Last Time

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Last Time

• We began to answer the question, How was the
  Universe created?
• To answer this question, we first have to come to
  an understanding of what the Universe is

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• One step towards doing this is to understand how
  big the Universe is
• But measuring distances in space is notoriously
  difficult
• There are no mile markers to help us

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• Astronomers use the concept of the distance
  ladder to measure distances
• Each rung on the distance ladder is a technique
  for measuring distances
• Each rung only gets us far, and each rung is
  dependent on the ones below it

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• An uncertainty in one rung propagates through the
  all other rungs
• We need to be as accurate as possible

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• The first rung on the distance ladder was the
  measurement of the Earth-Sun distance
• We know the relative distances of all the planets
• If we can measure the distance to other planets,
  we can determine the length of the AU

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• We use radar that is bounced off of other planets
• We know the speed of light
• We can measure the time it takes for the radar
  pulse to make a round trip
• We can calculate the distance to the planets

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• Once we know the AU, we can use parallaxes to
  measure the distance to the stars
• But we have to know the baseline (in this case, 2
  AU)

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• Both of these methods are direct and very
  reliable
• But parallax only works out to about 100
  light-years

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• Next, we use main-sequence fitting
• By using parallax, we can build an H-R diagram in
  terms of absolute magnitude

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• We can then make an H-R diagram for stars that
  are all the same, though unknown distance
• This will be in terms of apparent magnitude

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• Then we just adjust the H-R diagram so and use
  the distance modulus to find the distance
• This works out to about 300,000 light years

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• The next rung is to use Cepheid Variables
• Cepheid variables are pulsing stars
• The period of pulsation relates to their
  luminosity, so they are a type of standard candle

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• Measuring period is easyjust watch the star
• From period we can determine luminosity
• We can measure flux, and with the flux and
  luminosity, we can calculate distance
• But we must first calibrate using main sequence
  fitting

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• This works out to about 13 million light years,
  but past this point Cepheids are too dim
• Next, we use Type Ia supernovae
• These, too, are standard candles, but they are
  much brighter
• This gets us out to 1 billion light-years

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• Light that traveled 1 billion light-years must
  have traveled for at least 1 billion years
• The universe was a different place
• Finding standard candles that we can calibrate is
  hard

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• The next rung is the cosmological redshift

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• Hubble realized that there was a link between the
  recession velocity of a galaxy and its distance

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• This is Hubbles law
• The current best estimate for H0 is 72 km/s/Mpc
• Or, every 1 million parsecs, galaxies speed up by
  72 km/s

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• Why are all the galaxies rushing apart?
• Because the Universe is expanding!
• Space-time itself is growing, and the galaxies
  are being taken along for the ride

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• The cosmological redshift is just the stretching
  of lights wavelength due to this expanding
  Universe

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• But the Universe is not expanding in small
  patches where the local gravity is strong enough
  to overcome the expansion

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• Still, overall, the Universe is expanding
• And the expansion is Universalit is the same
  everywhere

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• If we follow the expanding Universe backwards in
  time, we come to the conclusion that the Universe
  must have been much smaller
• Everything was much closer together

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• In fact, everything in the Universe was contained
  in a singularity
• For some reason, though, the Universe began to
  grow

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• The explosion that caused our Universe to spring
  forth is called the Big Bang
• Before the Big Bang, there was nothingno space
  and no time

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• The Big Bang theory seems to claim quite a lot
• Why are we so confident?
• We traced the evolution of the Universe to answer
  this question

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• The Big Bang makes predictions that we can test
• One of these is that the Universe would have been
  very hot and energetic immediately after the Big
  Bang

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• Strange particles were being created and then
  quickly decaying back into energy
• But some particles, like protons, neutrons, and
  electrons, were stable

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• 100 second A.B.B., the conditions would have been
  right for protons and neutrons to come together
  to make the first atomic nuclei

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• We can predict the conditions during this time
  and from this predict the relative abundances of
  Hydrogen and Helium

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• By 300 A.B.B., fusion would have stopped and we
  expect there to have been 75 Hydrogen, 25
  Helium, 0.01 Deuterium
• This is what we observe!!!

