Chapter 7
Primordial
Matter

“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...”
“Here
is the letter that has destroyed my universe!”
7.1 Mommy—Why
Is It So Dark at Night?
Perhaps the most astonishing
feature of the night sky is its almost overwhelming darkness when seen on a
moonless night. This
feature is particularly surprising to the modern city
dweller who bravely ventures forth into remote deserts or high mountain peaks
away from the comforting womb of the bright lights and city streets that make
up humanity's ever expanding urban environment. The moonless night sky is
dark—really dark—interrupted every so often by the pinpoints of
light from a few relatively near bright stars or by the diffuse, white glow of
the Milky Way, like a thin fog lit by the headlights of an oncoming car. Why is
it so dark? This seemingly trivial question never occurs to most of us because
the answer is apparently so obvious—the Sun has set—the moon is
“new” and stars are the only thing that’s “out”
and there's not enough of them to provide any more light than we can see.
Perhaps if our solar system was closer to the galactic center or embedded in a
dense, globular cluster containing hundreds of thousands of stars, it might be
a lot brighter at night—but our solar system is where it is—in a
relatively star-free region of space, and so the night sky is dark.
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 20th 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.
Hubble estimated that the
distance to Andromeda was just under a million light years which put it well
outside the confines of the Milky Way. Hubble’s paper announcing this
result was read in his absence on New Year’s
Day 1925 at the meeting of the American Astronomical Society in Washington,
D.C. Shapley was present. The entire society of astronomers knew that the
debate had been decisively settled. In one swift stroke, Hubble had changed our
perception of the visible universe. Based on indisputable observation, the
universe was unquestionably far larger than anyone had yet deduced. There was
no question now—a new era in cosmology had begun—the Universe was a
very big place that was teaming with galaxies like the Milky Way. Hubble had
made what is arguably one of the three most important discoveries in 20th
century astronomy.
7.3 The
Scale of the Universe
Assuming that ET exists, it
will become increasingly apparent as we proceed through this text, that it is
not at all obvious that either of us will ever be able to find the other. To
appreciate this fact, it is worth making a quick guess at the distances that
are likely to separate ETs. The distances are enormous by human standards!
Scales used to measure the separations between locations on Earth (km) or even
locations within the solar system (AU) do them no justice. Any person can
travel between any two points on Earth within a day or two at most since the
distance that separates them is no more than 20,000 km and modern commercial
jets fly at speeds of about 1000 km / hr. However, the time it might take an ET
to travel to the site of its nearest neighbor could be as long as thousands of
years. Our Voyager II spacecraft, launched back in 1979—and now traveling
faster than any projectile ever launched from Earth—has just barely
cleared the outermost realm of the solar system and will take 100,000 years to
reach the nearest star. The distance to a star on the far side of the Milky Way
is 100,000 times further away than that! Such distance scales are by and large
unimaginable to the average person unless put in such terms.

The best way to visualize the
size of any structure is to scale it in terms of a standard of based upon
something of comparable size, that is, the standard should be neither
outrageously smaller nor larger than the size of the structure.
Figure 5 takes us out to the
remotest planets in our solar system—about 40 astronomical units (AU)
away from Earth—an unimaginable distance by our normal standards used to
measure distances on Earth. The Astronomical Unit (AU) is defined to be the
mean distance of
the Earth
from the Sun, about 150 x 10 6 km. Stating distances to the planets
in the solar system in units of km would be a bit like stating the height of a
human being in units of nanometers (about 2 x 10 9 nm). However, if
we list planetary distances using AU—the scale becomes
meaningful to
us. For example, our innermost planet, Mercury, is about 0.4 AU from the Sun
and the outermost planet, Neptune, is about 30 AU away. Light from the Sun
takes about 4 hours to reach Neptune. It took Voyager II about twelve years to
travel that far and a commercial jet would need about 100 years to make the
journey—better carry a lot of food!
![]()
We now look
outward through a field of stars containing the star, Alpha Centauri (Figure
6).[6]
The distance to Alpha Centauri is so great, about 280,000 AU or 40 trillion km,
that we need an entirely new scale—the Light Year
(ly)—to get a sense of it. A Light Year is the distance that
light, travelling
at 3 x 108 m/s, travels in one year. Alpha Centauri is 4.4 ly away.
If Voyager II, the spacecraft that left Earth in 1979, was heading directly
towards it, it would reach it sometime during the year 101,979, or 100,000
years from now!
Figure 7 shows us our home
galaxy—the Milky Way. We’re looking at it “edge on.”
Its diameter is about 100 Kly. Its “thickness” is about 1 Kly (Kilo,
or thousand, Light Years). We can see many individual stars,
clusters of stars and glowing clouds of gas and dust called nebulae. A lot of
gas and dust lies between the stars that is invisible to the human eye but can
be perceived by infrared, radio, ultraviolet and x-ray telescopes. There are
400 billion stars in the Milky Way and perhaps as many as 10 to 100 million
stars in a cube 1 Kly across. With any luck, ET might be living on a planet
going around one of them. But don't forget, it will take Voyager II 100,000
years just to travel to the nearest star and if there is only 1 ET somewhere
within this 1 Kly cube, they might be about 500 ly away—and if we knew
precisely where to go, a spaceship like Voyager II, would take several million
years to get there! Clearly, we have to do better than Voyager if we are to
visit ET in person—and equivalently, if ET wants to visit us,
she’ll have to do better, too—a lot better!

