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The Physics of CMB Anisotropies
and their
Cosmological Implications
Wayne Hu
10 100
20
40
60
80
100
l (multipole)
∆T (µ
K)
MAXIMA
BOOMERanG
Previous
COBE
W. Hu – Dec. 2000
CMB Isotropy
Actual Temperature Data
COBE 1992
Dipole Anisotropy
our motion1 part in 1000
COBE 1992
Large–Angle Anisotropies
10º–90º anisotropy1 part in 100000
COBE 1992
Precision Cosmology
de Bernardis, Hanany, et al. (2000) et al. (2000)
COBE
BOOMERanGMaxima
Acoustic Oscillations
A Brief Thermal History•At z>1000, photon-baryon plasma: perfect fluid
•Photons provide pressure; baryons add inertia
Coulomb InteractionsThomson Scattering
Perfect Fluid
Gravitational Ringing• Potential wells = inflationary seeds of structure
• Fluid falls into wells, pressure resists: acousticoscillations
Gravity
Pressure
Gravity
Pressure
Plane Waves• Potential wells: part of a fluctuation spectrum
• Plane wave decomposition
PotentialHill
PotentialWell
PotentialWell
Harmonic Modes• Frequency proportional to wavenumber: ω=kcs
• Twice the wavenumber = twice the frequency of oscillation
Extrema=Peaks•First peak = mode that just compresses
•Second peak = mode that compresses then rarefies: twice the wavenumber
•Harmonic peaks: 1:2:3 in wavenumber
Θ+Ψ
∆T/T
−|Ψ|/3 SecondPeak
Θ+Ψ
time time
∆T/T
−|Ψ|/3
Recombination RecombinationFirstPeak
k2=2k1k1=π/ soundhorizon
Seeing Sound• Oscillations frozen at recombination
• Compression=hot spots, Rarefaction=cold spots
• Extrema are harmonics of distance sound travels
The First Peak
First Peak Precisely Measured
10 100
20
40
60
80
100
l (multipole)1000
∆T (µ
K)
MAXIMA
BOOMERanG
Previous
∆l~250
l1≈200
Spatial Curvature•Physical scale of peak = distance sound travels
•Angular scale measured: comoving angular diameter distance test for curvature
Flat
Closed
A (Nearly?!) Flat Universe
•Hubble constant! Baryons: calibrate rulers
BOOMERanG
MA
XIM
Aclosed
open
0 0.2
0.2
0.4
0.6
0.8
1
0.4 0.6 0.8 1Ωm
ΩΛ
h<0.8
Ωbh 2<0.025
slightly closed or young universemarginally preferred
What Makes It Flat?
•Info on H0, Ωm, or ΩΛ breaks degeneracy H0: currently by assuming flatness, future by measuring Ωmh2
BOOMERanG
MA
XIM
Aclosed
open
0 0.2
0.2
0.4
0.6
0.8
1
0.4 0.6 0.8 1Ωm
ΩΛ
h<0.8
Ωbh 2<0.025
CosmicComplementarity
Clusters
Concordance!?
•Consistent and requires missing “dark” energy
BOOMERanG
MA
XIM
Aclosed
open
0 0.2
0.2
0.4
0.6
0.8
1
0.4 0.6 0.8 1Ωm
ΩΛ
h<0.8
Ωbh 2<0.025
ClustersRie
ss et
al. (
1998
)
Perlm
utte
r et a
l. (1
998)
The Second Peak
What is it Good For•Acoustic nature: beyond reasonable doubt
•Inflation: superhorizon potential perturbations defects already strongly disfavored: narrow first peak
Pow
er
l
2
500 1000 1500
4
6
Inflation 1:2:3Isocurvature
What is it Good For•Current: second peak unresolved
•Amplitude: constrained to be low
10 100
20
40
60
80
100
l (multipole)1000
∆T (µ
K)
MAXIMA
BOOMERanG
Previous
Baryon & Inertia• Baryons add inertia to
the fluid
• Equivalent to adding mass on a spring
• Same initial conditions
• Same null in fluctuations
• Unequal amplitudes ofextrema
EvenPeaks
OddPeaks
Low Baryons High Baryons
Initial Conditions(Maximal Rarefaction)
MaximalCompression
∆T=0
time ∆
T
zero pt
Low Baryons
A Baryon-meter•Baryons drag the fluid into potential wells
•Enhance compressional peaks (odd) over rarefaction peaks (even)
e.g. suppression of second peak
time|
| ∆
T
zero pt
Baryon Drag
A Baryon-meter•Baryons drag the fluid into potential wells
•Enhance compressional peaks (odd) over rarefaction peaks (even)
e.g. suppression of second peak
time|
| ∆
T
zero pt
Baryon Drag
A Baryon-meter•Baryons drag the fluid into potential wells
•Enhance compressional peaks (odd) over rarefaction peaks (even)
e.g. suppression of second peak
Second Peak•Second peak is (too?) suppressed
•At least as many baryons as nucleosynthesis (50% more preferred BBN consistent at 95% CL including variations in other parameters, e.g. spectrum tilt)
10 100
20
40
60
80
100
l (multipole)1000
∆T (µ
K)
MAXIMA
BOOMERanG
Previous
Higher Peaks
Radiation and Dark Matter• Radiation domination:
potential wells created by CMB itself
• Pressure support ⇒ potential decay ⇒ driving
• Heights measures when dark matter dominates
Decayand
Gravitational Driving
Radiation and Dark Matter• Radiation domination:
potential wells created by CMB itself
• Pressure support ⇒ potential decay ⇒ driving
• Heights measures when dark matter dominates
Decayand
Gravitational Driving
Radiation and Dark Matter• Radiation domination:
potential wells created by CMB itself
• Pressure support ⇒ potential decay ⇒ driving
• Heights measures when dark matter dominates
Decayand
Gravitational Driving
Diffusion Damping•Diffusion inhibited by baryons
•Random walk length scale depends on time to diffuse: horizon scale at recombination
Coulomb InteractionsThomson Scattering
Low Baryons High Baryons
Beyond the Peaks
Polarization•Thomson of quadrupole temperature anisotropy
•Linear polarization:QuadrupoleAnisotropy
Thomson Scattering
e–
Linear Polarization
Polarization Patterns•Pattern reflects the projection of quadrupole anisotropies
•Three types: density, vorticity, gravity waves
•Potential to isolate gravity waves
m=0
v
hot
hot
cold
m=1
vv
m=2
Density Vorticity Gravity Waves
Power in Secondaries•Gravitational ISW (redshift) Effect Weak Lensing
•Scattering Doppler Effect Vishniac Effect Kinetic SZ Effect Patchy Reionization Thermal SZ Effect
•Separation Arcminute Scales Spectrum Non-Gaussianity 10 100 1000
10–13
10–12
10–11
10–10
10–9
l
Pow
er
primary
ISW
doppler
SZlinear
nonlin
lensing Vis
hnia
c
patchnonl
in
linea
r
Summary•Age of precision cosmology
•Sound waves: inflationary/initial perturbations
•First peak nailed: (nearly?) flat universe (11 Gyr young universe preferred)
•Second peak constrained: baryonic dark matter (50% more baryons preferred)
•Degeneracies and ambiguities: dark energy: complementary measures dark matter: higher peaks gravity waves: polarization reionization: polarization & secondaries