AS 4022: Cosmology

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AS 4022 Cosmology

• HS Zhao
• Online notes
• star-www.st-and.ac.uk/hz4/cos/cos.html
• star-www.st-and.ac.uk/kdh/cos/cos.html
• Final Note in Library
• Summary sheet of key results (from John Peacock)
• take your own notes (including blackboard
  lectures)

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The Visible Cosmos a hierarchy of structure and
motion

• Cosmos in a computer

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Observe A Hierarchical Universe

• Planets
• moving around stars
• Stars grouped together,
• moving in a slow dance around the center of
  galaxies.

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• Galaxies themselves
• some 100 billion of them in the observable
  universe
• form galaxy clusters bound by gravity as they
  journey through the void.
• But the largest structures of all are
  superclusters,
• each containing thousands of galaxies
• and stretching many hundreds of millions of light
  years.
• are arranged in filament or sheet-like
  structures,
• between which are gigantic voids of seemingly
  empty space.

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Cosmic Village

• The Milky Way and Andromeda galaxies,
• along with about fifteen or sixteen smaller
  galaxies,
• form what's known as the Local Group of galaxies.
  
• The Local Group
• sits near the outer edge of a supercluster, the
  Virgo cluster.
• the Milky Way and Andromeda are moving toward
  each other,
• the Local Group is falling into the middle of the
  Virgo cluster, and
• the entire Virgo cluster itself,
• is speeding toward a mass
• known only as "The Great Attractor."

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Introducing Gravity and DM (Key players)

• These structures and their movements
• can't be explained purely by the expansion of the
  universe
• must be guided by the gravitational pull of
  matter.
• Visible matter is not enough
• one more player into our hierarchical scenario
• dark matter.

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1st main concept in cosmology

• Cosmological Redshift

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1st main concept Cosmological Redshift

• The space/universe is expanding,
• Galaxies (pegs on grid points) are receding from
  each other
• As a photon travels through space, its wavelength
  becomes stretched gradually with time.
• Photons wave-packets are like links between grid
  points
• This redshift is defined by

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• E.g. Consider a quasar with redshift z2. Since
  the time the light left the quasar the universe
  has expanded by a factor of 1z3. At the epoch
  when the light left the quasar,
• What was the distance between us and Virgo
  (presently 15Mpc)?
• What was the CMB temperature then (presently 3K)?
  

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Lec 2 Cosmic Timeline

• Past ? Now

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Set your watches 0h0m0s
Trafalgar Square London Jan 1
Fundamental observers
H
H
H
H
H
H
H
H
A comic explanation for cosmic expansion
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3 mins later
He
He
Homogeneous Isotropic Universe
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Feb 14 t45 days later
D2
D3
D1
C1
C2
C3
d?
B1
A1
R(t)
?
B2
d?
A2
B3
A3
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2nd Concept metric of 12D universe

• Analogy of a network of civilization living on an
  expanding star (red giant).
• What is fixed (angular coordinates of the grid
  points)
• what is changing (distance).

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Analogy a network on a expanding sphere
3
2
.
1
Angle f1
4
2
3
Expanding Radius R(t)
1
4
Fundamental observers 1,2,3,4 with Fixed angular
(co-moving) coordinates (?,f) on expanding
spheres their distances are given by Metric at
cosmic time t ds2 c2 dt2-dl2, dl2 R2(t)
(d?2 sin2 ? df2)
Angle ?1
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3rd Concept The Energy density of Universe

• The Universe is made up of three things
• VACUUM
• MATTER
• PHOTONS (radiation fields)
• The total energy density of the universe is made
  up of the sum of the energy density of these
  three components.
• From t0 to t109 years the universe has expanded
  by R(t).

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Eq. of State for Expansion analogy of baking
bread
?? ??

