The Physics of CMB Anisotropies

and their

Cosmological Implications

Wayne Hu

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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

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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

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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

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ΩΛ

h<0.8

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CosmicComplementarity

Clusters

Concordance!?

•Consistent and requires missing “dark” energy

BOOMERanG

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Aclosed

open

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ΩΛ

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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

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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 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)

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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