.7 billion years ago. Hence, the universe has a visible limit.

· Second—Hubble’s Law demonstrates that the greater the distance of a luminous object from us, the greater its redshift. Luminous objects more distant than several billion light years are receding at speeds approaching the speed of light and thus the light from those objects is so redshifted we cannot see it!

2. The CMBR—radiation left over from the time of recombination

The Big Bang theory leads to the conclusion that 380,000 years following the Bang, radiation should decouple from matter. At that time, these radiation photons made up a hot gas that that had been confined by their interaction with matter but suddenly were released when matter became electrically neutral. As the universe continued to expand this hot photon gas simply expanded and cooled off in the process. Since the time of decoupling, the universe has expanded a thousand-fold and the temperature of the photon gas has dropped a thousand-fold from 3000 K to about 3 K. These photons are now mostly very low energy microwave photons and would have a spectral distribution characteristic of light emitted by a 3 K blackbody. Such radiation should fill the universe and we call it the CMBR.

Its initial discovery was quite serendipitous. The U.S. was launching the first primitive communication satellites in the early 1960’s. Arno Penzias and Robert Wilson (Figure 16), two scientists at Bell Labs in Holmdel, N.J., had been working on a large microwave horn antenna (in the background of Figure 16) used to receive satellite signals. They needed to know how much background noise the antenna would pick up so that they could determine how strong they had to make the satellite communication signal to be detectable. Thus, they pointed their directional antenna all around the sky to make background noise measurements. They discovered a very low level background noise that, surprisingly, came from all directions in the sky. They were convinced that this unwanted background noise was caused by something in or around their antenna. They quickly saw that the inside of the antenna was covered with a suspicious white dialectric substance generated in abundance by a nest of roosting homing pigeons. They got rid of the pigeons—cleaned up their “crap”—but still the noise persisted.

Unbeknownst to Penzias and Wilson, a group of physicists led by Bob Dicke and Dave Wilkinson, a few miles down the road in Princeton, N.J., was in the process of building a microwave horn antenna to search for the CMBR. However, before completing the task, Dicke got a call from Penzias and Wilson, inquiring what the source of their uniformly distributed antenna noise might be—if there was any known astrophysical process that might cause it. Dicke was stunned—he called his group together and said to them, “Well, boys, we’ve been scooped!” Indeed, Penzias and Wilson had inadvertently detected the leftover whisper of creation, the CMBR! They were awarded the Nobel Prize for their discovery—the 3^rd greatest discovery in astronomy of the 20^th century—in 1978.

Since then, COBE and other groups have made incredibly accurate measurements of the CMBR and they agree precisely with the predictions of the Big Bang theory. The measurement and prediction of the CMBR spectral distribution is shown in Figure 23.

3. The observed abundances of the light elements: deuterium (₁H² or D), Helium-3 (₂He³), helium-4 (₂He⁴) and lithium-7 (₃Li⁷).

The Big Bang has left measurable imprints in our current universe caused by events that occurred much earlier than the origin of the CMBR. The relative abundances of the light nuclei provide a detailed fossil record of what happened when the universe was only a few seconds to a few minutes old—the epoch during which primordial nucleosynthesis took place. It is a profound fact that our universe is made up almost exclusively of hydrogen and helium and that is because of what happened during the Big Bang.

Cosmic nuclear evolution, since the Big Bang, has taken place mostly in the cores of stars where energy extracted from nuclear fusion reactions inexorably drives nuclei towards the most stable nucleus—iron-56 (₂₆ Fe⁵⁶).^{^[12]} These nuclei provide records of the nuclear activity in stars over billions of years of cosmic evolution, but stellar activity has only slightly modified the nuclear abundances generated during the Big Bang and found throughout the universe today. Our universe is still made up mostly of hydrogen and helium.

The nuclear abundances that are calculated from Big Bang theory are compared with measured nuclear abundances in Figure 24. The abundances have been calculated as a function of a parameter eta (horizontal axis labeled η), which represents the ratio of the number of baryons in the universe relative to the number of photons. The value of this ratio has a direct effect on the nuclear abundances, so we need to know its value in order to pin down the predicted values.

The presence of protons and neutrons in the early universe leaves a slight, but measurable imprint on the CMBR. This means that it is possible to ascertain the value of η with a really accurate measurement of the CMBR. The value of η that follows from recent high precision measurements with the Wilkinson Microwave Anisotropy Probe (WMAP) is indicated by the vertical golden strip at about 5 x 10^-9.

