Cosmology

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Cosmology
Does the universe have an edge? A center? What
is the big bang? How can the universe expand if
it has no edge? Why is the universe the way it is?
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The edge-center problem

• Suppose the universe has an edge
• It wouldnt be an edge to the distribution of
  matter it would be an edge to space itself!
• You couldnt just reach past it and feel around
• Seems to violate common sense
• We assume it has no edge
• No edge gt no center
• If the universe is infinite ? no center problem.
• What is the universe is finite (more on this in
  a moment)

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What about the beginning (if there is one)?

• When you look at the night sky, what do you see?
• Well for one thing, its dark!
• What if the universe were infinitely old, and
  infinite in extent?
• Then no matter where you looked, your eyes would
  fall on a star/galaxy.
• The night sky would be bright
• (Why couldnt dust block the light?)
• (Or, why is the universe so cold?)
• Olbers paradox
• Either the universe is finite in extent
• or finite in age (or both)

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Universe vs. observable universe
Minor distinction Universe all that
exists Observable universe all that we can
see The former could be infinite The latter is
most definitely finite
All of astronomy is reasonably unreasonable.
? Reasonable assumptions often lead to
unreasonable results
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Cosmic expansion

• Recall Hubbles observation in 1929
• Z distance ? everything is receding from
  everything else (on the whole)
• The universe is expanding
• In reference to the balloon,
• where is the edge? The
  center?
• Keep in mind that its a 2-D analogy

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The big bang
Okay so the universe is expanding What if we
trace the expansion backward in time? What would
we expect? Would we reach a beginning? Is there
a beginning? This beginning is what
cosmologists call the big bang
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So what is this big bang?

• If no edge, then no center
• The big bang did not happen at some spot, it
  happened everywhere
• and is still happening

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The age of the universe
Okay if there was a beginning, then we can ask
the question, how old is the universe? (Based
on what we observe that is) For starters, we
can use the definition of velocity v d / t In
this simple form, we can take the distance
between two galaxies divide by their velocity
of recession (from each other) and solve for the
time
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The Hubble time
Using H0 70 km/s/Mpc ? 14 billion years
Where does 1012 come from? Units of H0 are
km/s/Mpc Convert Mpc to km, and then s to years
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A side road tour the CMBR
CMBR cosmic microwave background
radiation Picture it 1960s, two physicists
(Penzias Wilson) studying the sky in radio
wavelengths, Their measurements showed a
peculiar noise They thought it was bird
droppings After cleaning the antennae, the
noise remained
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A side road tour the CMBR (part II)

• 1948
• Gamov ? early universe should be hot dense
• Should radiate as a black body
• 1949
• Alpher and Herman ? large redshift would stretch
  the wavelength into the IR and radio

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A side road tour the CMBR (part III)
Back to the 60s Princeton physicist Robert
Dicke realized that, with the technology
available, we should just now be able to detect
this radiation (the CMBR) When Penzias Wilson
heard of Dickes work, they realized thats what
they saw! Still as scientists, we dont like to
jump to conclusions We would like to have other
observations confirm or reject this
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A side road tour the CMBR (part IV)
This CMBR should be all over the sky come from
everywhere Specifically, theory predicted that
it should look like the radiation coming from a
black body at a temperature of 3K (in the
IR) 1990, COBE satellite Measured black body
radiation with a temp. of 2.725 /- 0.002 K
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A side road tour the CMBR (part V)
Wait a minute! Youre going to tell me that this
hot big bang only had a temp. of 2.725 /-
0.002 K !?! Keep in mind that it is redshifted
by 1100. Theory predicted that this stuff was
emitted when the universe had cooled to
3000K More on this in a moment
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Back to the highway, the story of the big bang

• Redshifts ? expansion
• dark night sky CMBR
• Big bang
• As yet, we cant trace the universe to time t
  0,
• The physics is not understood well enough yet
• But we can come pretty darn close!
• (10 millionths of a second old!)

