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CMB Observables
and their Cosmological Implications
Wayne HuMaryland, October 2002
frequency (cm–1)
Bν
(× 1
0–5 )
GHz
error × 50
50
2
4
6
8
10
12
10 15 20
200 400 600
l
∆P (µ
K)
cros
s (µK
2 )
W. Hu 9/02
E
TE
B
0.1
1
10
10 100 1000
-1000
100
Tegmark Compilation DASI Crew
10 100 1000
20
40
60
80
100
l
∆T (µ
K)
W. Hu 9/02
anisotropy
spectrum
polarization
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CMB Milestones• Blackbody spectrum COBE FIRAS '92 • Large-scale anisotropy COBE DMR '92 • Degree-scale anisotropy many '93-'99
• First acoustic peak Toco, Boom, Maxima '99-'00• Secondary acoustic peak(s) DASI, Boom '01• Damping tail CBI '02
• Polarization DASI '02• Secondary anisotropy? CBI '02 Spectrum?
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Power Spectra of Maps•Original
•Band Filtered
64º
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Anisotropy Power Spectrum
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Sound Physics
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Photon-Baryon Plasma• Before z~1000 when the CMB was T>3000K, hydrogen ionized
• Free electrons act as "glue" between photons and baryons by Compton scattering and Coulomb interactions• Nearly perfect fluid
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Acoustic Basics• ContinuityEquation: (number conservation)
Θ = −1
3kvγ
whereΘ = δργ/4ργ is thetemperature fluctuationwith nγ ∝ T 3
• EulerEquation: (momentum conservation)
vγ = k(Θ + Ψ)
with force provided bypressure gradients3kδpγ/4 = kδργ/4 = kΘργ and potential gradientskΨ.
• Combine these to form thesimple harmonic oscillatorequation
Θ + c2sk
2Θ = −k2
3Ψ
wherec2s ≡ p/ρ is thesound speedsquared
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Harmonic Peaks• Adiabatic (Curvature) Mode Solution
[Θ + Ψ](η) = [Θ + Ψ](0) cos(ks)
where thesound horizons ≡∫
csdη andΘ + Ψ is also theobserved temperature fluctuationafter gravitational redshift
• All modes arefrozenin at recombination
Θ(η∗) = Θ(0) cos(ks∗)
• Modes caught in theextremaof their oscillation will haveenhanced fluctuations
kns∗ = nπ
yielding afundamental scaleor frequency, related to the inversesound horizon
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Extrema=Peaks•First peak = mode that just compresses
•Second peak = mode that compresses then rarefies
Θ+Ψ
∆T/T
−|Ψ|/3 SecondPeak
Θ+Ψ
time time
∆T/T
−|Ψ|/3
Recombination RecombinationFirstPeak
k2=2k1k1=π/ soundhorizon
•Third peak = mode that compresses then rarefies then compresses
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Peak Location• Fundmental physical scale, the distance sound travels, becomes an
angular scaleby simple projection according to the angulardiameter distanceDA
θA = λA/DA
`A = kADA
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Peak Location• Fundmental physical scale, the distance sound travels, becomes an
angular scaleby simple projection according to the angulardiameter distanceDA
θA = λA/DA
`A = kADA
• In a flat universe, the distance is simply DA= D ≡ η 0− η∗ ≈ η0, thehorizon distance, andkA = π/s∗ =
√3π/η∗ so
θA ≈η∗η0
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Peak Location• Fundmental physical scale, the distance sound travels, becomes an
angular scaleby simple projection according to the angulardiameter distanceDA
θA = λA/DA
`A = kADA
• In a flat universe, the distance is simply DA= D ≡ η 0− η∗ ≈ η0, thehorizon distance, andkA = π/s∗ =
√3π/η∗ so
θA ≈η∗η0
• In amatter-dominateduniverseη ∝ a1/2 soθA ≈ 1/30 ≈ 2 or
`A ≈ 200
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Angular Diameter Distance Test
500 1000 1500
20
40
60
80
l (multipole)
DT
(mK
)
Boom98CBI
DASIMaxima-1
l1~200
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Curvature• In acurved universe, the apparent orangular diameter distanceis
no longer the conformal distance DA= R sin(D/R) 6= D
DA
D=Rθ
λ
α
• Objects in aclosed universearefurtherthan they appear!gravitationallensingof the background...
