Cosmology from CMB

1
Cosmology from CMB

• Dmitry Pogosyan
• University of Alberta

• Lecture 1 What can Cosmic Microwave Background
  tell us about the Universe ? A theoretical
  introduction.
• Lecture 2 Recent successes in the mapping of
  CMB anisotropy what pre-WMAP and WMAP data
  reveals.

Lake Louise, February, 2003
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Fundamentals of cosmology Expansion of the
Universe
H0 72 ? 8 km/s/Mpc (HST key project, 2001)
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Matter constituents according to modern view

• P -? ? const
• P 0 ? 1/a3
• P 0 ? 1/a3
• P ?/3 ? 1/a4

• Dark energy 70
• Dark matter 30
• Baryons 5
• 3K Radiation 0.01

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Fundamentals of cosmology existence of
Large-Scale Structures
Dark? Matter
?8 1, averaged in spheres of 8 Mpc radius
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What do cosmologists want to learn about the
Universe ?

• Matter content
• Geometry of the space
• Origin of structures and details of their
  formation
• Origin of the Universe as we observe now. What
  theory describes the early epoch of evolution ?

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• Cosmic Microwave Background
• Discovered 1965 (Penzias Wilson)
• 2.7 K mm-cm wavelentgh
• 400 photons/cm3
• Isotropic
• 1992 COBE satellite measures anisotropies 10-5

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• Primary Anisotropies
• Tightly coupled Photon-Baryon fluid oscillations
• Linear regime of perturbations
• Gravitational redshifting

• Secondary Anisotropies
• Non-Linear Evolution
• Weak Lensing
• Thermal and Kinetic SZ effect
• Etc.

Decoupling LSS
reionization
10h-1Mpc
14Gyrs
10Gyrs
today
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?T/T 10-5
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Matter constituents at T3000K

• Radiation 20 (?r)
• Baryons 15 (?b)
• Dark matter 65 (?cdm)
• Dark energy 0.000
• Curvature 0.0 ?

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Generation of the observable CMB temperature
anisotropy at last-scattering surface

• Constitutents baryonsradiation interacting via
  Thompson scattering dark matter.
• Modes adiabatic/isocurvature, tensor,
  growing/decaying
• Scale sound horizon rs
• Coherent standing waves
• Correlated Effects
• photon energy perturbation grav.potential
• Doppler effect from moving electrons
• Coherence one mode, one random, adds in
  quadrature.
• Effect of massive baryons

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Formation of CMB anisotropy at last scattering
Adiabatic cosine behaviour ¼ ?r ? Ak cos(k
rs) k ? 0, dT/T ? 0
?T/T(k)
?
2?
4?
5?
K rs
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CMB anisotropy at last scattering
Amplification of short waves when radiation
dominated gravity ¼ ?r ? f(k) cos(k rs)
?T/T(k)
?
2?
2?
2?
k rs
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Damping of short waves at last scattering
photon diffusion, shear viscosity of plasma,
non-instant recombination ¼ ?r ? f(k) cos(k
rs) exp(-k2/kD2)
?T/T(k)
4?
5?
?
2?
k rs
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Doppler effect (movement of scattering electrons)
Doppler part of dT/T i Ak sin (k rs)
?T/T(k)
?
2?
4?
5?
k rs
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Effect of baryon mass
Offset of ¼ ?r ? - const Decrease of electron
velocity i Ak sin (k rs) / sqrt(13/4 ?b/?r)
?T/T(k)
?
2?
4?
5?
k rs
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Phenomenology of the Angular Power Spectrum
Acoustic Oscillations
Sachs-Wolfe
Damping
Drag, Doppler
Tensors
large lt-- scales --gt small
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Mapping the anisotropy patternonto the sky

• Geometry (curvature) of the space
• Expansion rate, including presence and dynamical
  properties of the vacuum energy (quintessence
  field ?)
• But, both mainly affect angular diameter
  distance, thus degeneracy ? R/rs l
• Extra physics, modifying Cl
• ISW (photon propagation through varying grav.pot
  (large scales)
• Secondary reonization (at zgt5) damping of small
  scales. Relates physics of CMB to first stars
  formation

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Less well understood, thus more interesting
ingredients, relating CMB to fundamental physics

• Initial conditions adiabatic -gt inflation
  slope, amplitude, potential. Easy to check given
  theory, less satisfying general case. Until
  recently, only simplest power-law
  parameterization was justified by the data
  quality. With WMAP, situation starts changing.
• Generation of gravitational waves generation is a
  natural outcome of the early Universe. GW
  contributes to low l, its contribution is model
  dependent but to measure it would be an ultimate
  prize GR support, mapping inflaton potential
  directly.

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Minimal Set of 7 Cosmological Parameters
?c
?b, ?cdm
?k, ??
ns, ?8
Complex plasma at decoupling ?b/??0.8 ?m/??3.5
Geometry of the Universe wQ
Initial conditions (inflationary) nt,
At/As, broken scale invariance
Late-time damping due to reionization
Joint pre-WMAP CMB measurements ?k -0.05 ? 0.05
?b 0.022 ? 0.002 ns 0.95 ? 0.04
?cdm 0.12 ? 0.02
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Degeneracies

• Angular diameter of the sound horizon
• ?c ?8 as predicted from CMB
• ?c ns
• ?c gravitational waves
• Degeracies are especially limiting on partial
  data, but some are difficult to break overall
• One way combine CMB data with other
  experiments, which place limits on different
  combinations
• Another way use polarization

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Cosmic Parameter Near-degeneracies
Some parameters are measured better than others.
Particular degeneracies correlate some parameters
Certain combinations of parameters give same
projected power spectrum e.g. geometrical
degeneracy. If you dont constrain h and leave
matter components unchanged the peaks are
projected onto the same l values.
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CMB Polarization

• Full description of radiation is by polarization
  matrix, not just intensity Stockes parameters,
  I,Q,U,V
• Why would black-body radiation be polarized ?
  Well it is not in equilibrium, it is frozen with
  Plankian spectrum, after last Thompson
  scattering, which is polarizing process.
• Because, there is local quadrupole anisotropy of
  the flux scattered of electron. Thus, P and dT/T
  are intimately related, second sources first
  (there is back-reaction as well).
• There is no circular polarization generated, just
  linear Q,U. Level of polarization 10 for
  scalar perturbations, factor of 10 less for
  tensors. Thus need measurements at dT/T 10-6
  10-8.
• As field B, E modes (think vectors, but in
  application to second rank tensor), distinguished
  by parity.

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Why do we learn more from polarization ?

• No new physics (parameters) just new window to
  last scattering which is cleaner, albeit signal
  is weaker.
• Clear signature adiabatic mode.
• Grav waves are the only source which produces
  B-pattern direct detection of this fundamental
  physical effect is possible.
• Breaking degeneracy between parameters, in
  particular independent measurement of ?c

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The Seven Pillars of the CMB(of inflationary
adiabatic fluctuations)

• Large Scale Anisotropies
• Acoustic Peaks/Dips
• Damping Tail
• Polarization
• Gaussianity
• Secondary Anisotropies
• Gravity Waves

Minimal Inflationary parameter set
Quintessesnce
Tensor fluc.
Broken Scale Invariance