Text Box: Figure 24 Predicted (curves) and measured (horizontal stripes) values of the relative nuclear abundances. The predictions are presented as a function of eta, the ratio of baryons to photons in the universe. The abundances of all nuclei are plotted on the vertical axis as numbers relative to the number nuclei of hydrogen, the most abundant element—except for helium-4, which is plotted as a mass ratio (and labeled by a *)—the mass of helium-4 nuclei divided by the total mass of all protons and neutrons in the universe. The curves indicate the theoretical predictions from Big Bang nucleosynthesis. The horizontal stripes are the measured values. The thickness of the stripes represents estimated experimental error.

The intersection of the vertical golden stripe with each of the theoretical curves represents the values of the predicted abundances. These values are the ones to compare with the values obtained from the measurements, represented by the horizontal stripes. The agreement is impressive—well within experimental error—except for lithium-7, where there is an appreciable gap between prediction and observation. However, given the uncertainties of actually measuring the abundance of this universally rare element, we suspect that this discrepancy is likely to teach us more about stellar physics than about Big Bang nucleosynthesis. All in all, this agreement between theory and observation constitutes one of the big successes of the Big Bang theory.

7.11 Cosmogenesis—A Story of Creation

Our current level of scientific literacy has enabled us to piece together an impressive story of how we came to be, albeit not yet complete in many details. Space, time and the matter and energy in it, exploded into existence about 13.7 billion years ago in a spectacular act of creation known as the Big Bang. At the instant of creation, the universe was no larger than about 10^-52 meters—a tiny fraction of the size of a proton. Its temperature exceeded 10³² K! It was a small, hot, dense primeval fireball consisting mostly of radiation with a mere smattering of matter. Tremendous pressure caused the fireball to expand and cool quite rapidly. Within three minutes the matter and energy that make up the current universe had grown to a size about one hundred times greater than our solar system. By then, this primeval fireball had cooled down to a temperature of only 10⁹ K and the radiation in it had weakened sufficiently enough that elementary particles began to clump together to form the light elements hydrogen, deuterium, helium and traces of lithium. No heavier elements were created until the first stars were born several billion years later. The spatial fabric that contains all the matter in the known universe is still expanding outward at a rate that is, astonishingly enough, increasing with time.^{^[13]}

A large spiral structure known as the Milky Way Galaxy now lies somewhere in all that space. The Milky Way consists of 400 billion stars distributed throughout giant clouds of gas and dust from which new stars are continually born. One of those stars, our Sun, was born about 5 billion years ago. It arose from the death throes of a much more massive star that lived before it somewhere nearby. This massive progenitor lived a quiet existence for a few million years, supporting itself against gravitational collapse by tremendous heat and pressure generated by nuclear fusion reactions deep within its core. Eventually, it exhausted its supply of nuclear fuel, which provided the supporting pressure and it collapsed catastrophically under its own weight. The core stopped collapsing when all its nuclei were suddenly converted into a solid, rigid mass of neutrons. The outer layers of the star were no longer supported by the collapsed core and they crashed down onto its shrunken surface at supersonic speeds. Shock waves generated by the impact reverberated throughout these outer layers and blew the star apart, blasting its outer layers into the far reaches of outer space. The massive star had disappeared in a supernova explosion, one of the most violent events that can happen anywhere in the universe (Figure 25).

Figure 25 Supernova observed in a distant galaxy.

Mixed in with the explosive debris were heavy elements, some that were manufactured by the nuclear fusion reactions in the core of the massive star that had supported it against collapse and some that were radioactive—manufactured in the shock wave of the supernova explosion, itself. These heavy elements infused a giant cloud of gas and dust swirling around in the Milky Way galaxy as the shock wave from the explosion passed through it. The shock wave dissipated its energy by compressing the surrounding cloud, causing pieces of it to coagulate and collapse. Many of these collapsing pieces formed new protostars—made up mostly of hydrogen and helium, but also small amounts of heavier elements that had been manufactured by the massive star. Some of the dust and the heavy elements contained in one of these collapsing pieces formed a disk that swirled rapidly around its young protostar. The dust in the disk served as seeds upon which the hot swirling gasses condensed and grew into four small, inner terrestrial planets and four large, outer Jovian planets that orbited the young star.

The third planet in this group, called Earth, emerged unique among the total of eight planets that formed around this seemingly nondescript new star. Indeed, it became a unique planet among the billions of its sisters that orbit the hundreds of billions of stars that make up the Milky Way galaxy—a rather nondescript galaxy among the billions of others like it that make up most of the visible structures in the remote universe. In a little less than a billion years after the formation of Earth, conditions proved just right for simple organic chemical structures to form. Some of these structures somehow managed to initiate chemical reactions that produced copies of themselves and their number began to grow explosively. Natural selection took over and slowly turned these simple self-replicating structures into structures even more complex. They now possessed the property we call life. It took another 4 billion years of evolution for the human species to emerge. Indeed, as Carl Sagan was fond of remarking, “We are all star-stuff!”

