The observation of the expansion of the universe leads directly to
the conclusion that at some early time all the galaxies must have
been very much closer together.
Cosmology
Lecture #2
Paul Woodward
4/25/11
In fact, it is tempting to extrapolate this expanding motion
backward in time to a point when all the matter in the known
universe may have been located at the same place.
This line of thought leads to the “Big Bang” theory of the
evolution of the universe.
The idea is that at what we may call time zero, the entire universe
was contained in a single point, with zero spatial extent and
infinite energy density. In this idealized view, time zero was the
moment of creation (a moment science is careful to say nothing
about). Immediately afterward, the universe expanded, as if
from an enormous explosion.
Although scientists talk about this model, it is clear that no science
that we yet know makes any sense when all the matter of the
universe is located at a single point. This is what
mathematicians call a “singularity,” and in this context the word
is quite apt – all matter is at a single location.
Science that we know can perhaps begin to apply after the universe
has expanded enough to occupy just a little space.
Nevertheless the idea is that the cosmos – all of it – began as a
Nevertheless,
highly uniform blob of matter/energy, and that the structure that
we now see gradually emerged under the action of the physical
forces that we now experience, namely gravity,
electromagnetism, and the strong and weak nuclear forces.
Rather than extrapolate the positions of galaxies backward in time,
let’s start with a universe that is extremely small and essentially
homogeneous.
The most important measure of how small the universe is at any
given time, from the point of view of physics, is not its size but
instead the combination of its density and its temperature.
It is the temperature and the density of the universe that will
largely determine its physical state.
Clearly, the temperature and density start out very high. Infinitely
high, in fact, if we speak of the time zero.
On the next slide, from last year’s textbook, the temperature
history of a model of the universe is shown. It is a simple
power law. The temperature drops by a factor of 1030 as the
time increases by a factor of 1060. Thus for each quadrupling of
the time, the temperature drops by a factor of 2.
1
The picture we have of the development of structure in the universe
as it expands and cools is rather like a time-reversed version of
our earlier story of the evolution of the core of a massive star as it
collapses under its gravitational attraction and heats up.
At each state of heat and compression, certain reactions that we are
able to observe in experiments using powerful particle
accelerators are able to take place.
It does not make a lot of sense to talk about states of the universe
when it was, presumably, so hot and dense that our experiments
give absolutely no clue to what might have been going on.
Therefore we begin our story at a time of around 10-10 sec, when
in our model the temperature was about 1015 K.
Our experiments indicate that at extremely high temperatures, an
equilibrium is established between various forms of energy, be
they matter (remember Einstein’s formula, E = mc2) or radiation.
This equilibrium is established by reactions proceeding that
convert energy (a conserved quantity) from one form to the
other.
An example of such a reaction is shown on the next slide. This
reaction goes in two directions (“forward” and “backward”),
and an equilibrium is established when the populations of the
various forms of energy are such that there are, on the average,
as many forward reactions as backward ones.
At the top in the slide, the reaction is shown in which two gammaray photons collide, disappear, and an electron and a positron
appear in their place. In this reaction matter is created out of
pure energy. The positron is said to be the “antiparticle” of the
electron, because when this reaction runs backwards, as shown
at the bottom in the slide, the positron “annihilates” the electron
upon colliding with it, producing in the place of these two
material particles two gamma-ray photons (forms of pure,
radiant energy).
There are similar reactions that create (or annihilate) pairs of other
particles and antiparticles, such as protons and antiprotons.
At this stage, at the beginning of our story, we envision the
universe as a fairly uniform soup of particles and radiation in an
equilibrium mixture of very high density and temperature. This
first stage we will discuss is called in your textbook “the
particle era.”
positron
positron
At this stage particles were as numerous as photons, and
antiparticles were very nearly as numerous as particles.
Because of the very high temperature and density, these
particles included not only light particles like electrons and
neutrinos, but also rather heavy particles like quarks (the
building blocks of particles like protons and neutrons). When
the universe was about 0.1 msec old, the temperature had
grown too cold for free quarks to exist in equilibrium, and
they all became bound together in groups of 3 to form
protons and neutrons.
The binding of quarks in nucleons at around 0.1 msec is a process
that we can think of as akin to condensation. Below 100 ºC,
water molecules in the vapor phase bind together to form
droplets of water, and we no longer tend to find them by
themselves. It takes energy to get them out of their bound state
and into the gas phase again.
At room temperature on earth, quarks abound, but only extremely
tightly bound together in protons and neutrons. For us to verify
that protons and neutrons are actually made of quarks,
quarks we have
had to build extremely powerful particle accelerators so that we
could slam these particles together hard enough to break them
apart, so that the quarks could emerge.
