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How Do You Make a Universe?
Geary Albright
Saturday Morning Physics
March 3, 2012
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• The history of the Universe can be
summed up like this: Hydrogen is a
light, odorless, colorless gas, that if
given enough time, turns into people.
• In this lecture, I am going to try to fill
in some of the gaps in this statement….
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Whence the Universe?
Ripple in still water
When there is no pebble tossed
Nor wind to blow
lyric/haiku, R. Hunter
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The Great Nebula Debate
• Starting with Charles Messier in 1781,
astronomers began cataloging faint nebulae
(nebula is Latin for cloud) in the sky.
• Initially, they were assumed to be part of the
Milky Way (sipral nebulae). However, as
better telescopes came along, it was clear
that they were composed of stars.
Therefore, they might be other distant
systems of stars.
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M-31 The Andromeda Galaxy
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The Shapely-Curtis Debate
– In 1920, a debate was held at the National
Academy of Sciences in Washington, D.C.
to settle the question.
• Harlow Shapley argued that they must be part
of our Galaxy.
• Heber Curtis, who was a graduate of the
University of Virginia, argued that they are
separate “island universes.”
• Shapley won the debate, Curtis was correct.
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The Shapely-Curtis Debate
Harlow Shapely
Heber Curtis
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Distances to Galaxies
• In 1924, Edwin Hubble used the 100-inch
Hooker Telescope on Mt. Wilson to resolve
individual stars in the Andromeda Galaxy.
– Among these stars were some Cepheid variables.
– Using the method pioneered by Henrietta Leavitt,
Hubble was able to calculate the distance to these
nebulae.
– This proved once and for all that the spiral
nebulae were outside the Milky Way and were
galaxies just like the Milky Way.
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The Local Group
• The Milky Way is a member of the Local
Group of galaxies.
– The local group is spread over 3 million LY
and contains about 40 members.
– There are three large spirals (The Milky
Way, M-31 the Andromeda Galaxy, M-33).
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M-31
Andromeda
Galaxy
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Local
Group
Spiral
Galaxy
M-33
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M-87 Giant Elliptical Galaxy in the Virgo Cluster
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Hubble
Ultra Deep
Field
Area is
about 1/100
the size of
the full
Moon and
10,000
Galaxies!
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The Expanding Universe
• In 1912, the American astronomer
Vesto Slipher measured the spectra of
about 40 faint spiral nebulae.
– He found that almost all the galaxies
showed a redshift. That is, the absorption
lines in the spectrum were shifted to longer
(redder) wavelengths.
– This indicated that all the galaxies were
moving away from our Galaxy.
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If almost all the galaxies that we see are
moving away from the Milky Way, what does
that tell us about our location in the Universe?
1. We are at the exact center.
2. We are near the center, but not
necessarily at the exact center.
3. We are near the edge of the universe.
4. It tells us nothing about our location
in the universe.
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Edwin Hubble (1889-1953)
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The Expanding Universe
• In the late 1920’s, Edwin Hubble and
Milton Humason, began a systematic
survey of the distances to nearby spiral
galaxies and their recession velocity.
– In 1929, they published a paper showing
that the recession velocities of the galaxies
are directly proportional to their distances.
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The
Hubble
Law
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Velocity-Distance Relation 1929
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The Hubble Law
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The Expanding Universe
• The relationship between velocity and
distance is:
v  H0  D
– Where v is the recession velocity, H0 is the
Hubble constant (equals the slope of the
line), and D is the distance to the object.
– This equation is called the Hubble Law.
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The Hubble Law
• The most widely accepted value for the
Hubble constant is:
H0 = 71.0 ±2.5 km/s per Mpc
• An accurate value of the Hubble constant is
difficult to obtain.
– It requires accurately measuring the recession
velocity (easy) and distance (difficult) to a number
of galaxies.
– Mpc = Mega-parsec ~ 3 million light years
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The Hubble Law
• The Hubble Law simply says that a
galaxy moves away from us at a speed
of 71 km/s for every million pc of its
distance.
– A galaxy at 1 Mpc is receding at 71 km/s.
– A galaxy at 2 Mpc is receding at 142 km/s.
– A galaxy at 5 Mpc is receding at 355 km/s
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The Expansion of the Universe
• The Hubble Law implies that the
universe is expanding.