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The timeline of the big bang

• T 10-6 s
• High energy photons, T gt 1012 K, density gt 5 x
  1013 g/cm3 (close to that of an atomic nucleus!)
• (T for a photon means, the temp. of a blackbody
  that would radiate such a photon)
• (density of photons means, from E mc2, express
  the energy of the photons as if they had mass)
• Two high-energy photons can collide and create a
  particle-antiparticle pair which would then
  annihilate back into photons
• The early universe was a flickering soup of this
  stuff
• As the universe expanded, it cooled. The
  photons lost some of that energy

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The timeline of the big bang

• T 10-4 s
• High energy photons, T 1012 K
• The energy of the photons was not high enough to
  create n p particle-antiparticle pairs
• The remaining ns and ps annihilated back into
  photons, but
• For some reason, there were more particles than
  antiparticles!
• (For every billion pairs, one regular particle
  survived)
• While the photons didnt have enough energy to
  create p/anti-p pairs, they still had enough
  energy to create electron-positron pairs.
• This continued until

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The timeline of the big bang

• T 4 s
• T lt Tc where Tc corresponds to the temp. that the
  photons had enough energy to create
  electron-positron pairs
• All the n, p, e in the universe were created in
  the first 4 seconds!
• Meanwhile, the universe continued to expand and
  cool

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The timeline of the big bang

• T 2 minutes
• Before this time, photons still had enough energy
  to break apart atomic nuclei
• No nuclei before t 2 minutes
• T gt 2 minutes, deuterium could form (heavy
  hydrogen)

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The timeline of the big bang

• T 3 minutes
• He began to form (but hardly anything heavier
  since no stable nucleus with atomic weights of 5
  or 8 exist)
• A tiny amount of lithium formed, but nothing
  heavier

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The timeline of the big bang

• T 30 minutes
• T cooled enough to where nuclear reactions
  stopped
• 25 of the universe was He nuclei and 75 was
  H nuclei (protons)
• (This matches the abundances seen in the oldest
  stars)

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The timeline of the big bang

• T lt 50,000 years
• The universe was dominated by radiation (opaque)
• Photons couldnt travel far without hitting
  matter
• Radiation and matter were locked together in a
  dance
• Nuclei couldnt capture electrons to form atoms
  (and hence, couldnt emit light)
• The gas was ionized

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The timeline of the big bang

• T 50,000 years
• Around this time, the density of radiation was
  just about equal to the density of matter
• Before this, matter couldnt clump together
  because the photons kept everything smoothed
  out
• The universe was becoming matter dominated
• Now, matter could start to clump under the
  influence of gravity

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The timeline of the big bang

• T 105 years
• As the universe expanded, things continued to
  spread out
• Photons could travel a few kpcs without bumping
  into an electron
• The universe became more transparent
• Around the same time
• T cooled to about 3000K. At this temp., protons
  could capture electrons to form hydrogen!
• This epoch is referred to as recombination
• The photons could now travel without being
  scattered, and hence, retained this blackbody
  temp. of 3000K (which is what we see as the
  CMBR!)
• The universe glowed with the temp of 3000K, but
  as it expanded and cooled, that glow gradually
  shifted to the IR
• ? The universe became dark the dark age

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The timeline of the big bang

• T lt 109 years
• Darkness lasted until the first stars were formed
• Models suggest that these first stars were very
  massive, very luminous, and very short-lived
• They gave off enough UV light to start to ionize
  the gas in the universe
• This reionization marks the end of the dark
  age and the beginning of the age of stars and
  galaxies.
• (Looking at quasars reveals gas that has not yet
  been ionized observational support of the
  theory)

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The shape of space and time

• On the whole, the universe looks the same in
  every direction (with the exception of local
  variations) isotropic
• And also uniform homogeneous
• Isotropy homogeneity ?
  cosmological principle
• Any observer sees the same general features
• If you accept this, then there can be no edge,
  and no center
• (The redshifts of very distant objects are
  produced, not by the Doppler effect, but by space
  itself expanding)
• This leads us to ask what is the shape of
  space-time, i.e., the curvature

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The curvature of space and time
With a certain curvature, the universe can be
finite, yet have no edge or center And we can
make measurements to determine the
curvature! (specifically, the density)
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Open, closed, or flat?