• Vacuumair holes in bread
• Matter nuts in bread
• Photons words painted
• Verify expansion doesnt change Nhole, Nproton,
  Nphoton
• No Change with rest energy of a proton, changes
  energy of a photon

?? ??
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• VACUUM ENERGY
• MATTER
• RADIATIONnumber of photons Nph constant

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• The total energy density is given by

Radiation Dominated
log?
Matter Dominated
n-4
Vacuum Dominated
n-3
n0
R
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Key Points

• Scaling Relation among
• Redshift z,
• expansion factor R
• Distance between galaxies
• Temperature of CMB T
• Wavelength of CMB photons lambda
• Metric of an expanding 2Dtime universe
• Fundamental observers
• Galaxies on grid points with fixed angular
  coordinates
• Energy density in
• vacuum, matter, photon
• How they evolve with R or z
• If confused, recall the analogies of
• balloon, bread, a network on red giant star,
  microwave oven

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TopicsTheoretical and Observational

• Universe of uniform density
• Metrics ds, Scale R(t) and Redshift
• EoS for mix of vacuum, photon, matter
• Thermal history
• Nucleosynthesis
• He/D/H
• Structure formation
• Growth of linear perturbation
• Origin of perturbations
• Relation to CMB
• Hongsheng.Zhao (hz4)

• Quest of H0 /Omega (obs.)
• Applications of expansion models
• Distances Ladders
• (GL, SZ)
• SNe surveys
• Cosmic Background from
• COBE/MAP/PLANCK etc

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Acronyms in Cosmology

• Cosmic Background Radiation (CBR)
• Or CMB (microwave because of present temperature
  3K)
• Argue about 105 photons fit in a 10cmx10cmx10cm
  microwave oven. Hint 3kT h c / ?
• CDM/WIMPs Cold Dark Matter, weakly-interact
  massive particles
• At time DM decoupled from photons, T 1014K, kT
  0.1 mc2
• Argue that dark particles were
• non-relativistic (v/c ltlt 1), hence cold.
• Massive (m gtgt mproton 1 GeV)

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Acronyms and Physics Behind

• DL Distance Ladder
• Estimate the distance of a galaxy of size 1 kpc
  and angular size 1 arcsec? About 0.6 109 light
  years
• GL Gravitational Lensing
• Show that a light ray grazing a spherical galaxy
  of 1010 Msun at typical b1 kpc scale will be
  bent 4GM/bc2 radian 1 arcsec
• It is a distance ladder
• SZ Sunyaev-Zeldovich effect
• A cloud of 1kev thermal electrons scattering a 3K
  microwave photon generally boost the latters
  energy by 1kev/500kev0.2
• This skews the blackbody CMB, moving low-energy
  photons to high-energy effect is proportional to
  electron column density.

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• the energy density of universe now consists
  roughly
• Equal amount of vacuum and matter,
• 1/10 of the matter is ordinary protons, rest in
  dark matter particles of 10Gev
• Argue dark-particle-to-proton ratio 1
• Photons (3K 10-4ev) make up only 10-4 part of
  total energy density of universe (which is
  proton rest mass energy density)
• Argue photon-to-proton ratio 10-4 GeV/(10-4ev)
  109

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What have we learned?

• Concepts of Thermal history of universe
• Decoupling
• Last scattering
• Dark Matter era
• Compton scattering
• Gravitational lensing
• Distance Ladder
• Photon-to-baryon ratio gtgt1
• If confused, recall the analogy of
• Crystalization from comic soup,
• Last scattering photons escape from the
  photosphere of the sun

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The rate of expansion of Universe

• Consider a sphere of radius rR(t) ?,
• If energy density inside is ? c2
• ? Total effective mass inside is
• M 4 p? r3 /3
• Consider a test mass m on this expanding sphere,
• For Test mass its
• Kin.Energy Pot.E. const E
• ? m (dr/dt)2/2 G m M/r cst
• ?(dR/dt)2/2 - 4 pG ? R2/3 cst
• cstgt0, cst0, cstlt0
• (dR/dt)2/2 4 pG (? ?cur) R2/3
• where cst is absorbed by ?cur R(-2)

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Lec 4 Feb 22
A powerful scaling relation (approximate) t
-2 H2(dR/dt)2/R2 (?cur ?m ?r
?v ) R-n (1z)n T n
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Where are we heading?

