The Shape and Fate of the Universe

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The Shape and Fate of the Universe

• Assumptions in cosmology
• Expansion of the Universe
• Curvature of the Universe
• Fate of the Universe

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Assumptions in Cosmology

• Copernican principle
• We do not occupy a special place.
• There are no special places.
• The universe is homogeneous if viewed at
  sufficently large scales.
• The laws of physics are the same everywhere.

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Implications of the Copernican Principle

• The average density of matter and energy is the
  same throughout the Universe.
• The same Hubble expansion law is seen for all
  observers anywhere in the Universe.
• The curvature of the Universe is the same
  everywhere.

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How can we test the Copernican principle?

• Does the Universe look the same in all
  directions? (Isotropy)
• Are the spectral lines from atoms the same in
  distant galaxies?
• Do the same laws of gravity apply in other
  galaxies?

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Hubble expansion v H0d
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Expansion of the Universe
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Hubble expansion v H0d
Time distance/velocity d/H0d 1/H0
1/(71 km/s/Mpc) 13.8 Gyr
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Two dimensional geometry

• Only two directions up/down and left/right
• north/south
  and east/west
• All motion of particles, light confined to two
  dimensions
• Examples black board, piece of paper, surface of
  sphere, surface of donut, surface of saddle

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Geometry

• How are the diameter and circumference of a
  circle related?
• What is the sum of all of the angles in a
  triangle?

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Geometry in flat space

• Circumference 2? ? radius
• ? 3.1415926 2? 6.28
• The sum of the angles in a triangle is 180º

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Geometry in positively curved space

• Circumference lt 2? ? radius
• The sum of the angles in a triangle gt 180º

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Geometry in negatively curved space

• Circumference gt 2? ? radius
• The sum of the angles in a triangle lt 180º

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Curvature of the Universe

• The curvature of the Universe is determined by
• the density of matter and energy
• higher density produces positive curvature
• the expansion of the Universe
• more rapid expansion produces negative curvature

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Fate of the Universe
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Critical Density
At what density is the Universe balanced between
expanding forever versus contracting?
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Curvature of the Universe
The curvature of the Universe is determined by
the density parameter ?0
?0 lt 1 ? negative curvature ?0 gt 1 ? positive
curvature
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Fate of the Universe
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Age of the Universe
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Imagine that the circumference of a circle with a
radius of 1000 Mpc was measured to be 5500 Mpc.
This would imply that

• The Universe is flat.
• The Universe is positively curved and will
  eventually contract in a big crunch.
• The Universe is negatively curved and will expand
  forever.

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The Big Bang

• The Big Bang
• Tempature and density history of the Universe
• Cosmic Background Radiation
• Contents of the Universe

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Big Bang

• Our conclusion that the Universe actually began
  at some point in time is based on extrapolating
  back the observed Hubble expansion of galaxies
• Is there any other evidence?

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Big Bang
If the Universe was smaller in the past, but had
roughly the same amount of matter and energy,
then the density of matter and energy must have
been higher in the past.
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The Universe was hotter in the past
lower T
higher T

• Temperature is proportional to the average
  kinetic energy per molecule

k Boltzmann constant 1.38?10-23 J/K
8.62?10-5 eV/K
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Big Bang
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Big Bang
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Big Bang
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Big Bang
First protons and neutrons at about 1
second. Helium nuclei formed at about 100
seconds. Observed ratio of Helium/Hydrogen
matches Big Bang prediction. Universe is opaque.
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Opaque
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Big Bang
At one million years, electrons combine with
nuclei and atoms form. Universe becomes
transparent.
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Transparent
Transition occurs at around T 3740 K.
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Cosmic Microwave Background
The Universe glows at 2.7 K in every direction.
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CMB
Discovered by Arno Penzias and Robert Wilson in
1960-65 while employed by ATTs Bell Labs and
attempting to find the source of noise in an
antenna used to bounce telephone signals bounced
off metallic balloons high in the
atmosphere. They won the Nobel prize in 1978.
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CMB
Radiation is a blackbody spectrum originally
emitted at 3000 K but red shifted by a factor of
1000.
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Three pieces of evidence for the Big Bang model

• Hubble expansion galaxies are moving away from
  us with speed proportional to distance.
• The ratio of Helium to Hydrogen in gas clouds
  unaffected by stars.
• The cosmic microwave background a 2.7 K glow
  seen in all directions.