In the very early universe, it was so hot that particles “routinely”
slammed together this hard, and therefore quarks were all over
the place. As the universe expanded and cooled, these
collisions got softer, so that quarks could no longer be dislodged
in this fashion.
2
Last year’s textbook sets the end of the particle era at about 1
msec (or 0.001 sec), when the temperature fell below 1012 K.
At this point, the universe was no longer hot enough for protonantiproton and neutron-antineutron pairs to be produced
copiously from radiant energy.
As a result, the protons and antiprotons annihilated each other to
produce photons, as did the neutrons and anitneutrons, etc. The
annihilation reactions were still p
permitted,, but the creation
reactions (the reverse of the annihilation ones) did not occur due
to the increasing dearth of sufficiently energetic photons. (The
photons produced by annihilations “cooled,” to become less
energetic, as the universe continued its expansion.)
At present, we believe that there are about a billion times more
photons in the universe than there are protons. Thus we
believe that near the end of the particle era protons must have
outnumbered antiprotons by about one part in a billion.
Last year’s textbook designates the time between 1 msec and 3
minutes as the era of nucleosynthesis.
During this interval, the temperature of the universe fell from
1012 K to 109 K.
During this era, fusion reactions involving protons and neutrons and
resulting in the production of helium nuclei proceeded. They
were balanced by fission reactions that broke the helium nuclei
apart again, with the equilibrium number of helium nuclei varying
over the course of this era
era, as the density and temperature
dropped.
At the end of the era of nucleosynthesis, when the universe was
about 3 minutes old and about a billion degrees hot, fusion of
helium nuclei ceased (it could have continued at this temperature, had the density been high enough, but we think it wasn’t).
Figure 22.2 This diagram summarizes the era of the universe. The names of the
eras and their ending times are indicated on the left, and the state of matter during
each era and the events marking the end of each era are indicated on the right.
As we discussed in the context of the formation of neutron stars and
the supernova explosions of massive stars, it takes energy to get
an electron and a proton to fuse into a neutron.
So long as the universe was hotter than 1011 K, the proton-toneutron reactions went both ways, and the numbers of protons
and neutrons were very closely equal.
However, as the universe cooled, the neutron-to-proton direction was
favored, since it released energy.
Once the temperature fell below 1010 K, neutrons ceased to be
produced and they continued to be transformed into protons.
At the end of this era, the universe was left with 75% of its mass in
the form of hydrogen nuclei and 25% in the form of helium
nuclei, with trace amounts of deuterium and lithium nuclei.
Fusion reactions that bound protons and neutrons into deuterium
nuclei, and ultimately into helium nuclei proceeded throughout the
era of nucleosynthesis. But the helium nuclei were broken apart by
gamma rays. However, once the universe was 1 minute old,
these gamma rays were gone, and the helium nuclei stayed fused.
We believe that the proton-to-neutron ratio at this time was 7-to-1.
Figure 22.9 During the era of nucleosynthesis, virtually all the
neutrons in the universe fused with protons to form helium-4. This
figure illustrates one of several possible reaction pathways.
In step 1, a neutron and a proton fuse to form a deuterium nucleus,
releasing a photon. In step 2, two deuterium nuclei fuse to form
hydrogen-3, releasing a proton. In step 3, the hydrogen-3 nucleus
fuses with deuterium to create helium-4, releasing one of the
neutrons.
Figure 22.10 During helium synthesis, protons outnumbered neutrons 7 to 1, which is
the same as 14 to 2. The result was 12 hydrogen nuclei (individual protons) for each
helium nucleus. Thus, the hydrogen-to-helium mass ratio is 12 to 4, or 75% to 25%.
3
Last year’s textbook designates the time between 3 minutes and
300,000 years as the era of nuclei.
During this interval, the temperature of the universe fell from
109 K to 3000 K.
During this era, the universe consisted of a plasma of hydrogen
and helium nuclei and free electrons. The photons were
scattered by the electrons, and were not able to travel far
without hitting
g one and beingg deflected. Whenever a nucleus
managed to combine with an electron to form an atom, it was
immediately re-ionized by one of the many energetic photons.
This era of nuclei came to an end when the temperature fell to
about 3000 K, roughly half the temperature of the Sun’s surface
today. At this point, when the universe was about 300,000 years
old, the hydrogen and helium nuclei permanently captured
electrons to form atoms. The photons, due to the expansion and
cooling, were no longer able to ionize these atoms.
Because the electrons were now bound up in electrically neutral
atoms, the photons could now travel great distances without
interacting with the matter. The universe was now essentially
transparent to the photons. These photons, we believe, have
streamed through the universe ever since, gradually cooling as
the universe expanded, so that their temperature (they have a
black body spectrum) is now 2.73 K.