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Curvature in the Power Spectrum•Angular location of harmonic peaks
•Flat = critical density = missing dark energy
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Dark Energy in the Power Spectrum• Fundamental observable is sound horizon / ang. distance
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Baryon Photon Ratio
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Baryon Loading• Baryons add extramassto the photon-baryon fluid
• Controlling parameter is themomentum density ratio:
R ≡ pb + ρb
pγ + ργ
≈ 30Ωbh2
(a
10−3
)of orderunity at recombination
Θ = −k
3vγb
vγb = − R
1 + Rvγb +
1
1 + RkΘ + kΨ
Baryons addmassbut notpressure
• In the slowly varyingR limit
[Θ + (1 + R)Ψ](η) = [Θ + (1 + R)Ψ](0) cos(ks)
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Baryon & Inertia•Baryons add inertia to the fluid
•Equivalent to adding mass on a spring
•Same initial conditions
•Same null in fluctuations
•Unequal amplitudes of extrema
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time ∆
T
Low Baryons
–
A Baryon-meter•Low baryons: symmetric compressions and rarefactions
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time ∆
T
Baryon Loading
–
A Baryon-meter•Load the fluid adding to gravitational force
•Enhance compressional peaks (odd) over rarefaction peaks (even)
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time|
| ∆
T
A Baryon-meter
•Enhance compressional peaks (odd) over rarefaction peaks (even)
e.g. relative suppression of second peak
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Baryons in the Power Spectrum
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BBN Baryon-Photon Ratio
500 1000 1500
20
40
60
80
l (multipole)
DT
(mK
)
Boom98CBI
DASIMaxima-1
l2~550
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Matter-Radiation Ratio
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Radiation Driving• Matter-to-radiation ratio
ρm
ρr
≈ 24Ωmh2(
a
10−3
)of orderunity at recombination in a lowΩm universe
• Radiation is not stress free and soimpedesthe growth of structure
k2Φ = 4πGa2ρ∆
∆ ∼ 4Θ oscillatesaround a constant value,ρ ∝ a−4 so theNetwoniancurvature decaysΦ ≈ −Ψ.
• Decay is timed precisely todrive the oscillator – 5× the amplitudeof the Sachs-Wolfe effect!
• Effect goes away as expansion becomesmatter dominated.Fundamentally tests whether energy density driving expansion issmoothat recombination.
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Radiation and Dark Matter•Radiation domination:
potential wells created by CMB itself
•Pressure support ⇒ potential decay ⇒ driving
•Heights measures when dark matter dominates
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Dark Matter in the Power Spectrum
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Dark Matter in the Data
500 1000 1500
20
40
60
80
l (multipole)
DT
(mK
)
Boom98CBI
DASIMaxima-1
l3
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Damping Tail
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Damping• Tight coupling equations assume aperfect fluid: noviscosity, no
heat conduction
• Fluid imperfections are related to themean free path of thephotons in the baryons
λC = τ−1 where τ = neσT a
is the conformal opacity toThompson scattering
• Dissipation is related to thediffusion length: random walkapproximationλD =
√ηλC
• Fundamentalconsistency check, e.g.expansion rateatrecombination,fine structure constant.
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Maxima
BOOM
DASI
VSA
CBI
Damping Tail Measured
10 100 1000
20
40
60
80
100
l
∆T (µ
K)
W. Hu 9/02
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Further Implications of Damping• CMB anisotropies∼ 10% polarized
dissipation→ viscosity→ quadrupole
quadrupole→ linear polarization
• Secondary anisotropiesare observable at arcminute scales
dissipation→ exponential suppression of primary anisotropy→uncovery of secondary anisotropy from CMB photons traversingthelarge scale structureof the universe
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Polarization
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Polarization from Thomson Scattering • Quadrupole anisotropies scatter into linear polarization
aligned withcold lobe
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First Detection of Polarization!
l
∆P (µ
K)
cros
s (µK
2 )
W. Hu 9/02
DASIE
TE
B
0.1
1
10
10 100 1000
-1000
100
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Mapping the Dark Sector• Cosmic variance of CMB fields sets ultimate limit
• Polarization allows mapping to finer scales (~10')
Hu & Okamoto (2001)
100 sq. deg; 4' beam; 1µK-arcmin
mass temp. reconstruction EB pol. reconstruction
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Secondary Anisotropies
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Maxima
BOOM
DASI
VSA
CBI
Secondary Anisotropy?
10 100 1000
20
40
60
80
100
l
∆T (µ
K)
W. Hu 9/02
BIMA
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Sensitivity of SZE Power Amplitude of fluctuations•
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Sensitivity of SZE Power Dark energy•