Lecture 25 Problems with the Big Bang Inflation

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Lecture 25Problems with the Big BangInflation

• ASTR 340
• Fall 2006
• Dennis Papadopoulos

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The cosmic concordance

• What is our universe like?
• Matter content?
• Geometry (flat, spherical, hyperbolic)?
• Anything else strange?
• Remarkable agreement between different
  experimental techniques
• Cosmic concordance parameters

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Measurements of the matter content of the
Universe (recap)

• Primordial nucleosynthesis
• Theory predicts how present light element
  abundances (4He, 3He, D, 7Li) depend on mean
  baryon density
• Observed abundances ? ?B?0.04
• Galaxy/galaxy-cluster dynamics
• Look at motions of stars in galaxies, or galaxies
  in galaxy clusters
• Infer presence of large quantities of dark
  matter which gravitationally affects observed
  objects but cannot be seen with any telescope

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Nucleosynthesis
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• Analysis of galaxy motions suggests a total
  matter density of ?Matter?0.3
• Same conclusion from gravitational lensing by
  clusters (light from background objects is bent
  due to GR effects)

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• First stunning conclusion
• Compare ?B?0.04 and ?Matter?0.3
• Normal matter only accounts for about 1/8 of the
  total matter thats out there!
• Dark matter provides ?DM?0.26
• Were made of the minority stuff!

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• Can be confirmed by taking an inventory of a
  cluster, where diffuse gas is hot and emits
  X-rays
• Find that about 1/8 of a clusters mass is in
  baryons
• We believe that clusters should be representative
  samples of the universe
• Confirms ?DM?0.26

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MEASURING THE GEOMETRY OF THE UNIVERSE

• Recall that universe with different curvature has
  different geometric properties
• Adding up the angles in a triangle,
• Flat universe(k0) angles sum to 180?
• Spherical universe (k1) angles sum to gt180?
• Hyperbolic universe (k-1) angles sum to lt180?
• Similarly, for a known length L at a given
  distance D, the angular size on the sky varies
  depending on the curvature of space
• Flat universe (k0) angular size ?L/D
• Spherical universe (k1) angular size ?gtL/D
• Hyperbolic universe (k-1) angular size ?ltL/D

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L
L
L
D
k-1
k0
k1
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Angular size of fluctuations in the CBR

• Remember the cosmic microwave background
• It has fluctuations, with average separations
  corresponding to a known scale L at the distance
  where light last interacted with matter
  (matter/radiation decoupling)
• Distance D to this surface of last scattering
  is also known
• Can use apparent angular separations of
  fluctuations compared to L/D to infer geometry of
  Universe

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Surface of last scattering
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us
L
D
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Flat universe!

• Result
• The universe is flat
• In terms of omega curvature parameter,
• ?k0, i.e k0
• Recall that the sum of all three omega parameters
  as measured at present time must be 1
• How do we reconcile ?k0 with our measurement of
  the matter density, which indicates ?M0.3?
• There must be a nonzero cosmological constant,
  ??0.7!

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Non-zero ?

• Recall that with a non-zero, positive value of ?
  the universe expands more rapidly than it would
  if it contained just matter

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• Are there other indications of nonzero ??
• Yes, from direct measurement of deceleration
  parameter q0
• Recall q0 ?(d2R/dt2 )/(RH2) measures the rate
  of change of the Hubble parameter (expansion
  rate)
• The relation between q0 , ??, and ?M is
• q0 0.5? ?M ? ??
• If ?M 0.3 and ??0.7, would expect q0 -0.55
• More generally, any negative q0 means
  acceleration rather than deceleration in the
  cosmic expansion rate, and would imply ?? gt ?M
  /20.15
• Direct measurement of q0 would be able to confirm
  finding that ? is nonzero

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The accelerating Universe

• Huge clue came from observations of Type-1a
  Supernovae (SN1a)
• Very good standard candles
• Can use them to measure relative distances very
  accurately