• At first, the idea that all galaxies are
moving away from us seems to indicate
that we are at the center of the
universe. However, in a uniformly
expanding space, every galaxy is
moving away from every other galaxy.
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The Expansion of the Universe
• Imagine a rubber ruler with four ants on it.
• Assume that this ruler is expanding so that it
uniformly doubles it length every minute.
• Consider the distances from the ant at 2 cm
to the other ants after 1 minute (when the
ruler has doubled in length). Note that ant 2
is not at the center of the ruler.
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The Hubble Law
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As the ruler stretches, do all of the ants see all
of the other ants moving away from them?
1. Yes
2. No
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The Expansion of the Universe
• Ants that are farther apart move away
from each other with a greater velocity.
• The speed at which the distant ants
recede is proportional to their distance,
just like the Hubble Law!
• On this ruler, all the ants will see all the
other ants moving away from them.
Just like galaxies in our universe!
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The Expansion of the Universe
• For a three dimensional analogy, consider
raisins in a loaf of rising bread.
• Regardless of which raisin you pick, all the
other raisins are moving away from it.
• The reason they are receding from each
other is the bread between them is
expanding. The same is true for the
universe, the space between the galaxies is
expanding.
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The Hubble Law
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The Birth of the Universe
• The Hubble Law expansion of the universe
increases the distance between any two
points as time moves forward.
• This implies that at some time in the distant
past the distance between any two points
was zero and that the density of the universe
was infinite.
• The expansion of the universe from this
beginning is called the Big Bang.
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The Birth of the Universe
• Where, then, is the center of the expansion?
How far are we from the Big Bang that
created the universe?
• The universe has no center! All points in
space are expanding away from all other
points in space. They are NOT expanding
away from a single central point.
• To picture this, imagine living on the surface
of a balloon as it was being inflated.
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The Hubble Law
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The Birth of the Universe
• It is incorrect to think of the Big Bang as an
explosion from a single point.
• Since the entire universe was created in the
Big Bang, including all of space and time, the
explosion occurred everywhere at once.
• The universe is not expanding into some
“empty space” beyond the galaxies, since the
space in which the galaxies exist was created
in the Big Bang.
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The Birth of the Universe
• What came before the Big Bang?
– Since all of our laws of physics were created in the
Big Bang, we cannot use them to probe back to a
time before the Big Bang occurred.
• Are there parallel universes where, for
example, my parallel identity is getting an A+
in all my high school classes?
– Again, our laws of physics apply only to our
universe and are contained within it. We may not
be able to use them to probe the existence of
other universes outside our own.
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The Birth of the Universe
• In fact, the expansion of the universe is the
expansion of space itself.
– A better way to think about the expansion of the
universe is not that the distant galaxies are
moving away from us, but that they are stationary
and the space between the galaxies is expanding.
– As the space between the galaxies expands,
distant galaxies appear farther away.
– In addition, this expansion of space stretches the
waves of light as they travel. This expansion of
the wavelength creates the redshift.
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Expansion Redshift
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The Fate of the Universe
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Some say the world will end in fire,
Some say in ice.
From what I’ve tasted of desire
I hold with those who favor fire.
But if I had to perish twice,
I think I know enough of hate
To say that for destruction ice
Is also great
And would suffice.
Robert Frost
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Olber’s Paradox
• Consider this question “Why is the night sky
dark?”
– The answer has profound cosmological
implications.
– It was believed that the universe was infinite in
size and infinitely old. Everywhere you look your
line of sight will eventually end on the surface of a
star. Therefore, the night sky would be as bright
as the surface of a star!
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Olber’s Paradox
• Edmund Halley thought the darkness was due
to the distance of stars, making them appear
dim. However, as feeble as the light may be,
the combined light from an infinite number of
stars would still light the sky.
• Dust in the universe cannot solve the problem
either, since the dust would eventually heat
up and be as bright as a star.
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Olber’s Paradox
• The modern answer to Olber’s paradox is
that the universe has a finite age (about 13.7
billion years old).
– We can only see the light from objects that are
less than 13.7 billion LY away, only those objects
are close enough so their light has had the time to
get here since the origin of the universe
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Olber’s Paradox
– This solution was first proposed by Edgar
Allen Poe in 1848.
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The Age of the Universe
• Since all galaxies are receding from us, and
their velocity is proportional to their distance,
indicates that the Universe is expanding.
– If we could somehow make time run backward,
we would see the Universe contracting, that is,
the galaxies would be getting closer together.
