cmb anisotropy - university of chicagobackground.uchicago.edu/~whu/presentations/ias02.pdfcmb...

CMB Anisotropy

Recent and Future Milestones

Wayne HuIAS, November 2002

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Tegmark Compilation DASI Crew

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anisotropy polarization

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



• Polarization DASI '02• Secondary anisotropy CBI, BIMA? '02?

• Reionization Bump• Initial Spectrum & Stats. • Gravitational Lensing • Gravitational Waves



• Polarization DASI '02• Secondary anisotropy CBI, BIMA? '02?

• Reionization Bump• Initial Spectrum & Stats. • Gravitational Lensing • Gravitational Waves

Recent Collaborators: Matt Hedman Takemi Okamoto Matias Zaldarriaga

Anisotropy Power Spectrum

Projected MAP 2 Year Errors

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θ (degrees)

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W. Hu – Feb. 1998

Sound Physics

Photon-Baryon Plasma• Before z~1000 when the CMB had T>3000K, hydrogen ionized

• Free electrons act as "glue" between photons and baryons by Compton scattering and Coulomb interactions• Nearly perfect fluid

Peebles & Yu (1970)

Acoustic Basics• ContinuityEquation: (number conservation)

Θ = −1

3kvγ

whereΘ = δnγ/3nγ is the temperature fluctuation with nγ ∝ T 3


Θ = −1

3kvγ


• EulerEquation: (momentum conservation)

vγ = k(Θ + Ψ)

with force provided bypressure gradientskδpγ/(ργ + pγ) = kδργ/4ργ = kΘ and potential gradientskΨ.


Θ = −1

3kvγ


• EulerEquation: (momentum conservation)

vγ = k(Θ + Ψ)

with force provided bypressure gradientskδpγ/(ργ + pγ) = kδργ/4ργ = kΘ and potential gradientskΨ.

• Combine these to form thesimple harmonic oscillatorequation

Θ + c2sk

2Θ = −k2

3Ψ

wherec2s ≡ p/ρ is thesound speedsquared

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


[Θ + Ψ](η) = [Θ + Ψ](0) cos(ks)



• All modes arefrozenin at recombination

[Θ + Ψ](η∗) = [Θ + Ψ](0) cos(ks∗)


[Θ + Ψ](η) = [Θ + Ψ](0) cos(ks)



• All modes arefrozenin at recombination

[Θ + Ψ](η∗) = [Θ + Ψ](0) cos(ks∗)

• Modes caught in theextremaof their oscillation will haveenhanced fluctuations

kns∗ = nπ

yielding afundamental scaleor frequency, related to the inversesound horizon and series dependent on adiabatic assumption

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

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



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



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

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

• Comoving objects in a closed universe are further than they appear!gravitationallensingby the background...

• Future: gravitational lensing of large-scale structure

Curvature in the Power Spectrum•Flat = critical density = missing dark energy

•How flat (or how much d.e.) depends on matter-radiation ratio

Angular Diameter Distance Test

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DASIMaxima-1

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Location of the Peaks

• Peaks shift to lower multipoles as the dark energy densityincreases

Curvature and Dark Energy• Acoustic scale already precisely determined

Hu (2002): lA from Knox et al (2001)

0.2

0.2 0.4 0.6 0.8

0.4

0.6

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1

Ωm

ΩΛ

300<lA<308

flat

Curvature and Dark Energy• Error budget dominated by matter-radiation uncertainty

Hu (2002): lA from Knox et al (2001); Ωmh2 from Bond et al (2002)

0.2

0.2 0.4 0.6 0.8

0.4

0.6

0.8

1

Ωm

ΩΛ

300<lA<3080.12<Ωmh2<0.18

flat

Importance of Higher Peaks & Polarization

• Width: matter-radiation ratio, extent polarization and H0

0 0.2–1.0

–0.8

–0.6

–0.4

–0.2

0.4 0.6 0.8 1ΩΛ

w

PlanckMAP

with polarization

1%

7%

∆`A

`A≈ −0.11∆w − 0.24

∆Ωmh2

Ωmh2+ 0.07

∆Ωbh2

Ωbh2− 0.17

∆ΩΛ

ΩΛ− 1.1

∆Ωtot

Ωtot

Equation of State

• Degeneracy is broken at low multipoles, ISW effect

Baryon Photon Ratio

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



R ≡ pb + ρb

pγ + ργ

≈ 30Ωbh2

(a

10−3


• Baryons addmassbut notpressurein the equations of motion

Θ = −k

3vγb

vγb = − R

1 + Rvγb +

1

1 + RkΘ + kΨ



R ≡ pb + ρb

pγ + ργ

≈ 30Ωbh2

(a

10−3


• Baryons addmassbut notpressurein the equations of motion

Θ = −k

3vγb

vγb = − R

1 + Rvγb +

1

1 + RkΘ + kΨ

• In the slowly varyingR limit

[Θ + (1 + R)Ψ](η) = [Θ + (1 + R)Ψ](0) cos(ks)