• Next few lectures will cover a few chapters of
• Malcolm S. Longairs Galaxy Formation Library
  Short Loan
• Chpt 1 Introduction
• Chpt 2 Metrics, Energy density and Expansion
• Chpt 9-10 Thermal History

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Thermal Schedule of Universe chpt 9-10

• At very early times, photons are typically
  energetic enough that they interact strongly with
  matter so the whole universe sits at a
  temperature dictated by the radiation.
• The energy state of matter changes as a function
  of its temperature and so a number of key events
  in the history of the universe happen according
  to a schedule dictated by the temperature-time
  relation.
• Crudely (1z)1/R (T/3) 109 (t/100s)(-2/n)
  1000 (t/0.3Myr)-2/n, H1/t
• n4 during radiation domination

T(K) 1010 103
Radiation Matter
Recombination After this Barrier photons
free-stream in universe
He D 100s
Neutrinos decouple
???Myr
1012 109 106 103 1
1z
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A summary Evolution of Number Densitiesof ?, P,
e, ?
All particles relativistic
Neutrinos decouple while relativistic
Protons condense at kT0.1mp c2
Num Density
Electrons freeze-out at kT0.1me c2
Now
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A busy schedule for the universe

• Universe crystalizes with a sophisticated
  schedule, much more confusing than simple
  expansion!
• Because of many bosonic/fermionic players
  changing balance
• Various phase transitions, numbers NOT conserved
  unless the chain of reaction is broken!
• p p- lt-gt ????? (baryongenesis)
• e e lt-gt ?????, v e lt-gt v e (neutrino
  decouple)
• n lt? p e- v, p n lt? D ???(BBN)
• H e- lt? H ???????? e lt-gt ? e
  (recombination)
• Here we will try to single out some rules of
  thumb.
• We will caution where the formulae are not valid,
  exceptions.
• You are not required to reproduce many details,
  but might be asked for general ideas.

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What is meant Particle-Freeze-Out?

• Freeze-out of equilibrium means NO LONGER in
  thermal equilibrium, means insulation.
• Freeze-out temperature means a species of
  particles have the SAME TEMPERATURE as radiation
  up to this point, then they bifurcate.
• Decouple switch off the chain is broken
  Freeze-out

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A general history of a massive particle

• Initially mass doesnt matter in very hot
  universe
• relativistic, dense
• frequent collisions with other species to be in
  thermal equilibrium and cools with photon bath.
• Photon numbers (approximately) conserved, so is
  the number of relativistic massive particles

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Initially zero chemical potential ( Chain is on,
equilibrium with photon)

• The number density of photon or massive particles
  is
• Where we count the number of particles occupied
  in momentum space and g is the degeneracy
  factor. Assuming zero cost to
  annihilate/decay/recreate.
• 
  

for Fermions - for Bosons
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• As kT cools, particles go from
• From Ultrarelativistic limit. (kTgtgtmc2)
• particles behave as if they were massless?
• To Non relativistic limit ( ??mc2/kT gt 10 ,
  i.e., kTltlt 0.1mc2) Here we can neglect the ?1 in
  the occupancy number?

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When does freeze-out happen?

• Happens when KT cools 10-20 times below mc2, run
  out of photons to create the particles
• Non-relativisitic decoupling
• Except for neutrinos

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• Rule 2. Survive of the weakest
• While in equilibrium, nA/nph exp????? (Heavier
  is rarer)
• When the reverse reaction rate ?A? is slower than
  Hubble expansion rate H(z) , the abundance ratio
  is frozen NA/Nph 1/(?A?) /Tfreeze
• Question why frozen while nA , nph both drop as
  T3 R-3.
• ??A nph/(?A?) , if m Tfreeze

?A? LOW? (v) smallest interaction, early
freeze-out while relativistic
Freeze out
?A? HIGH? later freeze-out at lower T
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Effects of freeze-out

• Number of particles change (reduce) in this phase
  transition,
• (photons increase only slightly)
• Transparent to photons or neutrinos or some other
  particles
• This defines a last scattering surface where
  optical depth to future drops below unity.

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Number density of non-relativistic particles to
relativistic photons

• Reduction factor exp(- ??????mc2/kT, which drop
  sharply with cooler temperature.
• Non-relativistic particles (relic) become much
  rarer by exp(-?) as universe cools below mc2/???
• ??????????????
• So rare that infrequent collisions can no longer
  maintain coupled-equilibrium.
• So Decouple switch off the chain is broken
  Freeze-out

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After freeze-out

• Particle numbers become conserved again.
• Simple expansion.
• number density falls with expanding volume of
  universe, but Ratio to photons kept constant.

