Anthropic Principle

Anthropic Principle :
In the past 20 years our understanding of physics and biology has noted a peculiar specialness
to our Universe, a specialness with regard to the existence of intelligent life. This sends up
warning signs from the Copernican Principle, the idea that no scientific theory should invoke a
special place or aspect to humans.
All the laws of Nature have particular constants associated with them, the gravitational
constant, the speed of light, the electric charge, the mass of the electron, Planck's constant
from quantum mechanics. Some are derived from physical laws (the speed of light, for
example, comes from Maxwell's equations). However, for most, their values are arbitrary. The
laws would still operate if the constants had different values, although the resulting
interactions would be radically different.
Examples:
gravitational constant: Determines strength of gravity. If lower than stars would have
insufficient pressure to overcome Coulomb barrier to start thermonuclear fusion (i.e. stars
would not shine). If higher, stars burn too fast, use up fuel before life has a chance to
evolve.
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strong force coupling constant: Holds particles together in nucleus of atom. If weaker
than multi-proton particles would not hold together, hydrogen would be the only element
in the Universe. If stronger, all elements lighter than iron would be rare. Also radioactive
decay would be less, which heats core of Earth.
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electromagnetic coupling constant: Determines strength of electromagnetic force that
couples electrons to nucleus. If less, than no electrons held in orbit. If stronger, electrons
will not bond with other atoms. Either way, no molecules.
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All the above constants are critical to the formation of the basic building blocks of life. And,
the range of possible values for these constants is very narrow, only about 1 to 5% for the
combination of constants.

It is therefore possible to imagine whole different kinds of universes with different constants.
For example, a universe with a lower gravitational constant would have a weaker force of
gravity, where stars and planets might not form. Or a universe with a high strong force which
would inhibit thermonuclear fusion, which would make the luminosity of stars be much lower,
a darker universe, and life would have to evolve without sunlight.
The situation became worst with the cosmological discoveries of the 1980's. The two key
cosmological parameters are the cosmic expansion rate (Hubble's constant, which determines
the age of the Universe) and the cosmic density parameter ( ), which determines the
acceleration of the Universe and its geometry).
The flatness problem relates to the density parameter of the Universe, . Values for can
take on any number, but it has to be between 0.01 and 5. If is less than 0.01 the Universe is
expanding so fast that the Solar System flys apart. And has to be less than 5 or the Universe
is younger than the oldest rocks. The measured value is near 0.2. This is close to an of 1,
which is strange because of 1 is an unstable critical point for the geometry of the Universe.

Values slightly below or above 1 in the early Universe rapidly grow to much less than 1 or
much larger than 1 (like a ball at the top of a hill). So the fact that the measured value of 0.2 is
so close to 1 that we expect to find in the future that our measured value is too low and that the
Universe has a value of exactly equal to 1 for stability.
This dilemma of the extremely narrow range of values for physical constants is allowed for the
evolution of conscious creatures, such as ourselves, is called the anthropic principle, and has
the form:
Anthropic Principle: The Universe must have those properties which allow life to develop
within it at some stage in its history.
There are three possible alternatives from the anthropic principle;
There exists one possible Universe `designed' with the goal of generating and sustaining
`observers' (theological universe). Or...
1.
2. Observers are necessary to bring the Universe into being (participatory universe). Or...
An ensemble of other different universes is necessary for the existence of our Universe
(multiple universes)
Anthropic Principle and Circular Reasoning :
The usual criticism of any form of the anthropic principle is that it is guilty of a tautology or
circular reasoning.

With the respect to our existence and the Universe, the error in reasoning is that because we
are here, it must be possible that we can be here. In other words, we exist to ask the question
of the anthropic principle. If we didn't exist then the question could not be asked. So there is
nothing special to the anthropic principle, it simply states we exist to ask questions about the
Universe.
An example of this style of question is whether life is unique to the Earth. There are many
special qualities to the Earth (proper mass, distance from Sun for liquid water, position in
Galaxy for heavy elements from nearby supernova explosion). But, none of these
characteristics are unique to the Earth. There may exists hundreds to thousands of solar
systems with similar characteristics where life would be possible, if not inevitable. We simply
live on one of them, and we would not be capable of living on any other world.
This solution is mildly unsatisfying with respect to physical constants since it implies some
sort-of lottery system for the existence of life, and we have no evidence of previous Universes
for the randomness to take place.

Anthropic Principle and Many-Worlds Hypothesis

Anthropic Principle and Many-Worlds Hypothesis:
Another solution to the anthropic principle is that all possible universes, that can be imagined
under the current laws of Nature, are possible and do have an existence as quantum

This is the infamous many-worlds hypothesis used to explain how the position of an electron
can be fuzzy or uncertainty. Its not uncertain, it actual exists in all possible positions, each one
having its own separate and unique universe. Quantum reality is explained by the using of
infinite numbers of universes where every possible realization of position and energy of every
particle actually exists.