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• For the next 380,000 years, the Universe would
  still be very hot and electrons would not be able
  to combine with nuclei
• This means light could not travel freely

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• But after 380,000 years A.B.B., the Universe
  would have cooled enough for electrons to combine
  with nuclei, and light would be able to travel

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• This radiation would be black body radiation and
  the peak wavelength would correspond to a
  temperature of 3000 Kelvin

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• This light has been detected, but today it is
  redshifted, so that it appears to correspond to a
  2.725 Kelvin black body
• This is known as the Cosmic Microwave Background

39
Last Time

• We also discussed other observational signatures
  of the Big Bang that we will soon be able to see
• The Dark Ages
• The Epoch of Reionization

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Last Time

• Finally, we discussed the growth of large scale
  structure
• The slight anisotropies in the CMB are a map of
  the density of the early Universe

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Last Time

• We can follow this density pattern as it changes
  with time
• Do a computer simulation
• See if it resembles our current Universe

42
The Growth of Structure

• Lets do just that
• Structure Growth
• Another Example
• The Millennium Simulation

43
This Time

• Finish up the large scale structure of the
  Universe
• Look at some problems with the Big Bang
• Discuss the solution to those problemsInflation
• Start talking about dark energy

44
The Large Scale Structure

• Do these simulations match what we see?
• Finding out is not easy
• Requires us to know the distance to hundreds of
  thousands, even millions of galaxies
• Need lots of redshifts

45
The Large Scale Structure

• A few projects have done this
• 2MASS
• CfA Redshift Survey
• Sloan Digital Sky Survey
• 2dF Galaxy Redshift Survey

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2MASS

• 2MASS stands for 2 Micron All Sky Survey
• Map the entire sky at about 2 microns
• Catalogued over 1 million galaxies

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CfA Redshift Survey

• Started in 1977 by the Center for Astrophysics
  (Harvard)
• Completed 1982
• Got redshifts out to about 700 million light years

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CfA Redshift Survey

• The second survey (1985-1995) got redshifts for
  about 18,000 bright galaxies
• Saw out to about 600 million light-years

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The Sloan Digital Sky Survey

• Sloans goal is to map 25 of the sky
• Located at Apache Point, NM
• Uses advanced fiber-optic systems and a 120
  Megapixel CCD array
• Out to 2 billion light-years
• Goal is to observe 100 million objects
• 200 GB a night

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2dFGS

• Stands for 2 degree Field Galaxy Survey
• A deep survey of a 1500 degrees2
• Out to 600 million parsecs
• 232,155 Galaxies in the catalog

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Large Scale Structure

• The answer to our question of Does observation
  match simulation? is an emphatic yes
• For these, and other reasons, we can say with
  great confidence that the Big Bang theory is, at
  least, on the right track

58
Not So Fast

• But the Big Bang theory that we talked about is
  not perfect
• In fact, there are some real problems with it

59
Not So Fast

• The horizon problem
• The flatness problem
• The magnetic monopole problem
• All three of these problems are resolved by our
  next topic

60
Runaway Universe

• Inflation

61
Motivation

• These three problem could be a nail in the coffin
  of the Big Bang unless something in the theory
  changes
• Tweaking a theory is just part of how theories
  get better
• This is a great example

62
A Word of Caution

• Although it seems very likely that the Universe
  went through some type of inflationary phase, the
  exact nature of inflation is still debatable

63
A Word of Caution

• With that in mind, lets look at the three
  problems mentioned earlier

64
The Horizon Problem

• Take a another look at the picture of the CMB

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The Horizon Problem

• Those fluctuations are 300mK
• The entire CMB has the same temperature to within
  one part in a million!
• This is smootha little too smooth actually

67
The Horizon Problem

• Information cannot travel faster than the speed
  of light
• At the moment of recombination, certain parts of
  the Universe would have never been able to
  exchange information

68
The Horizon Problem

• We can estimate the angular size of one of these
  regions
• It is only 2
• This means that only parts of the Universe with
  an angular size of 2 should have been able to
  exchange information

69
The Horizon Problem

• But if that is true, how did every part of the
  Universe come to have almost the same
  temperature?
• We should only see the same temperature on areas
  about 2 big!