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Small Collision cross-section

• Decouple non-relativisticly once kTltmc2 . Number
  density ratio to photon drops steeply with
  cooling exp(- mc2/kT).
• wimps (Cold DM) etc. decouple (stop
  creating/annihilating) while non-relativistic.
  Abundance of CDM ? 1/ ?A?
• Tc109K NUCLEOSYNTHESIS (100s)
• Tc5000K RECOMBINATION (0.3 Myrs) (z1000)

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For example,

• Antiprotons freeze-out t(1000)-6 sec,
• Why earlier than positrons freeze-out t1sec ?
• Hint anti-proton is 1000 times heavier than
  positron.
• Hence factor of 1000 hotter in freeze-out
  temperature
• Proton density falls as R-3 now, conserving
  numbers
• Why it falls exponentially exp(-?) earlier on
• where ????mc2/kT? R.
• Hint their numbers were in chemical equilibrium,
  but not conserved earlier on.

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smallest Collision cross-section

• neutrinos (Hot DM) decouple from electrons (due
  to very weak interaction) while still hot
  (relativistic 0.5 Mev kT gtmc2 0.02-2 eV)
• Presently there are 3 x 113 neutrinos and 452 CMB
  photons per cm3 . Details depend on
• Neutrinos have 3 species of spin-1/2 fermions
  while photons are 1 species of spin-1 bosons
• Neutrinos are a wee bit colder, 1.95K vs. 2.7K
  for photons during freeze-out of
  electron-positions, more photons created

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Coupled radiation-baryon relativistic fluid
Radiation
Matter
Matter number density
Random motion energy Non-Relativistic IDEAL GAS

• Show C2s c2/3 /(1Q) , Q (3 ?m) /(4 ?r) , ?
  Cs drops
• from c/sqrt(3) at radiation-dominated era
• to c/sqrt(5.25) at matter-radiation equality

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Temperature and Sound Speed of Decoupled
Baryonic Gas
After decoupling (zlt500), Cs 6 (1z) m/s
because

T?
Te
R
Until reionization z 10 by stars quasars
Te 8 Cs2 8 R-2
dP
dP
dX
dX
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What have we learned?Where are we heading?

• Sound speed of gas before/after decoupling
• Topics Next
• Growth of chpt 11 bankruptcy of uniform
  universe
• Density Perturbations (how galaxies form)
• peculiar velocity (how galaxies move and merge)
• CMB fluctuations (temperature variation in CMB)
• Inflation (origin of perturbations)

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Peculiar Motion

• The motion of a galaxy has two parts

Proper length vector
Uniform expansion vo
Peculiar motion ?v
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Damping of peculiar motion (in the absence of
overdensity)

• Generally peculiar velocity drops with
  expansion.
• Similar to the drop of (non-relativistic) sound
  speed with expansion

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Non-linear Collapse of an Overdense Sphere

• An overdense sphere is a very useful non linear
  model as it behaves in exactly the same way as a
  closed sub-universe.
• The density perturbations need not be a uniform
  sphere any spherically symmetric perturbation
  will clearly evolve at a given radius in the same
  way as a uniform sphere containing the same
  amount of mass.

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R, R1
log?
Rmax
t-2
Rmax/2 virialize
t
Background density changes this way
logt
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Gradual Growth of perturbation
Verify d changes by a factor of 10 between z10
and z100? And a factor of 100 between z105 and
z106?
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Equations governing Fluid Motion
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Decompose into unperturbed perturbed

• Let
• We define the Fractional Density Perturbation

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• Motion driven by gravity
• due to an overdensity
• Gravity and overdensity by Poissons equation
• Continuity equation
• Peculiar motion dv and peculiar gravity g1 both
  scale with d and are in the same direction.

The over density will rise if there is an inflow
of matter
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THE equation for structure formation

• In matter domination
• Equation becomes

Gravity has the tendency to make the density
perturbation grow exponentially.
Pressure makes it oscillate
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• Each eq. is similar to a forced spring

F
m
Restoring
Term due to friction
(Displacement for Harmonic Oscillator)
x
t
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What have we learned? Where are we heading?

• OverDensity grows as
• R (matter) or R2 (radiation)
• Peculiar velocity points towards overdensities
• Topics Next Jeans instability

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Lec 8

• What have we learned chpt 11.4
• Conditions of gravitational collapse (growth)
• Stable oscillation (no collapse) within sound
  horizon if pressure-dominated
• Where are we heading
• Cosmic Microwave Background chpt 15.4
• As an application of Jeans instability
• Inflation in the Early Universe chpt 20.3

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Theory of CMB Fluctuations

• Linear theory of structure growth predicts that
  the perturbations
• will follow a set of coupled Harmonic Oscillator
  equations.