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Type 1A Supernovae
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• In the normal life of a star (main sequence)
• nuclear fusion turns Hydrogen into Helium
• In the late stages of the life of a massive star
• Helium converted into heavier elements (carbon,
  oxygen, , iron)
• At end of stars life, get an onion-like
  structure (see picture to right)

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• Whats special about iron?
• Iron has the most stable nucleus
• Fusing hydrogen to (eventually) iron releases
  energy (thus powers the star)
• Further fusion of iron to give heavier elements
  requires energy to be put in
• Can only happen in the energetic environment of a
  supernova explosion
• So, all heavier elements are created during
  supernova explosions

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Supernovae

• What produces a SN1a?
• Start off with a binary star system
• One star comes to end of its life forms a
  white dwarf (made of helium, or carbon/oxygen)
• White Dwarf starts to pull matter off other star
  this adds to mass of white dwarf (accretion)
• White dwarfs have a maximum possible mass the
  Chandrasekhar Mass (1.4 MSun)
• If accretion pushes White Dwarf over the
  Chandrasekhar Mass, it starts to collapse.

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• White Dwarf starts to collapse
• Rapidly compresses matter in white dwarf
• Initiated runaway thermonuclear reactions star
  turns to iron/nickel in few seconds
• Liberated energy blows star apart
• Resulting explosion briefly outshines rest of
  galaxy containing it these are the SN1a events
• SN1a
• No remnant (neutron star or black hole) left
• Since white dwarf always has same mass when it
  explodes, these are standard candles (i.e.
  bombs with a fixed yield, hence fixed luminosity)

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H0 and q0 with SN1as

• The program
• Search for SN1a in distant galaxies
• Compare expected power with observed brightness
  to determine distance
• Measure velocity using redshift
• Low redshift galaxies give measurement of H0
• High redshift galaxies allows you to look for
  deceleration of universe

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The results

• This program gives accurate value for Hubbles
  constant
• H72 km/s/Mpc
• Find acceleration, not deceleration, at large
  distance!
• Very subtle, but really is there in the data!
• Profound result!

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• What does the future hold? Increasingly rapid
  expansion!

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Dark Energy

• There is an energy in the Universe that is
  making it accelerate
• Call this Dark Energy
• This makes up the rest of the gravitating energy
  in the Universe, and causes it to be flat!
• Completely distinct from Dark Matter
• Remember Einsteins cosmological constant?
• Dark Energy has precisely the same effect as
  Einsteins cosmological constant
• So, he was probably right all along!

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What is dark energy?

• An energy that is an inherent component of
  space
• Consider a region of vacuum
• Take away all of the radiation
• Take away all of the matter
• Whats left? Dark energy!
• But we have little idea what it is

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The Age of the Universe

• Using this cosmological model, we can figure out
  the age of the Universe.
• Answer 13.7 billion years
• Prediction
• There should be no object in the Universe that is
  older than 14 Gyr.
• This agrees with whats seen!
• This was a big problem with old cosmological
  models that didnt include dark energy
• e.g age of the universe in ?M 1, ?k 0, ??0
  model is 9 billion years
• But there are globular star clusters whose
  estimated ages are 12-14 billion years!
• This was troubling since universe must be at
  least as old as the oldest stars it contains!

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Concordance model

• In summary, the parameters for our Universe,
  using best available data
• Hubble constant H072 km/s/Mpc
• Geometry ?k 0 (flat)
• Deceleration parameter q0?0.55
• Baryon density ?B0.04
• Dark matter density ?DM0.26
• Cosmological constant ??0.7
• Age t013.7 billion years

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Deceleration Acceleration The Saga Continues
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• although we are far from understanding all the
  properties of the Universe, recent observations
  are bringing us to the era of precision
  cosmology!

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Observing the Big Bang for Yourself

• Olbers Paradox
• Why is the darkness of the night sky evidence for
  the Big Bang?