70
The Horizon Problem

• This is the horizon problem
• Apparently, areas that should not have been able
  to talk to each other, did

71
The Horizon Problem is a result of the huge
differences in temperature in different parts of
the CMB.

• True
• False

72
The Flatness Problem

• Our Universe appears to have W 1.000.02
• This is an extraordinary result
• W could have been any been anything from 0 to 8
• It ended up being exactly the number needed for a
  flat Universe
  

73
The Flatness Problem

• Scientists dont like to make us special
• This extends to our Universe
• Why this seemingly special value of W?

74
The Flatness Problem

• It gets worse
• Any slight deviation from W 1 grows as time
  goes on
• If W 1.00 now, it must have been even closer 1
  in the early Universe

75
The Flatness Problem

• For example, even at a late age of 300 seconds,
  W had to be at least
• 1.0000000000000
• Why, how could our Universe have been created so
  close to a special value?

76
The Flatness Problem

• This is the flatness problemour Universe is too
  flat to be explained by random chance in a normal
  Big Bang model

77
Having W so close to 1 is the essence of the
Flatness Problem.

• True
• False

78
The Magnetic Monopole Problem

• This is a magnet ?
• It has a north and south pole
• Cut it in half, and it still has a north and
  south pole

79
The Magnetic Monopole Problem

• All magnets have both a north and south pole
• We have never seen a magnet with only a north, or
  only a south pole
• Such a magnet is referred to as a magnetic
  monopole

80
The Magnetic Monopole Problem

• The problem is, in our treatment of the Big Bang,
  we actually predict that there should be lots of
  magnetic monopoles
• Not actually usthese guys

81
The Magnetic Monopole Problem

• This is the magnetic monopole problem
• We see 0 of something we should lots of

82
A magnetic monopole is a very tiny magnet with
both a north and south pole.

• True
• False

83
The Solution

• We can fix all these problems if we do something
  weird
• Our baby Universe has to have a growth spurt

84
Inflation

• Growth spurt doesnt really describe it
• Our Universe needs to go through an era of
  exponential growth
• In about 10-33 seconds the Universe needs to grow
  1026 times

85
Back to The Beginning

• Lets revisit the Big Bang, and go into a little
  more detail during those first 10-32 seconds
• Like we said, the Universe was hot

86
Back to The Beginning

• Energies were so high, that something all
  together weird happened
• The electromagnetic force, the nuclear strong
  force, and the nuclear weak force were joined
• They made up one superforce

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???

• This seems worse than it is
• Electricity and magnetism seem to be two separate
  forces at first glance
• In fact, it is just one force, electromagnetism
• This is an idea we are used to

89
Separation

• As the Universe cooled, the strong force
  separated from electromagnetism and the weak
  force
• What implications does this have?

90
Separation

• This change would have dumped a huge amount of
  energy into the Universe
• Can we relate this to our everyday experiences?
• DunnoIll try

91
Separation

• It is possible to heat water to above the boiling
  point
• Need a smooth container
• The water is in a highly unstable state
• A slight disturbance is explosive

92
BOOM

• Something like this happened in the early
  Universe
• The Universe expanded and cooled, and was in an
  unstable state
• When the strong force separated, it blew up the
  Universe

93
Inflation

• This event is known as inflation
• Really, this was the BANG in the Big Bang

94
Inflation caused the Universe to grow

• linearly
• exponentially
• logarithmically

95
Inflation

• How does this fix the three problems we discussed
  earlier?
• Basically, by smoothing everything out

96
The Horizon Problem

• Inflation would cause the Universe to grow faster
  than the speed of light
• This sounds contradictorybut as long as no
  information is transferred, it is possible for
  things to travel faster than the speed of light

97
The Horizon Problem

• More accurately, space-time grew faster than
  light
• Space-time has no mass, so this OK

98
The Horizon Problem

• This means a very tiny piece of space, nice and
  connected, would have grown exponentially
• This initially tiny chunk of space would have
  been uniform

99
The Horizon Problem

• Light would have no problem crossing this tiny
  chunk
• Same temperature
• Same density
• Same laws of physics
• -)