With respect to the anthropic principle, we simply exist in one of the many universes where
intelligent life is possible and did evolve. There are many other universes where this is not the
case, existing side by side with us in some super-reality of the many-worlds. Since the
many-worlds hypothesis lacks the ability to test the existence of these other universes, it is not
falsifiable and, therefore, borders on pseudo-science.

Anthropic Principle and Inflation

Anthropic Principle and Inflation :
Another avenue to understanding the anthropic principle is through inflation. Inflation theory
shows that the fraction of the volume of the Universe with given properties does not depend
on time. Each part evolves with time, but the Universe as a whole may be stationary and the
properties of the parts do not depend on the initial conditions.
During the inflation era, the Universe becomes divided into exponentially large domains
containing matter in all possible `phases'. The distribution of volumes of different domains
may provide some possibility to find the ``most probable'' values for universal constants.
When the Universe inflated, these different domains separated, each with its own values for
physical constants.

Inflation's answer to the anthropic principle is that multiple universes were created from the
Big Bang. Our Universe had the appropriate physical constants that lead to the evolution of
intelligent life. However, that evolution was not determined or required. There may exist many
other universes with similar conditions, but where the emergent property of life or intelligence
did not develop.
Hopefully a complete Theory of Everything will resolve the `how' questions on the origin of
physical constants. But a complete physical theory may be lacking the answers to `why'
questions, which is one of the reasons that modern science is in a crisis phase of development,
our ability to understand `how' has outpaced our ability to answer if we `should'.

GUT matter

GUT matter :
Spacetime arrives when supergravity separates into the combined nuclear forces (strong, weak,
electromagnetic) and gravitation. Matter makes its first appearance during this era as a composite form
called Grand Unified Theory or GUT matter. GUT matter is a combination of what will become leptons,
quarks and photons. In other words, it contains all the superpositions of future normal matter. But, during
the GUT era, it is too hot and violent for matter to survive in the form of leptons and quarks.
Why can't matter remain stable at this point in the Universe's evolution? This involves the concept of
equilibrium, the balance between particle creation and annihilation.

During pair production, energy is converted directly into mass in the form of a matter and anti-matter
particle pair. The simplest particles are, of course, leptons such as an electron/positron pair. However, in
high energy regimes, such as the early Universe, the conversion from energy to mass is unstable compared
to the more probable mass to energy conversion (because the created mass must be so high in mass to
match the energy used). In other words, when temperatures are high, matter is unstable and energy is
stable.
Any matter that forms in the early Universe quickly collides with other matter or energy and is converted
back into energy. The matter is in equilibrium with the surrounding energy and at this time the Universe is
energy or radiation-dominated.
The type of matter that is created is dependent on the energy of its surroundings. Since the temperatures are
so high in the early Universe, only very massive matter (= high energy) can form. However, massive
particles are also unstable particles. As the Universe expands and cools, more stable, less massive forms of
matter form.

As the Universe expands, matter is able to exist for longer periods of time without being broken down by
energy. Eventually quarks and leptons are free to combine and form protons, neutrons and atoms, the
ordinary matter of today.

Quarks and Leptons

Quarks and Leptons :
After GUT matter forms, the next phase is for GUT matter to decay into lepton and quark matter. Lepton
matter will become our old friends the electron and neutrino (and their anti-particles). But quark matter is
unusual because of the property of quark confinement.
Quarks can never be found in isolation because the strong force becomes stronger with distance. Any
attempt to separate pairs or triplets of quarks requires large amounts of energy, which are used to produce
new groups of quarks.

With so much energy available in the early Universe, the endresult is a runaway production of quark and
anti-quark pairs. Trillions of times the amounts we currently see in the Universe. The resulting soup of
quark pairs will eventually suffer massive annihilation of its matter and anti-matter sides as soon as the
Universe expands and cools sufficiently for quark production to stop.
Notice that quark pairs are more stable than triplets, so that most of the quark production is done in pairs.
Later, pairs will interact to form triplets, which are called baryons.

Baryongenesis

Baryongenesis :
As the Universe cools a weak asymmetry in the direction towards matter becomes evident. Matter that is
massive is unstable, particularly at the high temperature in the early Universe. Low mass matter is stable,
but susceptible to destruction by high energy radiation (photons).

As the volume of the Universe increases, the lifetime of stable matter (its time between collisions with
photons) increases. This also means that the time available for matter to interact with matter also increases.

The Universe evolves from a pure, energy dominated domain to a more disordered, matter dominated
domain, i.e. entropy marches on.

The last two stages of matter construction is the combining of three quark groups into baryons (protons and
neutrons), then the collection of electrons by proton/neutron atomic nuclei to form atoms. The construction
of baryons is called baryongenesis.
Baryongenesis begins around 1 second after the Big Bang. The equilibrium process at work is the balance
between the strong force binding quarks into protons and neutrons versus the splitting of quark pairs into
new quark pairs. When the temperature of the Universe drops to the point that there is not enough energy
to form new quarks, the current quarks are able to link into stable triplets.