Or
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• The solution of the Harmonic Oscillator within
  sound horizon is
• Amplitude is sinusoidal function of k cs t
• if kconstant and oscillate with t
• or tconstant and oscillate with k.

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• We dont observe the baryon overdensity
  directly
• -- what we actually observe is temperature
  fluctuations.
• The driving force is due to dark matter over
  densities.
• The observed temperature is

Effect due to having to climb out of
gravitational well
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• The observed temperature also depends on how fast
  the Baryon Fluid is moving.

Doppler Term
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Horizon
x sun x
Why are these two galaxies so similar without
communicating yet?
Why is the curvature term so small (universe so
flat) at early universe if radiation dominates
n4 gt2?
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What have we learned?

• What determines the patterns of CMB at last
  scattering
• Analogy as patterns of fine sands on a drum at
  last hit.
• The need for inflation to
• Bring different regions in contact
• Create a flat universe naturally.

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Inflationary Physics

• Involve quantum theory to z1032 and perhaps a
  scalar field ?(x,t) with energy density

V(?)
finish
Ground state
?
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Inflation dilutes the effect of initial
curvature of universe
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Exotic Pressure drives Inflation
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What Have we learned?

• How to calculate Horizon.
• The basic concepts and merits of inflation
• Pressure of various kinds (radiation, vacuum,
  matter)

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List of keys

• Scaling relations among
• Redshift z, wavelength, temperature, cosmic time,
  energy density, number density, sound speed
• Definition formulae for pressure, sound speed,
  horizon
• Metrics in simple 2D universe.
• Describe in words the concepts of
• Fundamental observers
• thermal decoupling
• Common temperature before,
• Fixed number to photon ratio after
• Hot and Cold DM.
• gravitational growth.
• Over-density,
• direction of peculiar motion driven by
  over-density, but damped by expansion
• pressure support vs. grav. collapse

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Lecture 3Metrics for Curved Geometry
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Cosmological Observations in a Curved and
Evolving Universe
Non-Euclidian geometries ( positive / negative
curvature ) Evolving geometries
( expanding / accelerating /
decelerating ) Time-Redshift-Distance relations
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Non-Euclidean GeometryCurved 3-D SpacesHow
Does Curvature affect Distance Measurements
?
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Is our Universe Curved?
Closed Flat Open
Curvature
0 -- Sum
of angles of triangle
gt 180o 180o
lt 180o Circumference of circle
lt 2 ? r
2 ? r gt 2 ?
r Parallel lines converge remain
parallel diverge Size
finite infinite
infinite Edge
no no
no
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Embedded Spheres
R radius of curvature
?
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Metric for 3-D surface of 4-D sphere
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Lecture 4Space-Time Metric
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Fidos and co-moving coordinates
Distance varies in time
Fiducial observers (Fidos)
Co-moving coordinates
Labels the Fidos
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Coordinate Systems
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Luminosity Distance

• Luminosity ( erg s-1 )
• area of photon sphere ( when photons observed )
• redshift
• time dilation lower photon arrival rate
• observed flux ( erg cm-2 s-1 )
• Luminosity distance

Sources look fainter/farther.
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Lecture 5Time - Redshift - Distance
Relationships General RelativityGeodesics
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Time -- Redshift relation
Memorise this derivation!
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Lecture 6General Relativity
Field Equations Dynamics of the Universe
R(t) ?H(x) ?Friedmann Equation
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Einstein Field Equations
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Homogeneity and Isotropy
homogeneous not isotropic
isotropic not homogeneous
For cosmology, assume Universe is
Homogeneous. Simplifies the equations. )
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Homogeneous perfect fluid
Einstein field equations
---gt Friedmann equations
energy
momentum
Note energy density and pressure decelerate, ?
accelerates.
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Newtonian Analogy
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Density - Evolution - Geometry
R(t)
Open k -1
t
Flat k 0
Closed k 1
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Lecture 7Dynamics of the Universe Solutions
to the Friedmann Equation for R(t)
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Hubble Parameter Evolution -- H(z)
Dimensionless Friedmann Equation
Curvature Radius today
Density determines Geometry
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Hubble Parameter Evolution -- H(z)
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Look-Back Time and Age
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Lecture 8Observational Cosmology Parameters
of Our UniverseThe Concordance Model
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Concordance Model Parameters
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Our (Crazy?) Universe
Vacuum Dominated
accelerating
decelerating
Critical
Cycloid
Empty
Sub-Critical
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Concordance Model
Three main constraints
2
1
3
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HST Key Project
Freedman, et al. 2001 ApJ 553, 47.
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Hubble time and radius
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Age Constraints