Once the atoms formed, the formation of stars and galaxies
f ll
followed,
d according
di tto th
the th
theoretical
ti l id
ideas andd scenarios
i that
th t
we have discussed in earlier lectures.
A recent glitch on this scenario is that the starburst episodes upon
initial star and galaxy formation reionized the universe briefly.
It is not clear why this is a big deal. Perhaps it isn’t.
Researchers in this area have rather little that they can say with
any authority. This new item is at least something, and
everyone presently agrees on it.
Figure 22.6 Photons frequently collided with free electrons during the era of nuclei and thus could travel freely only
after electrons became bound into atoms. The photons released at the end of the era of nuclei make up the cosmic
background radiation.
In 1965, Arno Penzias and Robert Wilson were calibrating a
sensitive microwave antenna at Bell Labs in New Jersey. The
antenna was designed for satellite communications. They found
that wherever they looked with this antenna, and whatever they
did, there was a base level of noise. This noise was uniform
over the entire sky.
On an airline trip home from an astronomical meeting, Penzias sat
next to an astronomer who told him of the work at Princeton
(
(near
Bell
B ll Labs’
L b ’ Holmdel
H l d l site)
it ) that
th t suggested
t d that
th t the
th radiation
di ti
freed from its interaction with matter at the end of the era of
nuclei in the Big Bang model should be observable with a
microwave antenna.
Figure 22.2 This diagram summarizes the era of the universe. The names of the eras and their ending times are indicated
on the left, and the state of matter during each era and the events marking the end of each era are indicated on the right.
The result was a Nobel Prize for Penzias and Wilson, although it
seems to me that the Princeton astronomers deserved to share in
this glory. Discoveries are useless unless one recognizes their
proper significance. For example, just think of the difference
between Eric the Red’s discovery of America and Columbus’.
4
Figure 22.5 Arno Penzias and
Robert Wilson with the Bell Labs
microwave antenna.
For over a decade, astronomers labored to measure the spectrum of
the “cosmic microwave background radiation,” as it is called.
Penzias and Wilson had derived a temperature of 3 K for this
radiation by assuming that it had a black body spectrum. But the
critical portions of this black body spectrum lay in wavelength
bands where the Earth’s atmosphere is essentially opaque.
Attempts to verify the black-body nature of this radiation therefore
involved placing observing stations on very high mountains, etc.
It was nott until
til recently,
tl after
ft NASA putt up the
th COBE satellite
t llit
(Cosmic Background Explorer), that the spectrum of this
background radiation could unequivocally be measured. It is
shown on the next slide. It fits the theoretical black body curve
beautifully.
To observe this radiation is to look at the opaque surface of the
nearly uniform universe at the end of the era of nuclei. This is
the most distant sight we can now see. It is redshifted all the way
from 3000 K to 3 K, since it is so far away.
Figure 22.7 Spectrum of the cosmic background radiation from COBE. A theoretically calculated
thermal radiation spectrum (smooth curve) for a temperature of 2.73ºK perfectly fits the data (dots).
The COBE satellite was able to map extremely slight temperature
variations in the cosmic background radiation in different
directions. These variations are only a few parts in 100,000.
These variations show that the temperature (and therefore the
density also) in the 300,000-year-old universe varied slightly
from place to place, as we require in order to seed the formation
of galaxies and galaxy clusters in later eras.
y COBE are not large
g enough
g to
However,, the variations detected by
produce galaxies, we believe, in only a billion years. This is a
major problem.
One possible way around this problem is to assume that the
variations in the density of the matter that interacted with light
(that is, in luminous matter, or hydrogen and helium nuclei and
electrons) were only faint tracers for much larger variations in
WIMP dark matter that did not interact with light.
Oh well, there’s still lots of work for astronomers to do.
Figure 22.8 This all-sky map shows temperature differences in the cosmic background
radiation measured by COBE. The background temperature is about 2.73ºK
everywhere, but the brighter regions of this picture are slightly less than 0.0001ºK
hotter than the darker regions – indicating that the early universe was very slightly
lumpy. We are essentially seeing what the universe was like at the surface marked
“300,000 years” in Figure 22.2. (The central strip of this map, which corresponds to the
disk of the Milky Way, has been masked out because the brightness differences there
stem primarily from radio noise in the Milky Way.)
5
The most fashionable theoretical scenario today is to assume the
existence of dark matter that not only does not emit light but
also does not interact with light (does not absorb light).
At a very early era, this dark matter and normal matter might share
roughly the same distribution in space, with density variations
of comparable amplitudes on comparable length scales.