As all the anti-particles annihilate by colliding with their matter counterparts (leaving the small percentage
of matter particles, see next lecture) leaving the remaining particles in the Universe to be photons,
electrons, protons and neutrons. All quark pairs have reformed into baryons (protons and neutrons). Only
around exotic objects, like black holes, do we find any anti-matter or mesons (quark pairs) or any of the
other strange matter that was once found throughout the early Universe.
Soon after the second symmetry breaking (the GUT era), there is still lots of energy available to produce
matter by pair production, rather than quark confinement. However, the densities are so high that every
matter and anti-matter particle produced is soon destroyed by collisions with other particles, in a cycle of
equilibrium.

Note that this process (and quark confinement) produces an equal number of matter and anti-matter
particles, and that any particular time, if the process of pair production or quark confinement were to stop,
then all matter and anti-matter would eventual collide and the Universe will be composed only of photons.
In other words, since there are equal numbers of matter and anti-matter particles created by pair
production, then why is the Universe made mostly of matter? Anti-matter is extremely rare at the present
time, yet matter is very abundant.
This asymmetry is called the matter/anti-matter puzzle. Why if particles are created symmetrically as
matter and anti-matter does matter dominate the Universe today. In theory, all the matter and anti-matter
should have canceled out and the Universe should be a ocean of photons.

It is not the case that the Universe is only filled with photons (look around the room). And it is not the case
that 1/2 the Universe is matter and the other half is anti-matter (there would be alot of explosions).
Therefore, some mechanism produced more matter particle than anti-matter particles. How strong was this
asymmetry? We can't go back in time and count the number of matter/anti-matter pairs, but we can count
the number of cosmic background photons that remain after the annihilations. That counting yields a value
of 1 matter particle for every 1010 photons, which means the asymmetry between matter and anti-matter
was only 1 part in 10,000,000,000.
This means that for every 10,000,000,000 anti-matter particles there are 10,000,000,001 matter particles,
an asymmetry of 1 particle out of 10 billion. And the endresult is that every 10 billion matter/anti-matter
pairs annihilated each other leaving behind 1 matter particle and 10 billion photons that make up the
cosmic background radiation, the echo of the Big Bang we measure today. This ratio of matter to photons
is called the baryon number.

Even though the baryon number is extremely small (10-10) why isn't it zero? In Nature, there are only three
natural numbers, 0, 1 and infinity. All other numbers require explanation. What caused the asymmetry of
even one extra matter particle for every 10 billion matter/anti-matter pairs?
One answer is that the asymmetry occurs because the Universe is out of equilibrium. This is clearly true
because the Universe is expanding, and a dynamic thing is out of equilibrium (only static things are stable).
And there are particular points in the history of the Universe when the system is out of equilibrium, the
symmetry breaking moments. Notice also that during the inflation era, any asymmetries in the microscopic
world would be magnified into the macroscopic world. One such quantum asymmetry is CP violation.
CP Violation:
As the Universe expands and cools and the process of creation and annihilation of matter/anti-matter pairs
slows down. Soon matter and anti-matter has time to undergo other nuclear processes, such as nuclear
decay. Many exotic particles, massive bosons or mesons, can undergo decay into smaller particles. If the
Universe is out of equilibrium, then the decay process, fixed by the emergent laws of Nature, can become
out of balance if there exists some asymmetry in the rules of particle interactions. This would result in the
production of extra matter particles, rather than equal numbers of matter and anti-matter.
In the quantum world, there are large numbers of symmetric relationships. For example, there is the
symmetry between matter and anti-matter. For every matter particle, there is a corresponding anti-matter
particle of opposite charge. In the 1960's, it was found that some types of particles did not conserve left or
right-handedness during their decay into other particles. This property, called parity, was found to be
broken in a small number of interactions at the same time the charge symmetry was also broken and
became known as CP violation.

The symmetry is restored when particle interactions are considered under the global CPT rule (charge -
parity - time reversal), which states that that a particle and its anti-particle may be different, but will behave
the same in a mirror-reflected, time-reversed study. During the inflation era, the rapid expansion of
spacetime would have thrown the T in CPT symmetry out of balance, and the CP violation would have
produced a small asymmetry in the baryon number.
This is another example of how quantum effects can be magnified to produce large consequences in the
macroscopic world.

Nucleosynthesis

Nucleosynthesis:
The Universe is now 1 minute old, and all the anti-matter has been destroyed by
annihilation with matter. The leftover matter is in the form of electrons, protons and
neutrons. As the temperature continues to drop, protons and neutrons can undergo fusion
to form heavier atomic nuclei. This process is called nucleosynthesis.