100
The Horizon Problem

• In a very real way, this chunk becomes our
  Universe
• Is there something beyond our Universe?
• Maybe, but we could never observe it

101
The Horizon Problem

• Inflation creates our observable Universe
• This is the Universe that we can communicate with
• Anything outside of it was cut off from us long
  ago

102
The Horizon Problem

• Even though our long lost Universe was created by
  the same Big Bang, it is, for all intents and
  purposes, a separate Universe
• Could have different laws of physics

103
The Horizon Problem

• In this case, we expect the CMB to have the same
  temperature, and we expect the Universe to be
  uniform

104
The Horizon Problem

• But the CMB is not perfectly uniform
• Random quantum fluctuations would have cause very
  tiny changes in the temperature
• These changes have a very specific signature that
  would be imprinted on the CMB

105
The Horizon Problem

• These signatures have been observed
• A good thing for inflation
• In fact, it is these signatures that were used in
  our earlier simulations

106
The Horizon Problem

• So inflation not only solves the horizon problem,
  it helps explain the CMB and growth of structure
  even better than the Big Bang alone

107
The Flatness Problem

• Imagine the Earth
• We know the Earth is curved
• Does it look curved?
• Why not?

108
The Flatness Problem

• The Earth is big
• On small scales, like those of our everyday
  experience, the curvature is too small to detect

109
The Flatness Problem

• Even if the overall curvature of space is not
  flat, if the curvature is on a large enough
  scale, we would not notice it

110
The Flatness Problem

• Inflation would have taken a very small chunk of
  the Universe and grew it
• This small chunk must have been locally flat
• Since this chunk grew to become the whole
  observable Universe, the whole observable
  Universe must be nearly flat

111
The Flatness Problem

• The consequence is that the Big Bang almost
  certainly did not produce a flat Universe

112
The Flatness Problem

• But the entire Universe, including whatever is
  beyond our observable Universe, must have a
  curvature on a scale larger than about 14 billion
  light-years

113
The Magnetic Monopole Problem

• The Big Bang predicted lots of magnetic monopoles
• But do we expect lots in our tiny little chunk?
• No!

114
The Magnetic Monopole Problem

• The chances of having one in our chunk are small
• And so, it is natural that we dont see any

115
Summary and Pause

• Inflation seems almost impossible to wrap your
  mind around
• But it solves many problems that our original Big
  Bang picture had

116
Summary and Pause

• Do I expect you to really understand it?
• NO!!
• But you should be aware that something like this
  seems to have happened, and it is consistent with
  what we know about physics

117
One Last Problem

• The Big Bang still isnt perfect
• Someone once asked, Why is there any normal
  matter? Why didnt it all get destroyed by
  antimatter?

118
One Last Problem

• Physicists wonder about this same thing
• For some reason, there must have been more
  particles than antiparticles
• We do not yet know why

119
One Last Problem

• Still this, and the other disagreements over
  inflation, the nature of dark matter, and the
  dark energy (next topic), shouldnt kill the Big
  Bang
• Just needs a bit more tweaking

120
What Do You Think?

• So this is how we think the Universe was created
• I am curious to hear your thoughts

121
Fire and Ice

• Some say the world will end in fire,Some say in
  ice.From what I've tasted of desireI hold with
  those who favor fire.But if it had to perish
  twice,I think I know enough of hateTo say that
  for destruction iceIs also greatAnd would
  suffice.
• Robert Frost

122
Which death would you prefer?

• Fire
• Ice

123
The Accelerating Universe

• The Mystery of the Dark Energy

124
Some Perspective

• We have just journeyed through our pastwe are
  about to take a look into our future
• We will find that our Universe is much stranger
  than we ever imagined
• I also think the answer of How will the Universe
  end? will disappoint many you

125
The Quest for H

• Our universe is expanding, and the rate at which
  that expansion is slowing down can tell us the
  fate of our Universe

126
The Quest for H

• H is the rate of expansion of the Universe
• This rate of expansion changes, so H is not
  constant for all time
• H0 is the rate of expansion right now

127
The Quest for H

• If the Universe is closed then the expansion will
  slow down to a halt
• After that, the expansion turns into contraction
• We end in a Big Crunch