But the interaction of the normal matter with light radiation will
g , which finds the normal matter opaque,
p q , to
cause the light,
smooth out the spatial distribution as it scatters off of this
normal matter.
However, the distribution of dark matter will remain clumpy, as
illustrated on the following diagram from your textbook.
The distribution of normal matter is
smoothed out by its interaction with
light radiation, while dark matter is
unaffected.
The density variations in the dark matter are amplified by gravity
and can act as seeds for gravitational collapse of normal matter.
The dark matter cannot collapse to extreme density contrasts, since
it cannot radiate its kinetic energy away as light.
The normal matter that accumulates in the gravitational wells
formed by clumps of dark matter can, once the universe has
expanded and cooled enough, radiate its kinetic energy away as
light.
g
Therefore the normal matter can form stars and galaxies, and this
process can happen fast enough, since the earlier accumulations
of dark matter help the accumulation of normal matter to get
started.
Well, it’s a scenario.
In 20 years, we could have an altogether different scenario as the
conventional wisdom.
Dark matter clumps, amplified by gravity, seed the collapse of normal matter,
which can radiate away its kinetic energy and grow very, very dense.
Your textbook lists some problems with the fairly standard picture
of the evolution of the universe that I have just presented:
Your textbook suggests that the theory of inflation can perhaps
solve these problems.
1. What about the neutrinos left over from the proton-to-neutron
conversion reactions in the era of nucleosynthesis? There
should be about 100 of these in every cubic centimeter of the
universe today. If these neutrinos weigh even one ten
thousandth of the weight of an electron, then they are the
dominant form of mass in the universe.
The theory of inflation says that shortly after the big bang
(between 10-36 and 10-33 seconds) there was a tremendously
rapid phase of expansion, with the universe growing by a
factor between 1050 and 1078 from a truly minute size to the
size of either a grapefruit or possibly even that of a pumpkin.
2. Why more matter than antimatter?
If there were regions of one or the other, we should see the
gamma rays from annihilations at their boundaries.
3. Where did the density fluctuations in the universe that we see
from the cosmic background radiation come from?
4. Why was the universe at age 300,000 years so smooth?
How could the different regions communicate in order to agree
on a common temperature?
This inflation was caused by a repulsive force,
force allowable in
Einstein’s theory of general relativity through the introduction
of something called a “cosmological constant.”
Einstein referred to the cosmological constant as the greatest
mistake of his life.
You should make your own judgment.
6
Inflation is said to have taken place before any matter formed out
of the pure energy of the early universe. This energetic void is
said to have expanded faster than the speed of light, which is
necessary for regions that were once together at the same point
to become separated so that they can no longer communicate
until they eventually rediscover each other as their horizons
expand (at the speed of light).
The fact that all parts of the universe were once a single point
explains why the universe is so smooth (devoid of features) on
very large scales that have not, as yet, had time to
communicate by sending light at each other.
It also explains why those large regions still need to wait so that
they can see each other using light rays that require billions of
years to cross from one region to another.
Are you confused yet? You are not alone.
The inflation theory resolves impossible conundrums by
introducing new and more arcane impossible conundrums.
Few mortals understand it, which is very convenient.
But it’s in all the textbooks, because, after all, what else has
anyone got to say?
Inflation also somehow produced temperature fluctuations with the
property that they have about the same amplitude on all length
scales. This property is very helpful in forming galaxies and
clusters of galaxies as we see them today. Without this aspect
of inflation, galaxies would not have had time to form yet by
the simple action of gravity, we think.
Observations of the cosmic microwave background are said to
support the inflation theory, but this is circular reasoning, since
it was these observations that motivated the theory.
7
In early 2003, the Wilkinson Microwave Anisotropy Probe
(WMAP) mapped the slight variations in the temperature of the
cosmic microwave background radiation, producing the map on
the next slide.
Computer simulations based upon Einstein’s theory of general
relativity match the observations, in a statistical sense, with
a flat universe (paths of light rays are straight) composed of
•
4% ordinary atoms,
•
23% dark matter,
•
73% dark energy (which has an anit-gravity effect that
speeds up the expansion of the universe over time).
In this model, the universe is 13.7 billion years old, and the
first stars turned on just 200 million years after the big
bang.
Expect these numbers to change as our theories become better.
Map of variations in the temperature of the 2.73 K cosmic
microwave background radiation. Map made by the Wilkinson
Microwave Anisotropy Probe (WMAP), 2003.
Temperature fluctuations of millionths of a degree are resolved.
A computerdrawn portrait of
the WMAP
spacecraft,
which made its
observations at
the L2
Lagrangian point
of the EarthMoon system.
8