Announcements

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Announcements

• Monday, March 26 Midterm II
• Friday, April 6 Project outline due

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Lecture 27The expanding universe III How is it
curved?
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(No Transcript)
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The great synthesis (1930)

• Meeting by Einstein, Hubble and Lemaître
• Einstein theory of general relativity
• Friedmann and Lemaître expanding universe as a
  solution to Einsteins equation
• Hubble observational evidence that the universe
  is indeed expanding
• Consequence
• Universe started from a point? The Big Bang
  Model

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Lets apply Einsteins equation to the Universe

• What is the solution of Einsteins equation for a
  homogeneous, isotropic mass distribution?
• As in Newtonian dynamics, gravity is always
  attractive
• a homogeneous, isotropic and initially static
  universe is going to collapse under its own
  gravity
• Alternative expanding universe (Friedmann)

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Einsteins proposal cosmological constant ?

• There is a repulsive force in the universe
• vacuum exerts a pressure
• empty space is curved rather than flat
• The repulsive force compensates the attractive
  gravity ? static universe is possible
• but such a universe turns out to be unstable
  one can set up a static universe, but it simply
  does not remain static
• Einstein greatest blunder of his life, but is
  it really ?

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Edwin Hubble (1889-1953)

• Four major accomplishments
• in extragalactic astronomy
• The establishment of the Hubble classification
  scheme of galaxies
• The convincing proof that galaxies are island
  universes
• The distribution of galaxies in space
• The discovery that the universe is expanding

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Key results

• Most galaxies are moving away from us
• The recession speed v is larger for more distant
  galaxies. The relation between recess velocity v
  and distance d fulfills a linear relation
  v H0 ? d
• Hubbles measurement of the constant H0
  H0 500 km/s/Mpc
• todays best fit value of the constant
  H0 65 km/s/Mpc

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initial distance 1 length unit final
distance 2 length units recess velocity
1 length unit per time unit
initial distance 2 length units final
distance 4 length units recess velocity
2 length units per time unit
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A metric of an expanding Universe

• Recall flat space
• better using spherical coordinates (r,?,?)

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A metric of an expanding Universe

• But, this was for a static space. How does this
  expression change if we consider an expanding
  space ?
• R(t) is the so-called scale factor

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Example static universe
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Example expanding at a constant rate
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Example expansion is slowing down
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Example expansion is accelerating
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Example collapsing
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How old is the universe?

• A galaxy at distance d recedes at velocity vH0 ?
  d.
• When was the position of this galaxy identical to
  that of our galaxy? Answer

• tHubble Hubble time. For H0 65 km/s/Mpc
  tHubble 15 Gyr

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How big is the universe?

• We cant tell. We can only see (and are affected
  by) that part of the universe that is closer than
  the distance that light can travel in a time
  corresponding to the age of the Universe
• But we can estimate, how big the observable
  universe is

• dHubble Hubble radius. For H0 65 km/s/Mpc
  dHubble 4.6 Gpc

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A metric of an expanding Universe

• But, so far, we only considered a flat space.
  What, if there is curvature ?
• k is the curvature constant
• k0 flat space
• kgt0 spherical geometry
• klt0 hyperbolic geometry

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A metric of an expanding Universe

• But, so far, we only considered a flat space.
  What, if there is curvature ?
• k is the curvature constant
• k0 flat space
• kgt0 spherical geometry
• klt0 hyperbolic geometry

kgt0
klt0
k0
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Cosmological redshift

• While a photon travels from a distance source to
  an observer on Earth, the Universe expands in
  size from Rthen to Rnow.
• Not only the Universe itself expands, but also
  the wavelength of the photon ?.

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Cosmological redshift

• General definition of redshift? for
  cosmological redshift

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Cosmological redshift

• Examples
• z1 ? Rthen/Rnow 0.5
• at z1, the universe had 50 of its present day
  size
• emitted blue light (400 nm) is shifted all the
  way through the optical spectrum and is received
  as red light (800 nm)
• z4 ? Rthen/Rnow 0.2
• at z4, the universe had 20 of its present day
  size
• emitted blue light (400 nm) is shifted deep into
  the infrared and is received at 2000 nm
• most distant astrophysical object discovered so
  far z5.8

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Announcements

• Monday, March 26 Midterm II
• Friday, April 6 Project outline due