Its harder and harder to make nuclei with higher masses. So the most common substance
in the Universe is hydrogen (one proton), followed by helium, lithium, beryllium and
boron (the first elements on the periodic table). Isotopes are formed, such as deuterium
and tritium, but these elements are unstable and decay into free protons and neutrons.

Note that this above diagram refers to the density parameter, Omega, of baryons, which is
close to 0.1. However, much of the Universe is in the form of dark matter (see later
lecture).
A key point is that the ratio of hydrogen to helium is extremely sensitive to the density of
matter in the Universe (the parameter that determines if the Universe is open, flat or
closed). The higher the density, the more helium produced during the nucleosynthesis era.
The current measurements indicate that 75% of the mass of the Universe is in the form of
hydrogen, 24% in the form of helium and the remaining 1% in the rest of the periodic
table (note that your body is made mostly of these `trace' elements). Note that since
helium is 4 times the mass of hydrogen, the number of hydrogen atoms is 90% and the
number of helium atoms is 9% of the total number of atoms in the Universe.

There are over 100 naturally occurring elements in the Universe and classification makes
up the periodic table. The very lightest elements are made in the early Universe. The
elements between boron and iron (atomic number 26) are made in the cores of stars by
thermonuclear fusion, the power source for all stars.
The fusion process produces energy, which keeps the temperature of a stellar core high to
keep the reaction rates high. The fusing of new elements is balanced by the destruction of
nuclei by high energy gamma-rays. Gamma-rays in a stellar core are capable of disrupting
nuclei, emitting free protons and neutrons. If the reaction rates are high, then a net flux of
energy is produced.
Fusion of elements with atomic numbers (the number of protons) greater than 26 uses up
more energy than is produced by the reaction. Thus, elements heavier than iron cannot be
fuel sources in stars. And, likewise, elements heavier than iron are not produced in stars,
so what is their origin?.

The construction of elements heavier than involves nucleosynthesis by neutron capture. A
nuclei can capture or fuse with a neutron because the neutron is electrically neutral and,
therefore, not repulsed like the proton. In everyday life, free neutrons are rare because
they have short half-life's before they radioactively decay. Each neutron capture produces
an isotope, some are stable, some are unstable. Unstable isotopes will decay by emitting a
positron and a neutrino to make a new element.

Neutron capture can happen by two methods, the s and r-processes, where s and r stand
for slow and rapid. The s-process happens in the inert carbon core of a star, the slow
capture of neutrons. The s-process works as long as the decay time for unstable isotopes is
longer than the capture time. Up to the element bismuth (atomic number 83), the s-process
works, but above this point the more massive nuclei that can be built from bismuth are
unstable.
The second process, the r-process, is what is used to produce very heavy, neutron rich
nuclei. Here the capture of neutrons happens in such a dense environment that the
unstable isotopes do not have time to decay. The high density of neutrons needed is only
found during a supernova explosion and, thus, all the heavy elements in the Universe
(radium, uranium and plutonium) are produced this way. The supernova explosion also
has the side benefit of propelling the new created elements into space to seed molecular
clouds which will form new stars and solar systems.
Ionization:
The last stage in matter production is when the Universe cools sufficiently for electrons to
combine with the proton/neutron nuclei and form atoms. Constant impacts by photons
knock electrons off of atoms which is called ionization. Lower temperatures mean
photons with less energy and fewer collisions. Thus, atoms become stable at about 15
minutes after the Big Bang.

These atoms are now free to bond together to form simple compounds, molecules, etc.
And these are the building blocks for galaxies and stars.

Radiation/Matter Dominance

Radiation/Matter Dominance :
Even after the annihilation of anti-matter and the formation of protons, neutrons and
electrons, the Universe is still a violent and extremely active environment. The photons
created by the matter/anti-matter annihilation epoch exist in vast numbers and have
energies at the x-ray level.
Radiation, in the form of photons, and matter, in the form of protons, neutrons and
electron, can interact by the process of scattering. Photons bounce off of elementary
particles, much like billiard balls. The energy of the photons is transfered to the matter
particles. The distance a photon can travel before hitting a matter particle is called the
mean free path.

Since matter and photons were in constant contact, their temperatures were the same, a
process called thermalization. Note also that the matter can not clump together by gravity.
The impacts by photons keep the matter particles apart and smoothly distributed.
The density and the temperature for the Universe continues to drop as it expands. At some
point about 15 minutes after the Big Bang, the temperature has dropped to the point where
ionization no longer takes places. Neutral atoms can form, atomic nuclei surround by
electron clouds. The number of free particles drops by a large fraction (all the protons,
neutrons and electron form atoms). And suddenly the photons are free to travel without
collisions, this is called decoupling.

The Universe becomes transparent at this point. Before this epoch, a photon couldn't
travel more that a few inches before a collision. So an observers line-of-sight was only a
few inches and the Universe was opaque, matter and radiation were coupled. This is the
transition from the radiation era to the matter era.