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Cosmic Microwave Background
Small fluctuations are due to sound waves at
recombination.
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Temperature variations in the Cosmic Microwave
Background (CMB) are observed to be about 0.0003
K. The expected physical size of the hot/cold
regions can be calculated.
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Curvature of the Universe
The curvature of the Universe is determined by
the density parameter ?0
?0 lt 1 ? negative curvature ?0 gt 1 ? positive
curvature
Measurement of CMB fluctuations gives
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Contents of the Universe

• Normal matter
• Stars
• hot gas
• anything made of atoms
• Total is 4 of ?C

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Rotation curve of Milky Way
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Mass of the Milky Way
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Dark Matter

• Dark it doesnt produce light (any kind)
• Does have mass, produces gravity
• Nature is unknown
• Most likely it is elementary particles

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Contents of the Universe

• Normal matter is 4 of ?C
• Dark matter is 23 of ?C
• Total of normal and dark matter is ?M 0.3
• But, we need 100 of ?C
• Remainder, 73, is dark energy ?? 0.7

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Contents of the Universe
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Why can't we see radiation produced during the
first 300,000 years after the Big Bang?

• It was absorbed soon after it was emitted.
• It hasn't reached us yet.
• It has been deflected by black holes.
• It passed by our part of the universe a few
  billion years ago.

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Review Questions

• Give three pieces of evidence for the Big Bang
  model.
• What will happen to the Universe if the density
  is less than the critical density?
• A few seconds after the big bang did hydrogen
  atoms exists? Why or why not?

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Cosmology

• Einsteins greatest blunder
• Accelerating Universe
• Dark energy
• Problems with the Big Bang
• Solutions to the problems

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Einstein and Cosmology

• After Einstein wrote down the equations for
  General Relativity, he made a model of the
  Universe and found that the Universe had to be
  either expanding or contracting.
• He introduced a new term, the cosmological
  constant or ?, in his equations representing a
  energy field which could create antigravity to
  allow a static model.
• After Hubble found the expansion of the Universe,
  Einstein called ? his greatest blunder.

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Cosmological Constant

• Quantum physics predicts that some energy fields
  that act like ?.
• One such field is the one thought to cause the
  rapid expansion of the Universe during inflation.
• Another such field appears to be operating today.

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Matter slows down expansion
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Accelerating Universe
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Accelerating universe
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Accelerating Universe

• Hubble expansion appears to be accelerating
• Normal matter cannot cause acceleration, only
  deceleration of expansion
• Dark energy is required
• may be cosmological constant
• may be something else
• major current problem in astronomy

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Problems with the Big Bang

• The horizon problem
• The flatness problem

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Cosmic Microwave Background
The Universe glows at 2.7 K in every
direction. The temperature is the same to lt 0.1.
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Observable Universe
We can only see the parts of the Universe from
which light has had time to travel to us.
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The Horizon
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Horizon Problem
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Flatness problem
Any tiny deviation from the critical density is
amplified over time.
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Inflation makes the Universe flat
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Inflation
Size cm
Time seconds
Whole observable universe came from a tiny region.
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Inflation and cosmology

• The Universe is very uniformity and very close to
  flat.
• A new theoretical idea, inflation, gives an
  explanation for the uniformity and flatness of
  the Universe.
• Inflation still needs to be tested.
• NASA plans to fly a satellite to measure the
  polarization of the cosmic microwave background
  in order to test inflation.

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Review Questions

• What will happen to the Universe if the density
  is less than the critical density?
• A few seconds after the big bang did hydrogen
  atoms exists? Why or why not?
• How can fluctuations in the cosmic microwave
  background be used to determine the geometry of
  the Universe?
• What are the major components and their fraction
  of the total mass/energy in the Universe?

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Review questions

• Why is it surprising that the microwave
  background has almost exactly the same
  temperature in all directions on the sky?
• Why is it surprising that the geometry of the
  universe is so close to flat?
• What is the best explanation to date of why the
  Universe is uniform and flat?