– We can use this fact to calculate the age of the
Universe by determining when the distances
between the galaxies goes to zero.
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The Age of the Universe
• To calculate the age of the Universe
use:
d
T
v
v  H 0d
Hubble’s
Law
d
1
T

H 0d H 0
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The Age of the Univserse
• That is, the age of the Universe is
simply 1/H0 if the universe expanded at
a constant rate since the beginning.
– Note: you must convert the Mpc to
kilometers and the seconds to years to get
an age expressed in years.
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The Age of the Universe
• For H0=71 km/s per megaparsec we
have
1
1
T

H0 71 km/s/Mpc
1s Mpc
1yr
106 pc 3.0861016 m 1km
T




7
71km 3.158 10 s 1Mpc
1pc
1000 m
T  13.8 1010 years  13.8 billion years
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The Age of the Universe
• The only assumption made above is that the
Universe has been expanding at a constant
rate since the beginning.
– However, the gravity of objects will tend to slow
the expansion over time (deceleration).
– On the other hand, Einstein’s cosmological
constant, if it exists, could cause the expansion to
speed up (acceleration).
– Observations of the expansion rate of distant
galaxies can tell us which is the case.
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The Expanding Universe
• Immediately after developing his General
Theory of Relativity in 1915, Einstein realized
it could be applied to Universe as a whole.
– The matter and energy in the Universe would
warp the geomety of space.
– At the time, it was believed that the Universe was
infinite in extent and that it was static (neither
expanding nor contracting).
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The Expanding Universe
• Einstein’s calculations showed that an
infinite static universe was unstable.
– The gravity of all the bodies would cause it
to collapse.
– Therefore, there must be some repulsive
force, called the cosmological constant,
that balances gravity.
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The Expanding Universe
– When Edwin Hubble showed that the
Universe was expanding, Einstein realized
his equations showed an expanding
Universe was stable.
– He could have predicted the expansion of
the Universe well before it was discovered
observationally.
– He later referred to the introduction of the
cosmological constant as “the biggest
blunder of my life.”
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The Geometry of the Universe
• General relativity describes how matter
(and energy, since E=mc2) curve the
space around them.
• These ideas can be applied to the
universe as a whole. Indeed, the
geometry of space depends on the
mass and energy conained in the
Universe.
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The Geometry of the Universe
• The equations of general relativity show that
there are two possible states for the universe,
closed and open.
– In a closed universe there is enough matter and
energy and their combined gravitational pull will
stop the expansion and cause it to contract again.
– In an open universe the combined gravitational
pull of all the matter and energy is insufficient to
stop the expansion and the universe will expand
forever.
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The Geometry of the Universe
Unbound
Marginally
bound
Bound
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The Geometry of the Universe
– The parameter that determines the fate of
the universe is the combined density of
matter and energy.
– The dividing line between these two states
is a universe which has exactly the critical
density of material needed to stop the
expansion after an infinite
2 amount of time.
3H0
ρc 
8π G
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The Geometry of the Universe
– The critical density depends on the Hubble
Constant (a faster expansion would require
more gravitational attraction to stop it).
– For H0=71 km/s, the critical density is
about 10-26 kg/m3. That’s about 5
hydrogen atoms per cubic meter.
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A Closed Universe
• The geometry of spacetime is spherical.
• A closed universe is finite in size and
spacetime curves so that a beam of light
would come back to where it started.
– Some have speculated that closed universes could
give rise to another Big Bang. These “oscillating
theories” cannot be tested and are therefore more
philosophical than scientific.
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A Closed Universe
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An Open Universe
• In an open universe the current expansion
will continue forever.
• The geometry of an open universe is
hyperbolic (saddle shaped).
– An open universe is infinite in extent. Although
space and time began with the Big Bang, they
have no limit. The gravitational attraction of the
material in the universe can slow the expansion,
but cannot stop it.
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A Critical Universe
• In a critical, or flat, universe the
expansion can just barely continue
forever.
• The velocity of expansion will
asymptotically go to zero.
• The geometry is flat.
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Which Universe do we have?
• If we total up all the normal matter in
the Universe, we get a density about
4% of the critical density.
• Dark Matter seems to make up about
23% of the critical density.
• So matter is only 27% of the critical
density, and if there is no other
contribution, then the universe is open.
