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
Fundamentals of cosmology:
Expansion of the Universe
H0 = 72  8 km/s/Mpc
(HST key project, 2001)
Matter constituents according to
modern view
•
•
•
•
Dark energy ~ 70%
Dark matter ~ 30%
Baryons
~ 5%
3K Radiation ~0.01%
2
0
2
•
•
•
•
P ≈ -ρ
P=0
P≈0
P = ρ/3
H с ( a =a) = (8щG=3)
2
Т i = ъi =(3H =8щG)
P
ρ = const
ρ = 1/a3
ρ = 1/a3
ρ = 1/a4
2
ъi а K =a
2
! i = ъi =(3 б100 =8щG)
Fundamentals of cosmology:
existence of Large-Scale Structures
¿Dark? Matter
8 ~ 1, averaged in spheres of 8 Mpc radius
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 ?
Cosmic Microwave Background
•Discovered 1965 (Penzias & Wilson)
•2.7 K mm-cm wavelentgh
•400 photons/cm3
•Isotropic
•1992 COBE satellite measures anisotropies ~ 10-5
redshift
z
z? ш 1100
Secondary Anisotropies
•Tightly coupled
Photon-Baryon fluid
oscillations
•Linear regime of
perturbations
Decoupling LSS
Primary Anisotropies
•Non-Linear
Evolution
R?
•Gravitational
redshifting
•Weak Lensing
z= 0
•Thermal and
Kinetic SZ effect
•Etc.
reionization
~10h-1Mpc
14Gyrs
time t
10Gyrs
today
∆T/T ~ 10-5
Й T=T( n
к)
2
C` = hj a`mji
Й T=T( n
к) =
P
?
`
к)
a`mY`m( n
Matter constituents at T~3000K
• Radiation
~ 20%
(r)
• Baryons
~ 15%
(b)
• Dark matter ~ 65%
(cdm)
• Dark energy ~ 0.000%
• Curvature ~ 0.0 ?
Generation of the observable CMB
temperature anisotropy at last-scattering
surface
• Constitutents: baryons+radiation 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
Formation of CMB anisotropy at last scattering
Adiabatic cosine behaviour
¼ r + ~ Ak cos(k rs)
k → 0, dT/T ≠ 0
ΔT/T(k)

2
4
K rs
5
CMB anisotropy at last scattering
Amplification of short waves
when radiation dominated
gravity
¼ r + ~ f(k) cos(k rs)
ΔT/T(k)

2
2
k rs
2
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)
ΔT/T(k)

4
2
k rs
5
Doppler effect (movement of scattering electrons)
Doppler part of dT/T ~ i Ak sin (k rs)
ΔT/T(k)

2
k rs
4
5
Effect of baryon mass
Offset of ¼ r + - const
Decrease of electron velocity
i Ak sin (k rs) / sqrt(1+3/4 ρb/ρr)
ΔT/T(k)

2
4
k rs
5
Phenomenology of the Angular Power Spectrum
Acoustic
Oscillations
` pk ш R ?r s( с?)
Sachs-Wolfe
ш
1
3Р
Drag,
!
b
Doppler
Tensors
T=S щ 7(1 а n s)
large <-- scales --> small
Damping
à k 2=k 2
D
шe
Mapping the anisotropy pattern
onto 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 z>5) – damping of small
scales. Relates physics of CMB to first stars formation
Less well understood, thus more
interesting ingredients, relating CMB to
fundamental physics
• Initial conditions – adiabatic -> 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.
Minimal Set of 7 Cosmological
Parameters
b, cdm
k, 
ns, 8
c
Complex plasma
Geometry of
Initial conditions
Late-time damping
at decoupling
the Universe
(inflationary)
due to reionization
b/=0.8
wQ
nt, At/As,
m/=3.5
broken scale invariance
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
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
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
don’t constrain h and leave matter
components unchanged the peaks are
projected onto the same l values.
dA ( (Т Ë; Т k)
` peak ш kpeakdA ш
dA м
м
r s r ec
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.
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 Bpattern – direct detection of this fundamental physical
effect is possible.
• Breaking degeneracy between parameters, in particular
independent measurement of c
“The Seven Pillars” of the CMB
(of inflationary adiabatic fluctuations)
•Large Scale Anisotropies
Minimal
Inflationary
parameter
set
•Acoustic Peaks/Dips
•Damping Tail
•Polarization
Quintessesnce
Tensor fluc.
Broken Scale
Invariance
• Gaussianity
•Secondary Anisotropies
•Gravity Waves