Density Fluctuations

Density Fluctuations:
The time of neutral atom construction is called recombination, this is also the first epoch
we can observe in the Universe. Before recombination, the Universe was too dense and
opaque. After recombination, photons are free to travel through all of space. Thus, the
limit to our observable Universe is back in time (outward in space) to the moment of
recombination.

The time of recombination is also where the linked behavior between photons and matter
decouples or breaks, and is also the last epoch where radiation traces the mass density.
Photon/matter collisions become rare and the evolution of the Universe is dominated by
the behavior of matter (i.e. gravity), so this time, and until today, is called the matter era.
Today, radiation in the form of photons have a very passive role in the evolution of the
Universe. They only serve to illuminate matter in the far reaches of the Galaxy and other
galaxies. Matter, on the other hand, is free to interact without being jousted by photons.
Matter becomes the organizational element of the Universe, and its controlling force is
gravity.
Notice that as the Universe ages it moves to more stable elements. High energy radiation
(photons) are unstable in their interactions with matter. But, as matter condenses out of
the cooling Universe, a more stable epoch is entered, one where the slow, gentle force of
gravity dominates over the nuclear forces of earlier times.
Much of the hydrogen that was created at recombination was used up in the formation of
galaxies, and converted into stars. There is very little reminant hydrogen between
galaxies, the so-called intergalactic medium, except in clusters of galaxies. Clusters of
galaxies frequently have a hot hydrogen gas surrounding the core, this is leftover gas from
the formation of the cluster galaxies that has been heated by the motions of the cluster
members.
Baryon Fraction:
The amount of hydrogen in the Universe today, either in stars and galaxies, or hot gas between galaxies, is called the
baryon fraction. The current measurements indicate that the baryon fraction is about 3% (0.03) the value of closure for
the Universe (the critical density). Remember the value from the abundance of light elements is 10% (0.10) the closure
value.

The most immediate result here is that the mass density of the Universe appears to be much less than the closure value,
i.e. we live in an open Universe. However, the inflation model demands that we live in a Universe with exactly the
critical density, Omega of 1. This can only be true if about 90% of the mass of the Universe is not in baryons.

Neutrinos

Neutrinos :
There are two types of leptons, the electron and the neutrino. The neutrino is a strange particle, not discovered directly,
but by inference from the decay of other particles by Wolfgang Pauli in 1930. It has no charge and a very small mass. It
interacts with other particles only through the weak force (i.e. it is immune to the strong and electromagnetic forces). The
weak force is so weak, that a neutrino can pass through several Earth's of lead with only a 50/50 chance of interacting
with an atom, i.e. they are effectively transparent to matter.
The weakly interacting nature of neutrinos makes them very difficult to detect, and therefore measure, in experiments.
Plus, the only sources of large amounts of neutrinos are high energy events such as supernova, relics from the early
Universe and nuclear power plants. However, they are extremely important to our understanding of nuclear reactions
since pratically every fusion reaction produces a neutrino. In fact, a majority of the energy produced by stars and
supernova are carried away in the form of neutrinos (the Sun produces 100 trillion trillion trillion neutrinos every
second).
Detecting neutrinos from the Sun was an obvious first experiment to measure neutrinos. The pioneering experiment was
Ray Davis's 600 tonne chlorine tank (actually dry cleaning fluid) in the Homestake mine, South Dakota. His experiment,
begun in 1967, found evidence for only one third of the expected number of neutrino events. A light water Cherenkov
experiment at Kamioka, Japan, upgraded to detect solar netrinos in 1986, finds one half of the expected events for the
part of the solar neutrino spectrum for which they are sensitive. Two recent gallium detectors (SAGE and GALLEX),
which have lower energy thresholds, find about 60-70% of the expected rate.

The clear trend is that the measured flux is found to be dramatically less than is possible for our present understanding of
the reaction processes in stars. There are two possible answers to this problem: 1) The structure and constitution of stars,
and hence the reaction mechanisms are not correctly understood (this would be a real blow for models that have
otherwise been very successful), or 2) something happens to the neutrinos in transit to earth; in particular, they might
change into another type of neutrino, call oscillation (this idea is not as crazy as it sounds, as a similar phenomenon is
well known to occur with the meson particles). An important consequence to oscillation is that the neutrino must have
mass (unlike the photon which has zero mass).

By the late 1990s, the oscillation hypothesis is shown to be correct. In addition, analysis of the neutrino events from the
supernova 1987A indicates that the neutrinos traveled at slightly less than the speed of light. This is an important result
since the neutrino is so light that it was unclear if its mass was very small or exact zero. Zero mass particles (like the
photon) must travel exactly the speed of light (no faster, no slower). But objects with mass must travel at less than the
speed of light as stated by special relativity.