The recent appearance of our species and the brevity of our existence as an intelligent species can best be illustrated by compressing time between now and the Big Bang into one day—from 24 hours ago until now—call it a cosmic day. The Big Bang went off 24 hours ago and the Earth did not form until nearly 7 hours ago. The first fossils date back to 5 hours ago and the first humans appeared only 10 seconds ago. Columbus discovered America about 3.6 milliseconds ago and most of you were born sometime within the previous 0.14 milliseconds. Looked at this way, we have been an intelligent species for only 2 milliseconds or about 6 x 10^-9 (6 billionths) of a cosmic day. In real time, we became operationally intelligent only about 80 years ago—not a very long time for us or ET to find out the whereabouts of the other.

Review Questions:

1. What is Olbers’ paradox?

2. What are the premises that lead to Olbers’ paradox?

3. Explain why a thin shell of stars at any given distance from Earth should generate the same amount of light as another equally thin shell of stars that is much further away.

4. How did Harlow Shapley measure the distance to globular clusters?

5. Why did Shapley think that the Milky Way galaxy was the full extent of the known universe?

6. Why did Shapley overestimate the size of the Milky Way galaxy?

7. How did Edwin Hubble demonstrate that the spiral nebulae were, in fact, galaxies far removed from the Milky Way thus demonstrating that they universe was far larger than Shapley thought?

8. What is meant by the term primeval fireball?

9. What is a supernova?

10. What is a cosmic day?

11. For what length of time out of a cosmic day have operationally intelligent humans existed?

12. How long did it take Voyager II to reach Neptune?

13. How long will it take Voyager II to reach a distance equivalent to that of the nearest stars?

14. Why are distances beyond 13.7 Gly meaningless?

15. What is the Doppler effect? —a redshift? —a blueshift?

16. What shocking thing did Edwin Hubble and his colleague, Vesto Slipher, discover when examining the spectra of galaxies?

17. What is Hubble’s Law?

18. How can the age of the universe be estimated from Hubble’s Law?

19. What does Hubble’s Law imply about the spatial fabric of the universe?

20. How does the Steady State theory explain the expansion of the universe?

21. What does the Steady State theory imply about evolutionary change in the universe?

22. How does the Big Bang theory explain the expansion of the universe?

23. Should the universe change in time, i.e., have different characteristics, according to the Big Bang Theory? Why or why not?

24. What are the two major eras in the history of the universe?

25. What process produced matter right after the Big Bang?

26. Why did the universe change from being dominated by radiation to being dominated by matter?

27. What is meant by the terms freezeout and decoupling?

28. Why don’t we understand what exactly happened during the Planck epoch?

29. Why is our universe made of matter and not anti-matter?

30. Why didn’t the inflationary phase of the universe cause matter to exceed the ultimate speed limit—namely, the speed of light?

31. How and when did protons and neutrons form?

32. How and when were the nuclei, deuterium, helium-3, helium-4 and lithium-7 formed?

33. When and why did neutral atoms form?

34. What decoupling happened during the atomic epoch and why?

35. When did stars and galaxies begin to form?

36. How does the Big Bang Theory resolve Olbers’ paradox.

37. What is the CMBR? How was it discovered?

38. What were first generation stars made of? Could an Earth-like planet have formed around one of them? Why or why not?

39. How do we know that the process of primordial nucleosynthesis took place during the Big Bang?

Conceptual Questions:

1. Can you think of a way to resolve Olbers’ paradox if Hoyle’s Steady State Theory of the universe was correct? Explain.

2. The term standard candles is used in astronomy—it means that there exist certain astronomical objects, such as RR lyrae or Cepheid variables, whose intrinsic brightness, or luminosity, is well-known. Suppose one of them is found in, say, a globular cluster of stars. Explain how it can be used to determine the distance to that globular cluster.

3. If the universe started with a Big Bang, why is it not possible to find a central point from which it started?

4. Why do we use units like AU to measure the distance to planets and ly to measure the distance to nearby stars instead of meters, which is the fundamental unit of length in the SI system of units?

5. What is the reason that massive stars eventually “go supernova?”

6. If we had telescopes that were capable of seeing bright objects like giant elliptical galaxies as far away as 20 Gly, do you think we would see any? Why or why not?