• Curvature
• Three possibilities
• Open
• Negative curvature
• Infinite in extent
• Will expand forever
• Closed
• Positive curvature
• Finite
• Will collapse (big crunch/oscillate?)
• Flat
• In essence, no curvature
• Infinite
• ? Expansion will stop at t infinity

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The critical density
How the universe is curved depends on the
density The density which would make the
universe flat is called the critical density
?c ?c 9 x 10-30 g/cm3 ? lt ?c gt open ? gt ?c gt
closed All observable matter ? 5 of ?c Hubble
time revisited If flat ? But clusters are
older than this!
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Dark matter again
From gravitational lensing, rotation curves,
etc., we it appears that galaxies contain much
more matter than we can see Since we cant seem
to detect it, we call it dark matter Consider
the density of the early universe
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Dark matter early isotopes
Both 2H and 7Li are easily destroyed, in fact,
stars tend to destroy them, not create them ?
When we observe these isotopes at large
redshifts, we have very strong reason to believe
that they were produced only in the big bang
The early universe was a soup of photons,
protons, neutrons, and electrons Deuterium
(heavy hydrogen, 2H) was created in this soup of
particles If ? was high, ps and ns would have
collided with 2H and created He If ? was low,
more 2H would survive Lithium (6Li 7Li) was
also created in trace amounts (but nothing
heavier) If ? was high, more 7Li would be
created
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Dark matter limits on what its made of
The result is that neutrons and protons only make
up 4 of the critical density Yet we know that
26 of the critical density is made up of
stuff that attracts other stuff (from
gravitational lensing etc.) ? Much of the dark
matter must be non-baryonic, i.e., not made of
normal matter (exotic)
Measure the abundance of deuterium and lithium-7
at large look-back times (near quasars) We have
good reason to believe that they were produced
only in the big bang If the density of n, p was
low enough, more deuterium would survive If the
density of n, p was high enough, more lithium-7
would be created ? 2H sets a lower limit on the
density of normal matter (neutrons and protons-
baryonic matter), and 7Li sets an
upper limit on the density of normal matter!
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Dark matter candidates

• Only 4 of DM is baryonic (made of normal matter
  like protons and neutrons)
• Neutrinos? ? they do have mass 108 neutrinos
  for every normal particle
• However, they move at near the speed of light
  (they would be considered hot dark matter)
• The most successful models of galaxy formation
  require slower dark matter (cold dark matter)
  ? neutrinos not the complete answer
• Plus, DM doesnt interact easily with other
  particles except through gravity
• photons dont interact with DM
• DM not subject to the radiation pressure which
  hindered the clumping of normal matter
• Still, adding up the normal matter and the dark
  matter, we only get 30 of the critical
  density. It would seem we live in a open
  universe
• Not so fast

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Modern cosmology (inflation)
The big bang had two problems The flatness
problem It couldnt explain why the universe
seems to be nearly flat (even a small departure
in the early universe would have a dramatic
effect on the present universe, 1 part in 1049)
The horizon problem When we look at two parts
of the sky separated by only 1o, we see two parts
which werent causally connected (couldnt
communicate due to the speed of light), yet,
these parts (and all others) seem to share the
same temperature and properties Inflation
provides the solutions
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Modern cosmology (inflation)
In fact, quantum fluctuations could be the reason
for the big bang The reason there is
something instead of nothing is because nothing
is unstable. The beauty of inflation gives us
confidence that were on the right track.
What is inflation? In essence, the universe
underwent a sudden expansion at about time t
10-35 s, from the size of an atom to the size of
a cherry pit What caused this expansion? At this
time, the four forces decoupled from each other,
releasing a tremendous amount of energy which
inflated the universe That sudden inflation would
have forced the curvature to be nearly flat
(think of a balloon, the flatness problem) And
before inflation, the universe was small enough
to have equalize its temperature (the horizon
problem)
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Modern cosmology (acceleration)

• The universe seems to be flat, yet matter makes
  up only 30 of the critical density
• In the 1990s, two teams of astronomers set out
  to measure how the universe is slowing down using
  distant Type Ia supernovae
• They observed that the SNs were fainter than
  expected
• They are farther than expected
• The universe is speeding up!
• Note And it doesnt seem to be a problem with
  how the measurements are taken or dust extinction
  etc.