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Flatness Problem
• Astronomers and physicists have noted
that the universe is suspiciously close to
the “special” critical density.
– The universe could have had any density;
one thousands, millions, or billions of times
smaller or larger than the critical density.
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Acceleration of the Universe?
• In 1998, publications began to appear
showing that the expansion rate of the
universe appears to be accelerating.
– This new work is based on using Type I
supernovae as standard candles to find
their distance.
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Supernova in the News
• On Monday April 1, 2001, astronomers
using the Hubble Space Telescope
reported the most distant supernova
ever discovered.
• The supernova occurred in a faint
elliptical galaxy 10 billion light years
away in the Hubble Deep Field.
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SN
1997ff
in the
HDF
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Supernova in the News
• The supernova was found to be closer
than it would be if the universe
expanded at a constant rate.
• The Hubble Constant was therefore
found to be smaller at this great
distance, i.e. earlier in the Universe
• This supernova is the best evidence
that the expansion is accelerating.
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The Geometry of the Universe
• The current best fit model of our universe
looks like:
–
–
–
–
The universe is flat (at the critical density).
The density of normal matter is 4% of the critical density.
The density of dark matter is 23% of the critical density.
The energy that is causing the acceleration of the universe
(called Dark Energy) is about 73% of the critical density.
– When this energy is combined with the normal and dark
matter, we get a flat universe.
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Ultimate Fate of the Universe
• As time goes on, galaxies will recede
from one another with ever increasing
speed.
• Eventually, even the nearby galaxies
will be receding from us at a speed
greater than the speed of light.
• The Universe will grow cold and dark.
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Evidence for the Big Bang
• There are two major observational facts
that strongly support the Big Bang:
1) The Universe is expanding according to
Hubble’s Law.
2) The Universe is filled with electromagnetic
radiation with a blackbody temperature of
about 2.7 K.
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Cosmic Background Radiation
• In 1965, Arno Penzias and Robert Wilson
were using a very sensitive radio telescope to
study radio emission from the sky.
– They found a background source of noise with a
temperature of 3 K that they could not explain.
– After discussing the observations with other
astronomers, Penzias and Wison realized they had
discovered the radiation from the Big Bang.
– Nobel Prize in physics in 1978 for the discovery.
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Bell Lab’s Horn Antenna,
Holmdel, NJ
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Source of the Cosmic Radiation
• After nucleosynthesis, the temperature
of the universe is high enough that the
atoms are all ionized
• The electrons have too much energy
and are not bound to the atoms.
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End of the Radiation Era
• The free electrons can scatter photons.
• Light does not travel far before being
scattered by an electron, so the
universe is opaque.
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The End of the Radiation Era
• When the universe cools to ~3000 K
(~380,000 years), electrons are captured by
the protons to form hydrogen atoms.
• This process is called recombination.
– After recombination, the matter no longer scatters
the radiation and they decouple.
– The universe becomes transparent.
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Cosmic Background Radiation
• At this time, the photons had a blackbody
spectrum with a temperature 3000 K.
• Since then, the expansion of the universe has
stretched the wavelength of these photons.
• The expansion of the universe causes a
decrease in the temperature of the blackbody
radiation.
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COBE
• In 1989, NASA launched the Cosmic
Background Explorer satellite to study the
Cosmic Background Radiation.
– COBE showed that the microwave background is a
perfect black body with a temperature of 2.725 K.
– A slight temperature (Doppler) shift shows that
the Sun and Earth are moving through space at
500 km/s toward the constellation Hydra.
– COBE also found small clumps in the background
radiation, which indicate the formation of
structures even at this early stage.
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Wilkinson Microwave
Anisotropy Probe
• On June 30, 2001 NASA launched the
Wilkinson Microwave Anisotropy Probe
to study the fluctuations in the cosmic
microwave background.
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Wilkinson Microwave
Anisotropy Probe
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Wilkinson Microwave
Anisotropy Probe
• Universe is 13.7 billion years old with a
margin of error of close to 1%.
• First stars ignited 200 million years after the
Big Bang.
• Light in WMAP picture from 380,000 years
after the Big Bang.
• Content of the Universe:
– 4% Atoms, 23% Cold Dark Matter, 73% Dark
energy.
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• This is the way the world ends
• This is the way the world ends
• This is the way the world ends
• Not with a bang but a whimper
•
From The Hollow Men by T.S. Elliot
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