Since neutrino's interact very weakly, they are the first particles to decouple from other particles, at about 1 sec after the
Big Bang. The early Universe is so dense that even neutrinos are trapped in their interactions. But as the Universe
expands, its density drops to the point where the neutrinos are free to travel. This happens when the rate at which
neutrinos are absorbed and emitted (the weak interaction rate) becomes slower than the expansion rate of the Universe.
At this point the Universe expands faster than the neutrinos are absorbed and they take off into space (the expanding
space).
Now that neutrinos have been found to have mass, they also are important to our cosmology as a component of the
cosmic density parameter. Even though each individual neutrino is much less massive than an electron, trillions of them
are produced for every electron in the early Universe. Thus, neutrinos must make up some fraction of the non-baryonic
matter in the Universe (although not alot of it, see lecture on the large scale structure of the Universe).

Cosmic Background Radiation

Cosmic Background Radiation :
One of the foremost cosmological discoveries was the detection of the cosmic background radiation. The discovery of an
expanding Universe by Hubble was critical to our understanding of the origin of the Universe, known as the Big Bang.
However, a dynamic Universe can also be explained by the steady state theory.
The steady state theory avoids the idea of Creation by assuming that the Universe has been expanding forever. Since this
would mean that the density of the Universe would get smaller and smaller with each passing year (and surveys of
galaxies out to distant volumes shows this is not the case), the steady-state theory requires that new matter be produced

The creation of new matter would voilate the conservation of matter princple, but the amount needed would only be one
atom per cubic meter per 100 years to match the expansion rate given by Hubble's constant.
The discovery of the cosmic microwave background (CMB) confirmed the explosive nature to the origin of our
Universe. For every matter particle in the Universe there are 10 billion more photons. This is the baryon number that
reflects the asymmetry between matter and anti-matter in the early Universe. Looking around the Universe its obvious
that there is a great deal of matter. By the same token, there are even many, many more photons from the initial
annihilation of matter and anti-matter.
Most of the photons that you see with your naked eye at night come from the centers of stars. Photons created by nuclear
fusion at the cores of stars then scatter their way out from a star's center to its surface, to shine in the night sky. But these
photons only make up a very small fraction of the total number of photons in the Universe. Most photons in the Universe
are cosmic background radiation, invisible to the eye.
Cosmic background photons have their origin at the matter/anti-matter annihilation era and, thus, were formed as
gamma-rays. But, since then, they have found themselves scattering off particles during the radiation era. At
recombination, these cosmic background photons escaped from the interaction with matter to travel freely through the
Universe.
As the Universe continued to expanded over the last 15 billion years, these cosmic background photons also `expanded',
meaning their wavelengths increased. The original gamma-ray energies of cosmic background photons has since cooled
to microwave wavelengths. Thus, this microwave radiation that we see today is an `echo' of the Big Bang.

The discovery of the cosmic microwave background (CMB) in the early 1960's was powerful confirmation of the Big
Bang theory. Since the time of recombination, cosmic background photons have been free to travel uninhibited by
interactions with matter. Thus, we expect their distribution of energy to be a perfect blackbody curve. A blackbody is the
curve expected from a thermal distribution of photons, in this case from the thermalization era before recombination.

Today, based on space-based observations because the microwave region of the spectrum is blocked by the Earth's
atmosphere, we have an accurate map of the CMB's energy curve. The peak of the curve represents the mean temperature
of the CMB, 2.7 degrees about absolute zero, the temperature the Universe has dropped to 15 billion years after the Big
Bang.

Where are the CMB photons at the moment? The answer is `all around you'. CMB photons fill the Universe, and this
lecture hall, but their energies are so weak after 15 billion years that they are difficult to detect without very sensitive
microwave antennas.
CMB Fluctuations :
The CMB is highly isotropy, uniform to better than 1 part in 100,000. Any deviations from uniformity are measuring the
fluctuations that grew by gravitational instability into galaxies and clusters of galaxies.
Images of the CMB are a full sky image, meaning that it looks like a map of the Earth unfolded from a globe. In this
case, the globe is the celestial sphere and we are looking at a flat map of the sphere.
Maps of the CMB have to go through three stages of analysis to reveal the fluctuations associated with the early
Universe. The raw image of the sky looks like the following, where red is hotter and blue is cooler:

The above image has a typical dipole appearance because our Galaxy is moving in a particular direction. The result is
one side of the sky will appear redshifted and the other side of the sky will appear blueshifted. In this case, redshifting
means the photons are longer in wavelength = cooler (so backwards from their name, they look blue in the above
diagram). Removing the Galaxy's motion produces the following map:

This map is dominated by the far-infrared emission from gas in our own Galaxy. This gas is predominately in the plane
of our Galaxy's disk, thus the dark red strip around the equator. The gas emission can be removed, with some
assumptions about the distribution of matter in our Galaxy, to reveal the following map:

