iSkylab 4

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iSkylab 4

• Two rungs of cosmic distance ladder
• First measure distance to Cepheids with parallax,
  also note their periods
• Establish period-luminosity relationship as slope
  of luminosity vs period graph (L comes from
  BL/(4p d2)
• Then observe two other Cepheids in two galaxies,
  determine luminosity from period, distance from
  BL/(4p d2)
• Redshift gives recessional velocity ? Hubbles
  constant as slope in velocity vs distance plot

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General Relativity ?! Thats easy!

Rµ? -1/2 gµ? R 8pG/c4 Tµ?
OK, fine, but what does that mean?

• (Actually, it took Prof. Einstein 10 years to
  come up with that!)

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Planetary Orbits

• Sun
• Planets orbit

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More General than Special Relativity

• General Relativity is more general in the sense
  that we drop the restriction that an observer not
  be accelerated
• The claim is that you cannot decide whether you
  are in a gravitational field, or just an
  accelerated observer
• The Einstein field equations describe the
  geometric properties of spacetime

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The Idea behind General Relativity

• We view space and time as a whole, we call it
  four-dimensional space-time.
• It has an unusual geometry, as we have seen
• Space-time is warped by the presence of masses
  like the sun, so Mass tells space how to bend
• Objects (like planets) travel in straight lines
  through this curved space (we see this as
  orbits), so
• Space tells matter how to move

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Effects of General Relativity

• Bending of starlight by the Sun's gravitational
  field (and other gravitational lensing effects)

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Assumption Cosmological Principle

• The Cosmological Principle on very large scales
  (1000 Mpc and up) the universe is homogeneous and
  isotropic
• Reasonably well-supported by observation
• Means the universe has no edge and no center
  the ultimate Copernican principle!

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What General Relativity tells us

• The more mass there is in the universe, the more
  braking of expansion there is
• So the game is
• Mass vs. Expansion
• And we can even calculate who wins!

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The Fate of the Universe determined by a single
number!

• Critical density is the density required to just
  barely stop the expansion
• Well use ?0 actual density/critical density
• ?0 1 means its a tie
• ?0 gt 1 means the universe will recollapse (Big
  Crunch) ? Mass wins!
• ?0 lt 1 means gravity not strong enough to halt
  the expansion ? Expansion wins!
• And the number is ?0 lt 1 (probably)

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The size of the Universe depends on time!
Expansion wins!
Its a tie!
Mass wins!
Time
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The Shape of the Universe

• In the basic scenario there is a simple relation
  between the density and the shape of space-time
• Density Curvature 2-D example Universe
  Time Space
• ?0gt1 positive sphere closed,
  bound finite
• ?01 zero (flat) plane open, marginal
  infinite
• ?0lt1 negative saddle open, unbound
  infinite

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Back to Expansion of the Universe

• Either it grows forever
• Or it comes to a standstill
• Or it falls back and collapses (Big crunch)
• In any case Expansion slows down!

Surprise of the year 1998 (Birthday of Dark
Energy) All wrong! It accelerates!
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Enter The Cosmological Constant

• Usually denoted ?0, it represents a uniform
  pressure which either helps or retards the
  expansion (depending on its sign)

• Physical origin of ?0 is unclear
• Einsteins biggest blunder or not !
• Appears to be small but not quite zero!
• Particle Physics biggest failure

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Triple evidence for Dark Energy

• Supernova data
• Large scale structure of the cosmos
• Microwave background

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Microwave Background Signal from the Big Bang

• Heat from the Big Bang should still be around,
  although red-shifted by the subsequent expansion
• Predicted to be a blackbody spectrum with a
  characteristic temperature of 2.725 Kelvin by
  George Gamow (1948)
• ? Cosmic Microwave Background Radiation (CMB)

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Discovery of Cosmic Microwave Background
Radiation (CMB)

• Penzias and Wilson (1964)
• Tried to debug their horn antenna
• Couldnt get rid of background noise
• ? Signal from Big Bang
• Very, very isotropic (1 part in 100,000)

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CMB Heres how it looks like!
Peak as expected from 3 Kelvin warm object
Shape as expected from black body
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Latest Results PLANCK

• Measure fluctuations in microwave background
• Expect typical size of fluctuation of ½ degree
  if universe is flat
• Result
• Universe is flat !

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Experiment and Theory
Expect accoustic peak at l200 ? There it is!
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Supernova Data

• Type Ia Supernovae are
• standard candles
• Can calculate distance
• from brightness
• Can measure redshift
• General relativity gives us distance as a
• function of redshift for a given universe
• Supernovae are further away than
• expected for any decelerating (standard)
• universe

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Pie in the Sky Content of the Universe
5
Dark Energy Dark Matter SM Matter
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72

• ?We know almost everything about almost nothing!

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Properties of Dark Energy

• Should be able to explain acceleration of cosmic
  expansion ? acts like a negative pressure
• Must not mess up structure formation or
  nucleosynthesis
• Does not dilute as the universe expands ? will be
  different of content of universe as time goes
  by

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Threefold Evidence

• Three independent measurements agree
• Universe is flat
• 28 Matter
• 72 dark energy

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Cosmic Inflation

• Size of the universe suddenly increased
  exponentially

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Consequences

• Fluctuations at a tiny
• fraction of a second when all parts of the
  universe talked to each other (to make sure
  everyone was at the same temperature)
• Suddenly fluctuations are enlarged
• Fluctuations become imprinted on CMB, provide
  seeds for large scale structure of universe
  (clups that grow into galaxies)

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Inflation solves the Horizon Problem

• How does one side of the universe know what
  temperature the other side is at?
• It has no way, because light (signal velocity) is
  too slow
• Need inflation at larger than light speed

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History of the Universe Hot small ? cold big

• before 10-43 s ?????? (Planck Era)
• 10-43 s T1032 K gravity splits from other
  forces
• 10-43 to 10-35 s Grand Unification era
• 10-35 s T1028 K Strong force splits from
  others. Epoch of inflation?
• 10-35 s to 10-10 s Electroweak era
• 10-10 s T1015 K Electromagnetic force splits
  from others
• 10-10 to 10-4 s Quark era
• 10-4 s T1013 K Quarks combine to form protons
  and neutrons
• 10-4 to 500,000 years Radiation era
• 180 s (3 minutes) T109 K Protons and neutrons
  combine to form nuclei (mainly Helium,
  deuterium)
• 500,000 years T3,000 K Nuclei and electrons
  combine to form atoms Decoupling
• 500,000 years to present Matter era