The Physics of CMB Polarization - Wayne Hu's Tutorials

The Physics of CMB Polarization

Wayne Hu

10

2

0.1

0.2

0.3

0.4

4

6

100

10

multipole l

∆T (

µK)

Why Measure the Polarization?

• Virtues of polarization

• unlike temperature anisotropies, generated by scattering only

• tensor field on the sky; carries more info than scalar temperature





• Uses of polarization

• verify the gravitational instability paradigm: fluctuations present during last scattering (outside horizon ⇒ inflation)

• probe the reionization epoch: remove a leading source of ambiguity (degeneracy) in the temperature power spectrum

• get higher statistics on the acoustic peaks and their underlying parameters





• Uses of polarization

• verify the gravitational instability paradigm: fluctuations present during last scattering (outside horizon ⇒ inflation)

• probe the reionization epoch: remove a leading source of ambiguity (degeneracy) in the temperature power spectrum

• get higher statistics on the acoustic peaks and their underlying parameters

• reconstruct the scalar, vector, tensor nature of the perturbations and hence the cosmology even if ab initio models are wrong

• test inflationary models by measuring the gravity wave amplitude: energy scale and shape of inflaton potential

Polarization from Thomson Scattering

• Differential cross section depends on polarization and angle


• Isotropic radiation scatters into unpolarized radiation


• Quadrupole anisotropies scatter into linear polarization

aligned withcold lobe

Isotropization by Scattering

• Rock: polarization generated by Thomson scattering

• Hard Place: Thomson scattering destroys quadrupole source

Quadrupoles at Recombination's End

• Acoustic inhomongeneities become anisotropies by streaming/diffusion

Quadrupoles at Recombination's End

• Electron "observer" sees a quadrupole anisotropy

• Polarization pattern is a projection quadrupole anisotropy

Polarization Power Spectrum

• Quadrupole generation on diffusion scale (optically thin regime)

• Primary peak coincides with beginning of damping tail l~1000

• Secondary peak coincides with horizon scale at reionization l<10

10

2

0.1

0.2

0.3

0.4

4

6

100 1000

10

l

∆T (

µK) < 10%

Acoustic Peaks in the Polarization

Hu & White (1997)

• Scalar quadrupole follows the velocity perturbation

• Acoustic velocity out of phase with acoustic temperature

• Correlation oscillates at twice the frequency

0

1

–1

v/23

cross

temp.

vel.-quad.

ks

Scalar Power Spectra

Hu & White (1997)

100

10-1

10-2

101

101 102 103

102

103

reion.τ=0.1

l

Pow

er (

µK2 )

temperature

cross

E-pol.

m=0

v

Scalars:

hot

hot

cold

m=1

vv

Vectors:m=2

Tensors:

Hu & White (1997)

Polarization on the Sphere

• Polarization direction oriented with the cold lobe of the quadrupole

• A local observer will see a sin2θ pattern of Q-polarization: spin–spherical harmonic: l=2, m=0, s=2: 2Y2.

0


Hu & White (1997)

• Polarization is a projection of the quadrupole moments

êφ

êθ

n

θ=π/2θ=π/4θ=0

θ

0

π/2

π

θ

φπ/2 3π/2 2π


• Polarization due to gravitational waves follows similarly

• m=±2 quadrupole viewed at different angles

• Difference: no symmetry – Q and U polarization

• Coordinate independent description of polarization

Polarization Patterns

π/20

0

π/2

ππ 3π/2 2π

θ

l=2, m=0

l=2, m=1 π/20

0

π/2

ππ 3π/2 2π

θ

π/20

0

π/2

ππ 3π/2 2πφ

θ

l=2, m=2

Scalars

Vectors

Tensors

Electric & Magnetic Polarization(a.k.a. gradient & curl)

Kamionkowski, Kosowsky, Stebbins (1997)Zaldarriaga & Seljak (1997)

• Alignment of principal vs polarization axes (curvature matrix vs polarization direction)

E

B

Polarization Patterns

E-polarization B-polarization

Tensor Power Spectra

Hu & White (1997)

E-pol.

100

10-1

10-2

101

101 102 103

102

103

reion.τ=0.1

l

Pow

er (

µK2 )

temperature

cross

101 102 103

100

10-1

10-2

101

102

Pow

er (

µK2 )

l

temperature

cross

E-pol.

B-pol.

1σ MAP

Reionization and Gravitational Waves

• Distinguished by polarization power spectrum (B-modes)

Polarization and Parameter Estimation

Eisenstein, Hu & Tegmark (1998)

h 1.3Ωm 1.4ΩΛ 1.1ΩK 0.31

Ωmh2 0.029

Ωbh2 0.0027

Ωνh2 0.0094

ns 0.14α 0.30

T/S 0.48

log(A) 1.3

τ 0.69

0.0120.0160.0240.011

0.00820.00080.0019

0.0510.013

0.15

0.28

0.024

0.23

0.25

0.20

0.057

0.015

0.0013

0.0063

0.094

0.019

0.19

0.36

100% 75% 50% 25% 0%

Relative Errors

MAP(no pol)

MAP(pol)

MAP+SDSS(pol, 0.2hMpc-1)

Foregrounds & Parameter Estimation

Tegmark, Eisenstein, Hu, de Oliviera Costa (1999)

degr

adat

ion

fact

or

foreground amplitude(relative to fiducial model)

20

15

10

5

0× 0 × 1 × 3 × 10 × 0 × 1 × 3 × 10

τσ=0.0035

T/Sσ=0.0065

JointKnown

Planck

B-modes from Secondaries

• Beyond linear theory, density fluctuations generate B-modes • Secondary gravitational and scattering processes


• Beyond linear theory, density fluctuations generate B-modes • Secondary gravitational and scattering processes


Zaldarriaga & Seljak (1998)

• Gravitational lensing is a foreground for gravitational waves • B-modes can be used to map the dark matter

10 100 1000

0.1

1

multipole l

B–m

ode

Pola

riza

tion

(µK

)

gravitationalwaves

gravitationallensing

T/S=

0.5

Summary

•Polarization is hard!

Summary

•Polarization is hard! (unavoidable consequence of generation by scattering in an optically thin environment)

•Anisotropies are <10% polarized ⇒ 10–6 or µK level

•Polarization pattern traces the quadrupole anisotropy at last scattering

Summary




•Acoustic oscillations in the polarization enhance precision of parameter estimation

•Secondary peak measures reionization epoch & breaks degeneracies

•B-modes probe gravitational waves from inflation

Summary







•Foreground subtraction will likely be critical for B-modes

•Non-linear secondary anisotropies generate B-modes and need to be modeled

Summary









•A long road ahead....

Summary









•A long road ahead.... gainful employment for years!

Index

Details & Outtakeshttp://background.uchicago.edu

•Why Polarization

•Thomson Scattering

•Scalar Spectrum

•Acoustic Waves

•Cross Correlation

•Power Spectra

•Quadrupoles

•Orientation

•Quadrupoles

•Scalar, Vector, Tensor

•E and B

•Patterns

•Tensor Spectra

•Reionization & T/S

•Parameter Estimation

•Foregrounds

•Secondaries

•Lensing

•Summary

Microsoft

Documents

The Physics of CMB Polarization - Wayne Hu's Tutorials