This CMB image is a picture of the last scattering epoch, i.e. it is an image of the moment when matter and photons
decoupled, literally an image of the recombination wall. This is the last barrier to our observations about the early
Universe, where the early epochs behind this barrier are not visible to us.
The clumpness of the CMB image is due to fluctuations in temperature of the CMB photons. Changes in temperature are
due to changes in density of the gas at the moment of recombination (higher densities equal higher temperatures). Since
these photons are coming to us from the last scattering epoch, they represent fluctuations in density at that time.
The origin of these fluctuations are primordial quantum fluctuations from the very earliest moments of are echo'ed in the
CMB at recombination. Currently, we believe that these quantum fluctuations grew to greater than galaxy-size during the
inflation epoch, and are the source of structure in the Universe.
Fluctuations and the Origin of Galaxies :
The density fluctuations at recombination, as measured in the CMB, are too large and too low in amplitude to form
galaxy sized clumps. Instead, they are the seeds for galaxy cluster-sized clouds that will then later break up into galaxies.
However, in order to form cluster-sized lumps, they must grow in amplitude (and therefore mass) by gravitational
instability, where the self-gravity of the fluctuation overcomes the gas pressure.

The CMB fluctuations are a link between Big Bang and the large scale structure of galaxies in the Universe, their
distribution in terms of clusters of galaxies and filaments of galaxies that we observe around the Milky Way today.

Rotation Curve of Galaxy

Rotation Curve of Galaxy:
Dynamical studies of the Universe began in the late 1950's. This meant that instead of just looking
and classifying galaxies, astronomers began to study their internal motions (rotation for disk
galaxies) and their interactions with each other, as in clusters. The question was soon developed of
whether we were observing the mass or the light in the Universe. Most of what we see in galaxies
is starlight. So clearly, the brighter the galaxy, the more stars, therefore the more massive the
galaxy. By the early 1960's, there were indications that this was not always true, called the missing
mass problem.
The first indications that there is a significant fraction of missing matter in the Universe was from
studies of the rotation of our own Galaxy, the Milky Way. The orbital period of the Sun around the
Galaxy gives us a mean mass for the amount of material inside the Sun's orbit. But, a detailed plot
of the orbital speed of the Galaxy as a function of radius reveals the distribution of mass within the
Galaxy. The simplest type of rotation is wheel rotation shown below.

Rotation following Kepler's 3rd law is shown above as planet-like or differential rotation. Notice
that the orbital speeds falls off as you go to greater radii within the Galaxy. This is called a
Keplerian rotation curve.
To determine the rotation curve of the Galaxy, stars are not used due to interstellar extinction.
Instead, 21-cm maps of neutral hydrogen are used. When this is done, one finds that the rotation
curve of the Galaxy stays flat out to large distances, instead of falling off as in the figure above.
This means that the mass of the Galaxy increases with increasing distance from the center.

The surprising thing is there is very little visible matter beyond the Sun's orbital distance from the
center of the Galaxy. So, the rotation curve of the Galaxy indicates a great deal of mass, but there
is no light out there. In other words, the halo of our Galaxy is filled with a mysterious dark matter
of unknown composition and type.
Cluster Masses:
Most galaxies occupy groups or clusters with membership ranging from 10 to hundreds of
galaxies. Each cluster is held together by the gravity from each galaxy. The more mass, the higher
the velocities of the members, and this fact can be used to test for the presence of unseen matter.

When these measurements were performed, it was found that up to 95% of the mass in clusters is
not seen, i.e. dark. Since the physics of the motions of galaxies is so basic (pure Newtonian
physics), there is no escaping the conclusion that a majority of the matter in the Universe has not
been identified, and that the matter around us that we call `normal' is special. The question that
remains is whether dark matter is baryonic (normal) or a new substance, non-baryonic.

Mass-to-Luminosity Ratios

Mass-to-Luminosity Ratios:
Exactly how much of the Universe is in the form of dark matter is a mystery and difficult to
determine, obviously because its not visible. It has to be inferred by its gravitational effects on the
luminous matter in the Universe (stars and gas) and is usually expressed as the mass-to-luminosity
ratio (M/L). A high M/L indicates lots of dark matter, a low M/L indicates that most of the matter
is in the form of baryonic matter, stars and stellar reminants plus gas.
A important point to the study of dark matter is how it is distributed. If it is distributed like the
luminous matter in the Universe, that most of it is in galaxies. However, studies of M/L for a range
of scales shows that dark matter becomes more dominate on larger scales.