Baryon & Inertia•Baryons add inertia to the fluid like mass on a spring

time ∆

T

Low Baryons

–

Peak Modulation•Low baryons: symmetric compressions and rarefactions

time ∆

T

Baryon Loading

–

Peak Modulation•Low baryons: symmetric compressions and rarefactions

•Load the fluid adding to gravitational force

•Enhance compressional peaks (odd) over rarefaction peaks (even)

time|

| ∆

T

Peak Modulation

e.g. relative suppression of second peak

•Enhance compressional peaks (odd) over rarefaction peaks (even)

•Load the fluid adding to gravitational force

•Low baryons: symmetric compressions and rarefactions

boosting of third peak

Baryons in the Power Spectrum

http://background.uchicago.edu/~whu/Presentations/darke.pdf

BBN Baryon-Photon Ratio

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Boom98CBI

DASIMaxima-1

l2~550

Ωbh2 = 0.023± 0.006 Wang et al.

Matter-Radiation Ratio

Radiation Driving• Matter-to-radiation ratio

ρm

ρr

≈ 24Ωmh2(

a

10−3

)of orderunity at recombination in a lowΩm universe


ρm

ρr

≈ 24Ωmh2(

a

10−3


• Radiation is not stress free and soimpedesthe growth of structure

k2Φ = 4πGa2ρ∆

∆ ∼ 4Θ oscillatesaround a constant value,ρ ∝ a−4 so theNewtonian curvature decays Φ ≈ −Ψ.


ρm

ρr

≈ 24Ωmh2(

a

10−3


• Radiation is not stress free and soimpedesthe growth of structure

k2Φ = 4πGa2ρ∆

∆ ∼ 4Θ oscillatesaround a constant value,ρ ∝ a−4 so theNewtonian curvature decays Φ ≈ −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.

Radiation and Dark Matter•Radiation domination:

potential wells created by CMB itself

•Pressure support ⇒ potential decay ⇒ driving

•Heights measures when dark matter dominates

Dark Matter in the Power Spectrum

Dark Matter in the Data

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DASIMaxima-1

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Ωdmh2 = 0.12± 0.03 Wang et al. = 0.13± 0.03 Bond et al.

Damping Tail

Damping• Tight coupling equations assume aperfect fluid: noviscosity, no

heat conduction


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 toThomson scattering

• Dissipation is related to thediffusion length: random walkapproximationλD =

√ηλC


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 toThomson scattering

• Dissipation is related to thediffusion length: random walkapproximationλD =

√ηλC

• Fundamentalconsistency check, e.g.expansion rateatrecombination,fine structure constant.

Maxima

BOOM

DASI

VSA

CBI

Damping Tail Measured

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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

last scat

tering

surfa

cedamping and po

lariz

atio

nquadrupole

quad ∼ k

τvγ

∼ `

`D

1

10(∆T

T+ 90)

Polarization

Polarization from Thomson Scattering

• Differential cross section depends on polarization and angle

Polarization from Thomson Scattering

• Isotropic radiation scatters into unpolarized radiation

Polarization from Thomson Scattering • Quadrupole anisotropies scatter into linear polarization

aligned withcold lobe

Polarization Detected!

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DASIE

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Seljak (1997)

Polarization Frontiers

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reionization grav. lensing

grav. waves

Lensing of a Gaussian Random Field• CMB temperature and polarization anisotropies are Gaussian

random fields – unlike galaxy weak lensing

• Average over many noisy images – like galaxy weak lensing

B-Mode Mapping• Lensing warps polarization field and generates B-modes out of E-mode acoustic polarization - hence correlation

Zaldarriaga & Seljak (1998) Hu (2000); Benabed et al. (2001)

Temperature E-polarization B-polarization

Remapping• Lensing is a surface brightness conservingremappingof source to

image planes by the gradient of theprojected potential

φ(n) = 2

∫ η0

η∗

dη(D∗ −D)

D D∗Φ(Dn, η) .

where conformal timeη =∫

dt/a, D comoving ang. diam.distance,

x(n) → x(n +∇φ) ,

wherex ∈ Θ, Q, U temperature and polarization.

• Taylor expansion leads toproductof fields and Fouriermode-coupling

Lensing by a Gaussian Random Field• Mass distribution at large angles and high redshift in

in the linear regime

• Projected mass distribution (low pass filtered reflectingdeflection angles): 1000 sq. deg

rms deflection2.6'

deflection coherence10°

Lensing in the Power Spectrum• Lensing smooths the power spectrum with a width ∆l~60

• Convolution with specific kernel: higher order correlations between multipole moments – not apparent in power

Pow

er

10–9

10–10

10–11

10–12

10–13

lensedunlensed

∆power

l10 100 1000

Seljak (1996)

Reconstruction from the CMB• Correlation betweenFourier momentsreflectlensing potentialκ = ∇2φ

〈x(l)x′(l′)〉CMB = fα(l, l′)φ(l + l′) ,

wherex ∈ temperature, polarization fieldsandfα is a fixed weightthat reflects geometry

• Each pair forms anoisy estimateof the potential or projected mass- just like a pair of galaxy shears

• Minimum variance weightall pairs to form an estimator of thelensing mass

Requires map with low and statistically homogenous noise. Crosslinking like ACT!