• Nuclear decay ( U, Th -gt Pb )
• Decay times for (232Th,235U,238U) (20.3, 1.02,
  6.45) Gyr
• 3.7 Gyr oldest Earth rocks
• 4.57 Gyr meteorites
• 10 Gyr time since supernova produced U, Th
• ( 235U / 238U 1.3 --gt 0.33, 232Th / 238U
  1.7 --gt 2.3 )
• Stellar evolution
• 13-17 Gyr oldest globular clusters
• White dwarf cooling
• 13 Gyr coolest white dwarfs in M4

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Globular Cluster Ages
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Coolest White Dwarfs
Hansen et al. 2002 ApJ 574,155
White dwarf cooling ages --gt
star formation at z gt 5.
Cooling times have been measured using ZZ Ceti
oscillation period changes.
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Lecture 9Observational Cosmology Discovery
of Dark Energy
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Observable Distances
Verify these low-z expansions.
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Finding faint Supernovae
Observe 106 galaxies. Again, 3 weeks later. Find
new stars. Measure lightcurves. Take
spectra. ( Only rare Type Ia Supernovae work ).
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Hi-Z Supernova Spectra
H?
H?
SN II --- hydrogen lines (collapse and rebound
of the core of a massive star)
SN I --- no hydrogen lines (no H-rich envelope
surrounding the core)
SN Ia --- best known standard
candles (implosion of 1.4 Msun white dwarf,
probably due to accretion in a mass-transfer
binary system).
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Calibrating Standard Bombs
Absolute magnitude M B gt
1. Brighter ones decline more slowly. 2. Time
runs slower by factor (1z).
AFTER correcting Constant peak brightness MB
-19.7
Observed peak magnitude m M 5 log (d/Mpc)
25 gives the distance!
Time gt
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SN Ia at z 0.8 are 25 fainter than expected
Acceleration ( ! ? ) 1. Bad Observations? --
2 independent teams agree 1. Dust ? --
corrected using reddening 2. Stellar populations
? -- earlier generation of stars -- lower
metalicity 3. Lensing? -- some brighter, some
fainter -- effect small at z 0.8
Reiss et al. 1998 Perlmutter et al. 1998
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1998 cosmology revolution
Acceleration ( ! ? ) matter-only models ruled
out cosmological constant ? gt 0 Dark Energy
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HST Supernova Surveys
Tonry et al. 2004.
HST surveys to find SN Ia beyond z 1
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25 HST SN 1a beyond z 1
Reiss et al. 2007.
Most distant Supernova SN 2007ff z
1.75
SNAP SuperNova Acceleration Probe 1.5m
wide-angle multi-colour space telescope --- 1000
SN 1a (Not Yet Funded)
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Lecture 10Checking the Distance Ladder
Sunyaev-Zeldovich EffectGravitational Lensing
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HST Key Project
Freedman, et al. 2001 ApJ 553, 47.
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Galaxy Clusters arefilled with hot X-ray gas
optical (galaxies)
X-ray (hot gas)
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Gravitational Lensing

• Luminous arcs in clusters of
  galaxies

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Gravitational Lensing
multiple images of background galaxy lensed by
the cluster
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The Lensed Galaxy
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Lensing by a Point Mass
2 images opposite sides of lens major image
outside ring minor image inside ring net
magnification (sum of 2 images) vs time
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Quasars Lensed by Galaxies
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Masses from Einstein Rings
Perfect alignment gives an Einstein Ring
Mass usually less certain than distance, so use
theta and D to calculate M.
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Time Delay Measurement

• Light curves of the images show a shift in time.

146 days
Hjorth et al. 2003.
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But, no simple lenses.
Almost always several galaxies involved. Prevents
very accurate distance measurements.
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Dark Matter Galaxy CountsRedshift
SurveysGalaxy Rotation CurvesCluster
DynamicsGravitational Lenses
2
1
3
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Mass Density by Direct Counting

• Add up the mass of all the galaxies per unit
  volume
• Volume calculation as in Tutorial problem.
• Need representative volume gt 100 Mpc.
• Cant see faintest galaxies at large
  distance. Use local Luminosity Functions to
  include fainter ones.
• Mass/Light ratio depends on type of galaxy.
• Dark Matter needed to bind Galaxies and Galaxy
  Clusters dominates the normal matter (baryons).
• Hot x-ray gas dominates the baryon mass of Galaxy
  Clusters.