7. Suppose “Smoky the bear” is sitting in his police car beneath an overpass above I-15 and has his radar gun trained upon oncoming traffic. Explain how “Smoky” concludes that an approaching car might be exceeding the speed limit.

8. Explain how the Doppler effect can be used to measure the speed of distant galaxies relative to the Earth.

9. What two measurements of the characteristics of remote galactic clusters were needed to determine Hubble’s Law?” Is there some other physical mechanism that could explain Hubble’s Law other than that the universe is expanding?

10. Why can’t a group of bugs get together in “Bugworld” to determine the center of their universe?

11. Why is the term The Big Bang a misnomer?

12. What are the two eras in the history of the universe? Why do we divide the history of the universe into those two eras?

13. What defines the Planck epoch?

14. Why did the process of primordial nucleosynthesis halt about 20 minutes after the Big Bang?

15. What is meant by the term symmetry?

16. Why does water exhibit “perfect symmetry” while ice, which is frozen water, does not?

17. A number of characteristics of the universe could not be understood until Alan Guth hypothesized that the universe must have undergone a period of inflation, during which the space between any matter in the universe expanded more rapidly than the distance that a beam of light could travel in that same time. These characteristics of the universe were:

i. The Isotropy Problem—the universe was incredibly smooth, i.e., the matter and radiation in it were spread out very uniformly. The temperature of the universe was almost the same throughout, even though distant parts on opposite sides could not have been “causally connected,” i.e., they were further apart than the light travel time between them.

ii. The Flatness Problem—the geometry of the universe is incredibly flat—like Euclidean geometry in a two dimensional space rather than the curved geometry of the surface of a sphere. The density of material in the universe has to be just right for this—it leads to a universe that is on the cusp of either expanding forever or halting its expansion and eventually contracting.

How does the process of inflation resolve these problems?

18. Why did the process of primordial nucleosynthesis essentially terminate with the production of He-4?

19. Can you explain why light can penetrate a thin gas made of neutral atoms, but it cannot penetrate a thin plasma of electrically charged particles? (Hint: Think of light as an electromagnetic wave travelling through space.)

20. Why did radiation eventually decouple from matter about 380,000 years after The Big Bang? What currently measurable effect did this decoupling lead to?

21. What were first generation stars made of? Could an Earth-like planet have formed around one of them? Why or why not?

22. As time goes on, what is happening to the relative abundances of hydrogen and helium in the universe?

Problems:

1. An astronomer finds a Cepheid variable in the Andromeda Galaxy whose period of variability is 4 days. She measures its brightness. Let’s call the value she obtains B watts. The distance to the Andromeda Galaxy is known to be 2.1 Mly. Suppose she now finds a Cepheid variable in the galaxy NGC2403 whose period is also 4 days and she determines that its brightness is B/25 watts. How far away is NGC2403?

2. As the universe expanded and cooled after the time of recombination, the wavelength of the radiation increased as the temperature of the universe decreased. You can estimate the wavelength λ_2max of the peak of the CMBR by multiplying the wavelength λ_1max of the radiation at the time of recombination by the ratio of the temperature T₁ of the universe at that time to the current temperature T₂, i.e.,

Data

· λ_1max~ 1000 x 10^-9 m

(The wavelength at the peak of the blackbody distribution lies in the infrared portion of the electromagnetic spectrum)

· T₁ ~ 3000 K

· T₂ ~ 2.726 K

In what portion of the electromagnetic spectrum does can this value be found?

3. During the Big Bang Nuclear Epoch, 2 protons and 2 neutrons fused together to make ₂He⁴. The mass of ₂He⁴ is actually somewhat less than the sum of the individual masses of the 2 protons and 2 neutrons. This mass defect occurs because the protons and neutrons are bound together in the nucleus and this binding reduces the overall energy of the 4 individual nucleons. Professor Einstein tells us that E = mc² and thus the energy reduction that occurs when the protons and neutrons are bound together inside the helium nucleus is equivalent to a mass loss. Your job here is to calculate how much energy (in units of MeV) is released when 2 protons and 2 neutrons are fused together to make ₂He⁴.