128
The Big Crunch

• A Big Crunch would be hot
• Densities and temperatures would increase as the
  Universe shrank

129
A Cold Death

• A flat Universe will slow down, but never quite
  stop expanding
• It just sort of coasts, getting close to zero
  expansion

130
A Cold Death

• In this scenario, all the stars will burn out
• No more fusible material
• Many particles will simply decay away
• Light will become so scarce, as the Universe gets
  bigger ad bigger, that it will get dark

131
A Cold Death

• It is a slow, painful death by freezing
• Eventually, all that is left is the stray proton
  or electron, and maybe a photon here or there

132
A Cold Death

• An open Universe is even worse
• The expansion doesnt even get close to stopping
• It will slow down, but never approach zero

133
Or So We Thought

• But that was 15 years ago
• While trying to measure the rate of deceleration,
  and thus the determine the fate of the Universe,
  astronomers found somethingstrange

134
Standard Candles?

• Type Ia supernovae form very far away seemed
  dimmer than we expected
• It was as if they were farther away than any of
  the above three scenarios allowed for

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Standard Candles?

• One explanation is that Type Ia supernovae are
  not good standard candles
• But we think they are

137
The Accelerating Universe

• The other explanation is that the Type Ia
  supernovae really are farther away than predicted
  by our naïve approach

138
The Accelerating Universe

• What could cause the supernovae to be farther
  away?
• The expansion of the Universe must not be slowing
  downit must be speeding up

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Could gravity cause the expansion to accelerate?

• Yes
• No

140
The Dark Energy

• But what could possibly cause the expansion to
  speed up?
• Gravity is supposed to be the dominant force, but
  it causes collapse, not expansion

141
The Dark Energy

• To cause the Universe to expand, we need to put
  some extra energy into the system
• Similar to inflation
• But where would this energy come from?

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The Dark Energy

• We dont know what it is, but we call it the Dark
  Energy
• We represent it by the Greek letter L

143
The Dark Energy

• When this discovery was made, it was fairly
  unexpected, but not unprecedented
• Einstein invoked a similar idea

144
The Cosmological Constant

• Einstein realized that GR predicted an expanding
  or contracting universe, but he didnt like the
  idea
• He introduced a cosmological constant into the
  equations

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The Cosmological Constant

• It was called a constant because it was the same
  for all times in the history of the Universe
• This constant was symbolized by L and
  counteracted any expansion or collapse
• Einstein would later call this my greatest
  blunder

146
The Cosmological Constant

• If the constant was big enough, it could actually
  increase the expansion
• This idea was invoked and abandoned several times
  during the 20th century
• This time, it looks like it is here to stay

147
The Dark Energy

• We do have some good contenders for the dark
  energy
• Perhaps the most promising is a vacuum energy

148
Vacuum Energy

• Remember our atoms?
• The electrons had a lowest energy level they
  could be in
• This energy level was not zero

149
Vacuum Energy

• We think space-time is the same way
• On subatomic scales, we think the very fabric of
  space seethes

150
Virtual Particles

• Particles and antiparticles seem to pop into
  existence out of nowhere, and then annihilate
  each other in tiny fractions of a second
• Called virtual particles

151
Virtual Particles

• Quantum mechanics allows for this as long as the
  particles are destroyed quickly
• It is like pulling a quick one on the Universe

152
Virtual Particles

• This quantum weirdness gives the vacuum a
  non-zero, lowest energy state
• This is a property of the vacuumof space itself
• Since we always have space, it would always be
  present
• This matches up with an idea like the
  cosmological constant

153
The Casimir Effect

• Can we detect this?
• Yes!
• It is called the Casimir effect

154
The Casimir Effect

• If we place two plates together, it limits the
  vacuum energy
• There will be more virtual particles outside of
  the two plates than between them

155
The Casimir Effect

• This imbalance causes the plates to be pushed
  together
• This is not gravity or electromagnetic forces
• It is the virtual particles

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The Casimir Effect

• As strange as it sounds, this has been measured
  in the lab
• It isnt too difficult