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Cluster Masses from X-ray Gas
Coma Cluster M(gas)M(stars)3x1013 Msun
often M(gas) gt M(stars)
M/L100-200
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Cluster Masses from X-ray Gas
T108K
M 1014 Msun
total mass
g 3x10-8 cm s-2
stars
gas
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Masses from Gravitational Lensing
General agreement with Virial Masses.
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Evidence for Dark Matter ?
Galaxies ( r 20 Kpc ) Flat Rotation Curves V
200 km/s Galaxy Clusters ( r 200 Kpc
) Galaxy velocities V 1000 km/s X-ray Gas T
108 K Giant Arcs
X-ray Optical
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Or . Has General Relativity Failed ?
4 Normal Matter
22 Dark Matter ?
74 Dark Energy ?
Can Alternative Gravity Models fit all the data
without 2 miracles ? ( Dark Matter, Dark
Energy )
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MOND and TeVeS
MOdified Newtonian Dynamics
MOND acceleration parameter
Milgrom 1983
MOND gives flat rotation curves V( r ) const
and Tully-Fischer V4 M
Tensor Vector Scalar
Bekenstein 2004
Covariant metric gravity theory that reduces to
MOND in weak-field low-velocity limit.
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Cosmic Microwave BackgroundFlat Geometry
2
1
3
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1965 -- Penzias Wilson
Bell Labs telecommunications engineers
find excess microwave noise from the sky. 1
of thermal ( T 300o K ) noise ---gt T 3o
K Afterglow of the Big Bang CMB Cosmic
Microwave Background Confirms a forgotten 1948
prediction by Gamow. Nobel Prize -gt PW
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Recombination Epoch ( z1100 )ionised plasma
--gt neutral gas

• Redshift z gt 1100
• Temp T gt 3000 K
• H ionised
• electron -- photon Thompson scattering

• z lt 1100
• T lt 3000 K
• H recombined
• almost no electrons
• neutral atoms
• photons set free

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NASA 1992 - COBECOsmic Background Explorer
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COBE spectrum of CMB
A perfect Blackbody ! No spectral lines -- strong
test of Big Bang. Expansion preserves the
blackbody spectrum. T(z) T0 (1z)
T0 3000 K z 1100
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Cosmic Microwave Background
Almost isotropic
T 2.728 K
Dipole anisotropy Our velocity
Milky Way sources anisotropies
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COBE - tiny ripples
Resolution 7o
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Tiny Ripples at Redshift 1100
Ripples are relics of the Big Bang
initial quantum fluctuations expanded by early
inflation the seeds of later galaxy/cluster
formation. standard yardsticks for measuring
curvature ( and other cosmology
parameters )
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1999 - Boomerang in Antarctica
Baloon Observations Of Millimetric Extragalactic
Radiation ANisotropy and Geophysics
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Boomerang in Antarctica
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Boomerangs Baloon
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Boomerangs Stratospheric Flight Track
Altitude 37 km 10 days
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Resolution 0.3o
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Spherical Harmonics
Fit temperature map with a series of
m cycles in longitude l - m nodes in latitude
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Supernovae CMB ripples
Pre-WMAP constraints From BOOMERANG and MAXIMA
circa 2002
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WMAP
NASA 2001... Wilkinson Microwave Anisotropy Prob
e
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2003 -- WMAP Power Spectrum
Spergel et al. 2003 ApJSup 148,175.
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Sound Horizon at z 1100
Standard Ruler
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Angular scale --gt Geometry
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Sound Horizon at z 1100
recombination at z 1100
dt - dx / x H( x ) R( t ) R0 / x
H( x ) from Friedmann Eqn.
keep 2 largest terms.
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Sound Horizon at z 1100

Expands by factor 1 z 1100
to 120 Mpc today.
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Precision Cosmology
( From the WMAP 1-year data analysis)
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Dark Energy ? Vacuum energy?Bubble
Cosmology?Dark Matter ? Large-Scale Structure
Galaxy Rotation CurvesCluster
DynamicsGravitational LensesMACHOs? --- No
WIMPs? --- MaybeModified Gravity ?MOND ,
TeVeS