the physics of cmb polarization - university of...
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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
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
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
• 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
• 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.
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
Polarization on the Sphere
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 on the Sphere
• 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
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
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
B-modes from Secondaries
• Beyond linear theory, density fluctuations generate B-modes • Secondary gravitational and scattering processes
B-modes from Secondaries
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! (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
•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
•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
•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
•Acoustic oscillations in the polarization enhance precision of parameter estimation
•Secondary peak measures reionization epoch & breaks degeneracies
•B-modes probe gravitational waves from inflation
•Foreground subtraction will likely be critical for B-modes
•Non-linear secondary anisotropies generate B-modes and need to be modeled
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
•Acoustic oscillations in the polarization enhance precision of parameter estimation
•Secondary peak measures reionization epoch & breaks degeneracies
•B-modes probe gravitational waves from inflation
•Foreground subtraction will likely be critical for B-modes
•Non-linear secondary anisotropies generate B-modes and need to be modeled
•A long road ahead....
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
•Acoustic oscillations in the polarization enhance precision of parameter estimation
•Secondary peak measures reionization epoch & breaks degeneracies
•B-modes probe gravitational waves from inflation
•Foreground subtraction will likely be critical for B-modes
•Non-linear secondary anisotropies generate B-modes and need to be modeled
•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
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