159
Which best describes the vacuum energy?

• It is a property of space, and is the same
  everywhere
• It is the result of a non-zero energy state
• It creates virtual particles
• All of the above

160
Vacuum Energy and Acceleration

• Could the vacuum energy cause the acceleration
• Yes, but

161
Vacuum Energy and Acceleration

• A complete understanding of vacuum energy
  requires a theory that uses both GR and quantum
  mechanics
• They hate each other

162
Vacuum Energy and Acceleration

• Since we dont yet have a good theory, we have
  trouble estimating the strength of the vacuum
  energy
• We can try, but the number we get is 1023 times
  too big!!!
• This is the worst guess in science!

163
Vacuum Energy and Acceleration

• If vacuum energy is the best way to describe dark
  energy, we need to do a lot more work to
  understand it
• There is at least one other contenderdont
  understand it well

164
Got Anything Else?

• Just relying on the Type Ia supernovae is not
  good enough for me
• Maybe we really dont understand them
• But there is other evidence

165
Back to Flatness

• As mentioned earlier, we know the Universe is
  flat
• But how?
• The CMB

166
Back to Flatness

• We can predict how big the angular size of all
  the different fluctuations in the CMB should be
• Remember that the curvature affects angles

167
Back to Flatness

• If the Universe was positively curved, the
  angular sizes would appear too big
• If the Universe was negatively curved, the
  angular sizes would be too small
• But they are just right

168
Back to Flatness

• Our measurements of the CMB are some of the best
  in science
• This is very convincing evidence that the
  Universe is indeed flat
• But that poses a problem

169
Back to Flatness

• Even our most optimistic measurements for the
  density of normal matter and dark matter give
• Wnm 0.04 Wdm 0.26

170
Back to Flatness

• This would mean that the total W is only 0.3
• But if we live in a flat Universe, W must be 1
• Something else must be out there that makes up
  the missing 0.7

171
Back to Flatness

• This is the dark energy
• Remember that both energy and mass contribute to
  curvature
• So we think all the densities are
• Wnm 0.04 Wdm 0.26 WL 0.7

172
Oops

• That means we dont know what 96 of the Universe
  is
• But we are convinced that something is out there

173
There is More

• The growth of structure simulations we saw also
  used dark energy
• They work pretty well
• And attempts to measure the curvature of the
  Universe using advanced techniques involving
  gravitational lensing also support dark energy

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A Cosmic Mystery

• So even though we dont know what dark energy is,
  it seems like it is not going anywhere
• There is hope for learning more

176
Back to H

• Turns out that if we can measure the history of
  the Hubble parameter (the rate of expansion), we
  can at least tell which contender is on the right
  track
• Why is H so important?

177
Back To H

• H can tell us many, many things
• A full history of H tells us the age of the
  Universe
• H tells us the critical density
• H tells us how far away things are

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The Age of the Universe

• This is how we know that the Universe is 13.7
  billion years old
• A very well known number
• We also know the critical density is 10-27 kg /
  m3

180
The Ultimate Fate of the Universe

• We can now answer, with great confidence, the
  question of how our Universe will end
• Even though it is flat, the Universe will
  continue to expand at an increasing rate due to
  dark energy
• We are headed for a colder, darker death than we
  ever thought

181
The Ultimate Fate of the Universe

• Stars will burn out, leaving only used up stellar
  cores
• Eventually, neutrons may decay, releasing protons
  and electrons
• Even the protons could decay to simpler
  particles, some day

182
The Ultimate Fate of the Universe

• Galaxies will get farther apart, or collapse to
  form single, isolated giants
• But these stars, too, will eventually die

183
The Ultimate Fate of the Universe

• The Universe will become so big that photons will
  become a rarity
• No light, no heat
• Just infinite, cold, darkness

184
The Ultimate Fate of the Universe

• Luckily, this fate lies in the very, very distant
  future
• So sleep soundly

185

• And the end of all our searching shall be to
  return to the place where we started and know it
  for the first time.
• -T.S. Eliot

186

• I hope that you can look back on the beginning of
  this course, and feel like you now know it for
  the first time.
• If you walk away with a new found sense of
  appreciation, and awe, then I am happy.