Mapping the Dark Sector• Gravitational lensing of CMB correlates multipoles

• Reconstruct mass from multipole pairs

Hu & Okamoto (2002) [earlier work: Guzik et al 2000; Benabed et al 2001; ML: Hirata & Seljak (2002)]

100 sq. deg; 4' beam; 1µK-arcmin

mass temp. reconstruction EB pol. reconstruction

Matter Power Spectrum• Measuring projected matter power spectrum to cosmic vari-

ance limit across whole linear regime 0.002< k < 0.2 h/Mpc

Hu & Okamoto (2002)

10 100 1000

10–7

10–8

defle

ctio

n po

wer

Reference

Linear

Lσ(w)∼0.06 or reionization or neutrinos

Matter Power Spectrum• Measuring projected matter power spectrum to cosmic vari-

ance limit across whole linear regime 0.002< k < 0.2 h/Mpc

Hu & Okamoto (2002)

10 100 1000

10–7

10–8

defl

ectio

n po

wer

ReferencePlanck

Linear

Lσ(w)∼0.06; 0.14

Cross Correlate with Cosmic Shear• Cross correlation with cosmic shear – mass tomography

anchor in the decelerating regime, massive neutrinos

Hu (2001); Hu & Okamoto (2002)10 100 1000

10–6

10–7

10–6

10–7

10–6

10–7

zs>1.5

1<zs<1.5

zs<1

ReferencePlanck

cros

s po

wer

L

1000sq. deg.

ISW Effect

• Gravitational blueshift on infall does not cancel redshift on climbing out

• Contraction of spatial metric doubles the effect: ∆T/T=2∆Φ

• Effect from potential hills and wells cancel on small scales

ISW and Equation of State• Large effect on low multipoles - probes smoothness of dark energy

we

-0.8 -0.6 -0.4 -0.2 0

20

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80

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(µK

)

10 100 1000

l

Cross Correlation with Temperature

• Any correlation is a direct detection of a smooth energy density component through the ISW effect

• 5 nearly independent measures in temperature & polarization

10 100 1000

10–9

10–10

10–11

ReferencePlanck

cros

s po

wer

LHu (2001); earlier work Goldberg & Spergel (1999); Seljak & Zaldarriaga (1999)

Cross Correlation with Temperature

• Any correlation is a direct detection of a smooth energy density component through the ISW effect

• Dark energy smooth >5-6 Gpc scale, test scalar field nature

Hu & Okamoto (2002)

10 100 1000

10–9

10–10

10–11

ReferencePlanck

cros

s po

wer

L

Contamination for Gravitational Waves• Gravitational lensing contamination of B-modes from gravitational waves cleaned to Ei~0.3 x 1016 GeV

Hu & Okamoto (2002) limits by Knox & Song (2002); Cooray, Kedsen, Kamionkowski (2002)

1

10 100 1000

0.1

0.01

∆B (µ

K)

l

g-lensing

1

3

0.3

E i (1

016 G

eV)

g-waves

Contamination for Gravitational Waves• Gravitational lensing contamination of B-modes from gravitational waves cleaned to Ei~0.3 x 1016 GeV

Hu & Okamoto (2002) limits by Knox & Song (2002); Cooray, Kedsen, Kamionkowski (2002)

1

10 100 1000

0.1

0.01

∆B (µ

K)

l

g-lensing

1

3

0.3

E i (1

016 G

eV)

g-waves

monopole (γa, γb)dipole (da, db)quadrupole (q)

γb

γa

da

q

db

Stability!Space?

calibration (a)rotation (ω)pointing (pa, pb)flip (fa, fb)

ω

a

pb

pafafb

Hu, Hedman & Zaldarriaga (2002)

10-3 rms10-2 rms

Hu & Okamoto (2002)Hu & Okamoto (2002)

Foregrounds?

Space?

MAP will tell...

Future Milestones

• Acoustic polarization peaks• Reionization polarization bump• Initial curvature spectrum (beyond tilt) • Statistics of curvature spectrum (non-Gaussianity)

• Survey of secondary effects in clusters• Survey of secondary effects in field (e.g. Ostriker-Vishniac)• Gravitational lensing of peaks

• ISW probe of dark energy• B-mode polarization from gravitational waves

Summary• All fundamental CMB observables have been observed! • But there is room for even qualitative advancement

Summary• All fundamental CMB observables have been observed! • But there is room for even qualitative advancement • Inflationary prediction of nearly scale-invariant adiabatic (curvature) fluctuations confirmed


• Acoustic scale: sound horizon / ang. diam distance: dark energy modulation: photon-baryon ratio: BBN confirmed amplitude: smooth-clustered component: dark matter damping & polarization: expansion rate & recombination initial spectrum: consistent & constrains exotica


• Acoustic scale: sound horizon / ang. diam distance: dark energy modulation: photon-baryon ratio: BBN confirmed amplitude: smooth-clustered component: dark matter damping & polarization: expansion rate & recombination initial spectrum: consistent & constrains exotica

• Precision polarization and secondary anisotropy for the two ends of time: inflation/origins & dark energy/first objects

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