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Why is the darkness of the night sky evidence for
the Big Bang?
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Olbers Paradox If universe were 1)
infinite 2) unchanging 3) everywhere
the same Then, stars would cover the night sky
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Olbers Paradox If universe were 1)
infinite 2) unchanging 3) everywhere
the same Then, stars would cover the night sky
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Night sky is dark because the universe changes
with time As we look out in space, we can look
back to a time when there were no stars
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Night sky is dark because the universe changes
with time As we look out in space, we can look
back to a time when there were no stars
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• Why is the darkness of the night sky evidence for
  the Big Bang?
• If the universe were eternal, unchanging, and
  everywhere the same, the entire night sky would
  be covered with stars
• The night sky is dark because we can see back to
  a time when there were no stars

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What aspects of the universe were originally
unexplained with the Big Bang theory?
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Inflation

• What aspects of the universe were originally
  unexplained with the Big Bang theory?
• How does inflation explain these features?
• How can we test the idea of inflation?

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What is Inflation

• Power law expansion rate of change R gets
  longer as the Universe expands. i.e. if R was 50
  smaller 10 Gyars ago it will be a factor of 2
  bigger 30 Gyears later
• Rate of change of R constant expansion
  exponential- Universe could expand by a factor of
  1050 in a fe10-30 seconds
• In GR rate of expansionr1/2 (doubling
  time1/r1/2)

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Mysteries Needing Explanation

• Where does structure come from?
• Why is the overall distribution of matter so
  uniform?
• Why is the density of the universe so close to
  the critical density?

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Mysteries Needing Explanation

• Where does structure come from?
• Why is the overall distribution of matter so
  uniform?
• Why is the density of the universe so close to
  the critical density?
• An early episode of rapid inflation can solve all
  three mysteries!

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How does inflation explain these features?
1 meter
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Inflation can make all the structure by
stretching tiny quantum ripples to enormous
size These ripples in density then become the
seeds for all structures
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How can microwave temperature be nearly identical
on opposite sides of the sky?
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Regions now on opposite sides of the sky were
close together before inflation pushed them far
apart
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Overall geometry of the universe is closely
related to total density of matter energy
Density Critical
Density gt Critical
Density lt Critical
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Inflation of universe flattens overall geometry
like the inflation of a balloon, causing overall
density of matter plus energy to be very close to
critical density
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How can we test the idea of inflation?
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Patterns of structure observed by WMAP show us
the seeds of universe
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Observed patterns of structure in universe agree
(so far) with the seeds that inflation would
produce
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Seeds Inferred from CMB

• Overall geometry is flat
• Total massenergy has critical density
• Ordinary matter 4.4 of total
• Total matter is 27 of total
• Dark matter is 23 of total
• Dark energy is 73 of total
• Age of 13.7 billion years

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Seeds Inferred from CMB

• Overall geometry is flat
• Total massenergy has critical density
• Ordinary matter 4.4 of total
• Total matter is 27 of total
• Dark matter is 23 of total
• Dark energy is 73 of total
• Age of 13.7 billion years

In excellent agreement with observations of
present-day universe and models involving
inflation and WIMPs!
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What have we learned?

• What aspects of the universe were originally
  unexplained with the Big Bang theory?
• The origin of structure, the smoothness of the
  universe on large scales, the nearly critical
  density of the universe
• How does inflation explain these features?
• Structure comes from inflated quantum ripples
• Observable universe became smooth before
  inflation, when it was very tiny
• Inflation flattened the curvature of space,
  bringing expansion rate into balance with the
  overall density of mass-energy

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What have we learned?

• How can we test the idea of inflation?
• We can compare the structures we see in detailed
  observations of the microwave background with
  predictions for the seeds that should have been
  planted by inflation
• So far, our observations of the universe agree
  well with models in which inflation planted the
  seeds