Data:

· Proton mass: 1.6726 x 10^-27 kg

· Neutron mass: 1.7749 x 10^-27 kg

· 2He4 mass: 6.6447 x 10^-27 kg

· 1 MeV: 1.602 x 10^-12 Joules

· Joule units: 1 J = 1 kg•m²/s²

· c: 3 x 10⁸ m/s

(Hint: Calculate the mass loss and multiply that value by c² to convert it to an energy in Joules. Then convert that to MeV)

Provocare in Mathematicam:

1. Let’s estimate roughly how much light the Milky Galaxy produces on Earth. Assume that the Milky Way is spherically shaped and that its radius is about 10,000 ly so that only those stars within about a 10,000 light year radius contribute to the light. Assume that the number density of stars is n_⨀ ~ 1 star / ly³ and that each of these stars puts out about the same amount of light as the Sun. The solar flux on Earth is about F_⨀= 1 KW / m². Assume that the flux from any star decreases as the inverse square of its distance R away from Earth, i.e.,

where R_⨀ = 1 AU = 16 x 10^-6 ly

Also assume that there is no gas and dust between the stars. Given these assumptions, calculate the total light flux F_MW produced by all the stars in the Milky Way. (Hint: See section 7.1 Olbers’ paradox) Ans: F_MW ~ 3 x 10^-5 F_⨀

2. Now let’s estimate how much light all the galaxies in the visible universe produce on Earth. There are about 100 x 10⁹ galaxies in the visible universe (whose radius is R_U = 13.7 x 10⁹ ly), which means that the number density of galaxies is about n_G ~ 10^-21 galaxies / ly³. Now assume that each of these galaxies produces about the same amount of light as the Milky Way and that the light flux from them decreases as its distance R from Earth increases—

where R_MW = 10,000 ly

Assume that the universe is static, i.e., not expanding and that there is no gas and dust between the galaxies. Calculate the total light flux F_U produced by all the galaxies in the visible universe. Ans: F_U ~ 5 x 10^-7 F_⨀

3. Now calculate the value R_U^*— how large the universe would have to be in order to generate the same light flux on Earth as does the Sun. Assume the same galactic number density as above. Ans: R_U^* ~ 2 x 10⁶ R_U

1000 - Word Essays:

1. If Hoyle’s Steady State Theory was correct and the Big Bang Theory was not, would that increase or decrease the odds that other intelligent civilizations would exist somewhere else in the universe? What would it imply about whether or not we should have evidence that they existed? Write a paper discussing this issue.

^{^[1]} Olbers' originally considered that individual stars were spread uniformly throughout space, not knowing that they were concentrated in galaxies.

^{^[2]} (See Focus Box 1)—the brightness B of stars (or light bulbs) decreases inversely with the square of distance away from the observer, i.e. B ~ 1 / R². Thus, if R doubles, the light flux from the source drops by a factor of 4.

^{^[3]} The number of stars in a shell is just the area of the shell 4πR² times the thickness ΔR times the density of stars n per unit volume of space, assumed to be the same everywhere on a large enough scale. Thus, if R doubles, the number of stars in the shell goes up by a factor of 4.

[4] Ironically, the poet, Edgar Allan Poe, might have been the first to propose what is essentially the modern day solution to Olbers’ paradox in his poem, Eureka: a Prose Poem in 1848— “Were the succession of stars endless, then the background of the sky would present us a uniform luminosity, like that displayed by the Galaxy —since there could be absolutely no point, in all that background, at which would not exist a star. The only mode, therefore, in which, under such a state of affairs, we could comprehend the voids which our telescopes find in innumerable directions, would be by supposing the distance of the invisible background so immense that no ray from it has yet been able to reach us at all.”

^{^[5]} The period of RR Lyrae, the archetype of these stars, is 13.6 hours.

[6] Alpha Centauri, our nearest neighbor, is actually part of a triple star system—Alpha Centauri A and B—and Proxima Centauri. Proxima is currently the nearest member of the group, about 4.2 ly away.

[7] The distance unit in Figure 13 is labeled Mpc, which stands for Megaparsec, or 10⁶ pc. The parsec (pc) is a unit of distance typically used in astronomy that we have not discussed—nor will we. Suffice it to say that 1 pc = 3.26 ly, 1 Mpc = 3.26 million light years!

[8] Radiation in this context means particles of light or photons. It comprises the electromagnetic entire spectrum from the most energetic gamma rays to the least energetic radio wave photons.

[9] Careful! Nothing travelled through space faster than the speed of light—the space between stuff expanded faster than the speed of light!

[10] Gluons are particles that mediate—or exert—the strong force that binds quarks together in structures to form protons and neutrons.

[11] Intermediate vector bosons behave like photons at very high temperatures, but they are particles with rest mass and behave differently at low temperatures where they mediate —or exert—the weak interaction force.

[12] Heavier nuclei do form in cataclysmic supernova explosions but they radioactively decay into lighter nuclei.

[13] Some form of dark energy might fill the universe, which would have the effect of accelerating its rate of expansion—se, for example, http://imagine.gsfc.nasa.gov/docs/science/mysteries_l1/dark_energy.html.