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Modern cosmology (dark energy)

• If the universe is accelerating, then there must
  be some repulsive force accelerating it
• 1916, Einstein, GR
• Einstein realized that his theory predicted that
  the universe should either expand or contract
• But at the time, it was thought the universe was
  in a steady state
• So Einstein introduced a fudge factor into his
  theory called the cosmological constant
• When, in 1929, Hubble observed that the universe
  was indeed expanding, Einstein commented that
  inserting the cosmological constant was his
  greatest blunder his original theory
  predicted the expansion!

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Modern cosmology (dark energy)

• Okay so reinserting the cosmological constant
  into GR, we have a working theory of this dark
  energy
• But need it be constant?
• Quintessence
• Vacuum energy
• Even seemingly empty space has energy
• Quintessence is a theory that allows the
  cosmological constant to vary with time
• Since the 90s, more measurements of Type Ias
  were taken
• Some even more distant seem to be too bright! (?
  they are closer than expected)
• Problem for dark energy? No!
• DE actually predicts that when the universe was
  much smaller, gravity would overpower the DE and
  hence, these extremely distant objects should be
  closer!

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Age and fate of the universe
Problem The universe seems to be flat ? age 9
billion years But we observe clusters that are
older than this! But if the universe has been
accelerating, expanding slower in the past, then
the universe would be older than 9 Gry. (Solves
the age problem) The ultimate fate of the
universe depends on the nature of dark
energy Cosmological constant ? will expand
forever Quintessence ? big rip
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The cosmological constant vs. quintessence
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Age and fate of the universe
Chandra X-ray observatory Measured hot gas
dark matter in galaxy clusters Compare results
with known clusters ? solve for distance Results
confirm that of the Type Ias (that the universe
is indeed accelerating) and also seems to almost
rule out quintessence (i.e., the cosmological
constant indeed seems to be constant) ? No big
rip
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Origin and structure of the curvature
Study the distribution of galaxies, large scale
structure Measure distance position and plot
the results (i.e., create a map of the
universe) Seems like the universe tends to
cluster along filamentary structures This
presents a puzzle The CMBR seems to be uniform
(corresponds to the time of recombination the
universe was uniform then) The look-back time to
the farthest galaxies is 93 of the way back to
the beginning How did this uniform gas coagulate
so quickly to form galaxies and the structure we
see? Why filaments?
The Two-Degree-Field (2DF) survey mapped the
position and distance of 250,000 galaxies and
30,000 quasars Analysis of the distribution also
confirms the acceleration independent of the Type
Ias and that of Chandra
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Theoretical models of large-scale structure
Quantum fluctuations in space would have been
stretched and enhanced at the time of inflation ?
filaments
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Origin and structure of the curvature
Inflation makes very specific predictions about
the sizes of the fluctuations we on Earth should
see in the CMBR WMAP mapped the CMBR at high
accuracy ? reveals small irregularities If these
irregularities were produced by inflation, then
the size of them depends on the sound speed of
the universe at the time of recombination Inflati
on predicts these irregularities to be about 1o
if the universe is flat, smaller if open, and
larger if closed
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Origin and structure of the curvature
Predictions of inflation in the three panels to
the left, the observed CMBR in the last
panel Observations fit well with a flat universe
(which is exactly what inflation did it
flattened the curvature of space-time!) This
also indirectly confirms dark energy and
acceleration
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Origin and structure of the curvature
Graphically, the data also fit well with
predictions of a flat universe
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The abundance of stuff in the universe
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The modern picture
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Latest analysis of the properties of the universe
Seems to be flat Accelerating Will expand
forever Age 13.7 billion years 4 baryonic
matter 23 dark matter 73 dark energy H0 71
km/s/Mpc Inflation on strong ground Cosmological
constant supported, but quintessence not entirely
ruled out Dark matter is of the cold variety in
order to clump and produce the universe we see
today
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Wormholes