Most importantly, on very large scales of 100 Mpc's (Mpc = megaparsec, one million parsecs and
kpc = 1000 parsecs) the amount of dark matter inferred is near the value needed to close the
Universe. Thus, it is for two reasons that the dark matter problem is important, one to determine
what is the nature of dark matter, is it a new form of undiscovered matter? The second is the
determine if the amount of dark matter is sufficient to close the Universe.
Baryonic Dark Matter:
We know of the presence of dark matter from dynamical studies. But we also know from the
abundance of light elements that there is also a problem in our understanding of the fraction of the
mass of the Universe that is in normal matter or baryons. The fraction of light elements (hydrogen,
helium, lithium, boron) indicates that the density of the Universe in baryons is only 2 to 4% what
we measure as the observed density.
It is not too surprising to find that at least some of the matter in the Universe is dark since it
requires energy to observe an object, and most of space is cold and low in energy. Can dark matter
be some form of normal matter that is cold and does not radiate any energy? For example, dead
stars?
Once a normal star has used up its hydrogen fuel, it usually ends its life as a white dwarf star,
slowly cooling to become a black dwarf. However, the timescale to cool to a black dwarf is
thousands of times longer than the age of the Universe. High mass stars will explode and their
cores will form neutron stars or black holes. However, this is rare and we would need 90% of all
stars to go supernova to explain all of the dark matter.

Another avenue of thought is to consider low mass objects. Stars that are very low in mass fail to
produce their own light by thermonuclear fusion. Thus, many, many brown dwarf stars could make
up the dark matter population. Or, even smaller, numerous Jupiter-sized planets, or even plain
rocks, would be completely dark outside the illumination of a star. The problem here is that to
make-up the mass of all the dark matter requires huge numbers of brown dwarfs, and even more
Jupiter's or rocks. We do not find many of these objects nearby, so to presume they exist in the
dark matter halos is unsupported.

Non-Baryonic Dark Matter

Non-Baryonic Dark Matter:
An alternative idea is to consider forms of dark matter not composed of quarks or leptons, rather
made from some exotic material. If the neutrino has mass, then it would make a good dark matter
candidate since it interacts weakly with matter and, therefore, is very hard to detect. However,
neutrinos formed in the early Universe would also have mass, and that mass would have a
predictable effect on the cluster of galaxies, which is not seen.
Another suggestion is that some new particle exists similar to the neutrino, but more massive and,
therefore, more rare. This Weakly Interacting Massive Particle (WIMP) would escape detection in
our modern particle accelerators, but no other evidence of its existence has been found.

The more bizarre proposed solutions to the dark matter problem require the use of little understood
relics or defects from the early Universe. One school of thought believes that topological defects
may have appears during the phase transition at the end of the GUT era. These defects would have
had a string-like form and, thus, are called cosmic strings. Cosmic strings would contain the
trapped remnants of the earlier dense phase of the Universe. Being high density, they would also be
high in mass but are only detectable by their gravitational radiation.
Lastly, the dark matter problem may be an illusion. Rather than missing matter, gravity may
operate differently on scales the size of galaxies. This would cause us to overestimate the amount
of mass, when it is the weaker gravity to blame. This is no evidence of modified gravity in our
laboratory experiments to date.

Current View of Dark Matter

Current View of Dark Matter:
The current observations and estimates of dark matter is that 1/2 of dark matter is probably in the
form of massive neutrinos, even though that mass is uncertain. The other 1/2 is in the form of
stellar remnants and low mass, brown dwarfs. However, the combination of both these mixtures
only makes 10 to 20% the amount mass necessary to close the Universe. Thus, the Universe
appears to be open.

Origin of Structure :
As we move forward in time from the beginning of the Universe we pass through the
inflation era, baryongenesis, nucleosynthesis and radiation decoupling. The culmination is
the formation of the structure of matter, the distribution of galaxies in the Universe.
During radiation era growth of structure is suppressed by the tight interaction of photons
and matter. Matter was not free to response to its own gravitational force, so density
enhancements from the earliest times could not grow.
Density enhancements at the time of recombination (having their origin in quantum
fluctuations that expanded to galaxy-sized objects during the inflation era) have two
routes to go. They can grow or disperse.

The `pressure effects' that density enhancements experience are due to the expanding
Universe. The space itself between particles is expanding. So each particle is moving
away from each other. Only if there is enough matter for the force of gravity to overcome
the expansion do density enhancements collapse and grow.

Top-Down Scenario

Top-Down Scenario:
Structure could have formed in one of two sequences: either large structures the size of
galaxy clusters formed first, than latter fragmented into galaxies, or dwarf galaxies
formed first, than merged to produce larger galaxies and galaxy clusters.
The former sequence is called the top-down scenario, and is based on the principle that
radiation smoothed out the matter density fluctuations to produce large pancakes. These
pancakes accrete matter after recombination and grow until they collapse and fragment
into galaxies.

This scenario has the advantage of predicting that there should be large sheets of galaxies
with low density voids between the sheets. Clusters of galaxies form where the sheets
intersect.
Bottom-Up Scenario:
The competing scenario is one where galaxies form first and merge into clusters, called
the bottom-up scenario. In this scenario, the density enhancements at the time of
recombination were close to the size of small galaxies today. These enhancements
collapsed from self-gravity into dwarf galaxies.

Once the small galaxies are formed, they attract each other by gravity and merge to form
larger galaxies. The galaxies can then, by gravity, cluster together to form filaments and
clusters. Thus, gravity is the mechanism to form larger and larger structures.