Figure 8 shows us our local
galactic neighborhood, called the Local Group, of which the Milky Way Galaxy is
a member. Two spiral galaxies, the Milky Way and Andromeda, are the two major
members of the Local Group. The distance to Andromeda is 2.5 Mly (Million
Light Years). If Voyager II had taken off for Andromeda at the
moment of the Big Bang, it would now be only about 1/5 of the way there!
Reaching another galaxy is out of the question for any spaceship operating with
any technology the future might bring—save some rather outlandish
possibilities we’ll mention in a later chapter dealing with space travel.
One final step takes us out to the remotest structures
in the universe that we can see (Figure 9)—clusters of galaxies as far
away as almost 13 Gly (Giga, or billion, Light Years). Our
Local Group is but one of many galactic clusters, all part of a larger group,
called the Virgo Supercluster. Larger
superclusters
may extend up to a Gly or so across. Such structures are the most distant we
can ever hope to see for another step outward would “remove us from the
universe” as we know it—not so much in the spatial sense
as in the time sense. It would take us so far away from Earth that light would
take longer to get here than the time the universe has existed! Distance scales
beyond 13.7 Gly are therefore meaningless.
This survey of the features
of our universe seen from different distance scales should give us a sense of
perspective regarding our place in the cosmos—we occupy a tiny speck in
the midst of a very, very large space.
7.4 The
Expanding Universe
By 1929, it
was known that the spiral nebulae were galaxies. Evidence for the expansion of
the universe was now sitting on Edwin Hubble’s desk—buried in the
measurements that he had used to ascertain the distance, size and brightness of
44 galaxies—and the velocities of each one of them, 39 of which had been
measured earlier by his colleague, Vesto Slipher. The velocities of the
galaxies had been measured with respect to the observer, who, of course, was
attached to planet Earth, which was whizzing around the Sun—which,
itself, was whizzing around the center of the Milky Way galaxy. Of all these
motions, the one that dominates is the speed of the Sun in orbit about the
galactic center. This value is about 220 km/s but it wasn’t yet known.
That is what Hubble wanted to measure. He assumed that all the galaxies ought
to be moving more or less in a random fashion relative to the Milky Way. The
Sun, in orbiting its center, ought to be approaching those galaxies along its
direction of travel and receding from those lying behind it. Thus, on the
average, the ones in front should have velocities toward the observer and the
ones in back should have velocities away from it. Hubble found only traces of
this effect for those galaxies that were relatively nearby. All the others
appeared to be moving away at remarkably large speeds. This astonished Hubble,
as it had astonished Slipher a decade earlier. It was almost as though the
Milky Way had once upon a time been the center of a titanic explosion that had
flung out all the galaxies, but since many of them were as big, or bigger, than
the Milky Way itself,
this notion
made no sense.
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
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.
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 20th
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
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
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 -52 m Temperature : >10 32 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 -35 s Radius : <10 -52 – 10 -50 m Temperature : 10 32 – 10 28 K
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 -12 s 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 10 28 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 10 28 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 -6 s 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 – 1 s 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 – 100 s Radius
: 137 light da – 1.2 ly Temperature : 1010 – 10 9
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
: 10 9– 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 – 3.8x10 5 yr Radius : 38,000 –
1.5x10 6 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 x10 9 yr Radius : 1.5x10 6 – 13.7 x10 9 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 3rd greatest discovery in astronomy of the 20th 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.

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
10 32 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 10 9 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.
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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 λ2max of the peak of the CMBR by multiplying the wavelength λ1max 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.,
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Data
· λ1max ~ 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•m 2/s 2
· c: 3 x 10 8 m/s
(Hint: Calculate the mass loss and multiply that value by c 2 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 / ly 3 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 / m 2. 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 FMW produced by all the stars
in the Milky Way. (Hint: See section 7.1 Olbers’ paradox) Ans: FMW
~ 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 10 9 galaxies in the visible universe (whose radius is RU = 13.7 x 10 9 ly), which means that the number density of galaxies is about nG ~ 10 -21 galaxies / ly 3. 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 RMW
= 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 FU produced by all the galaxies in the visible universe. Ans: FU ~ 5 x 10 -7 F⨀
3. Now calculate the value RU* — 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: RU* ~ 2 x 10 6 RU
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.