Outtakes - University of Chicagobackground.uchicago.edu/~whu/Presentations/outtakes.pdf · Doppler...

The Outtakes

• CMB Transfer Function

• Testing Inflation

• Weighing Neutrinos

• Decaying Neutrinos

• Testing Λ• Testing Quintessence

• Polarization Sensitivity

• SDSS Complementarity

• Secondary Anisotropies

• Doppler Effect

• Vishniac Effect

• Patchy Reionization

• Sunyaev-Zel'dovich Effect

• Rees-Sciama & Lensing

• Foregrounds

• Doppler Peaks?

• SNIa Complementarity

• Polarization Primer

• Gamma Approximation

• ISW Effect

Back to Talk

Doppler Effect• Relative velocity of fluid and observer

• Extrema of oscillations are turning points or velocity zero points

• Velocity π/2 out of phase with temperature

Velocity minima

Velocity maxima

Doppler Effect• Relative velocity of fluid and observer

• Extrema of oscillations are turning points or velocity zero points

• Velocity π/2 out of phase with temperature

• Zero point not shifted by baryon drag

• Increased baryon inertia decreases effectmeff V2 = const. V ∝ meff

–1/2 = (1+R)–1/2

V||

V||

η

∆T/T

η∆T

/T

−|Ψ|/3

−|Ψ|/3Velocity minima

Velocity maxima

No baryons

Baryons

Doppler Peaks?• Doppler effect has lower amplitude and weak features from projection

observer

jl(kd)Yl0 Y1

0

l

(2l+

1)j l'

(100

)no peak

observer

d d

jl(kd)Yl0 Y0

0

l

(2l+

1)j l(

100)

peakTemperature Doppler

Hu & Sugiyama (1995)

Relative Contributions

5

500 1000 1500 2000

10

Spat

ial P

ower

kd

totaltempdopp

Hu & Sugiyama (1995); Hu & White (1997)

Relative Contributions

5

10

5

500 1000 1500 2000

10

Ang

ular

Pow

erSp

atia

l Pow

er

l

kd

totaltempdopp

Hu & Sugiyama (1995); Hu & White (1997)

Projection into Angular Peaks

• Peaks in spatial power spectrum

• Projection on sphere

• Spherical harmonic decomposition

• Maximum power at l = kd

• Extended tail to l << kd

• Described by spherical bessel function jl(kd)

observer

d

jl(kd)Yl0 Y0

0

l

(2l+

1)j l(

100)

peak

Bond & Efstathiou (1987) Hu & Sugiyama (1995); Hu & White (1997)

Projection into Angular Peaks

• Peaks in spatial power spectrum

• Projection on sphere

• Spherical harmonic decomposition

• Maximum power at l = kd

• Extended tail to l << kd

• 2D Transfer Function T2(k,l) ~ (2l+1)2 [∆T/T]2 jl

2(kd)

Hu & Sugiyama (1995)

0.5 1 1.5 2

-3.5

-3

-2.5

-2

-1.5

0.5 1 1.5 2

log(

k · M

pc)

log(

x)

SW

Acoustic

StreamingOscillations

0.5

1

1.5

2

2.5

log(l)

ProjectionOscillations

Main Projection

Transfer Function Bessel Functions

Measuring the Potential

• Remove smooth damping(independent of perturbations)

• Measure relative peak heights

• Relate to RΨ at last scattering

• Compare with large scale structure Ψ today

• Residual is smooth potentialenvelope and measuresmatter–radiation ratio

Hu & White (1996)

Uses of Acoustic Oscillations

• Distinct features

• Presence/absence unmistakenable

• Sensitive to background parametersthrough fluid parameters

• Sensitive to perturbations throughgravitational potential wellswhich later form structure

• Robust measures of

Angular diameter distance (curvature)Baryon–photon ratio

Uses of Baryon Drag

• Measures baryon–photon ratioat last scattering + zlast scattering + TCMB → Ωbh2

• Measures potential wells at lastscattering (compare with large–scalestructure today)

• Removes phase ambiguity by distinguishingcompression from rarefaction peaks(separates inflation from causal seed models)

Uses of Damping

• Sensitive to thermal history and baryon content

• Independent of (robust to changes in) perturbation spectrum

• Robust physical scale for angular diameter distance test(ΩK, ΩΛ)

Integrated Sachs–Wolfe Effect

• Potential redshift: g00=–(1+Ψ)2 δij

blueshift redshift

Kofman & Starobinskii (1985) Hu & Sugiyama (1994)



• Perturbed cosmological redshiftgij=a2(1+Ψ)2 δij δT/T = –δa/a = Ψ

blueshift redshift




• Perturbed cosmological redshiftgij=a2(1+Ψ)2 δij δT/T = –δa/a = Ψ

• Time–varying potentialRapid compared with λ/c

δT/T = –2∆ΨSlow compared with λ/c

redshift–blueshift cancel

• Imprint characteristic timescale of decay in angular spectrum

blueshift redshift

(2Ψ)2

Pow

er

l

lISW~ d/∆η


Testing Inflation / Initial Conditions• Superluminal expansion (inflation) required to generate superhorizon

curvature (density) perturbations

• Else perturbations are isocurvature initially with matter moving causally

• Curvature (potential) perturbations drive acoustic oscillations

• Ratio of peak locations

• Harmonic series:curvature 1:2:3...isocurvature 1:3:5...

Θ+Ψ

−Ψ

−Ψ

η

∆Τ/Τ

(a) Adiabatic

Θ+Ψ

η

∆Τ/Τ

(b) Isocurvature

Hu & White (1996)

Testing Inflation / Initial Conditions• Superluminal expansion (inflation) required to generate superhorizon

curvature (density) perturbations

• Else perturbations are isocurvature initially with matter moving causally

• Curvature (potential) perturbations drive acoustic oscillations

• Ratio of peak locations

• Harmonic series:curvature 1:2:3...isocurvature 1:3:5...

Hu & White (1996)

Pow

er

l

2

500 1000 1500

4

6

CDM InflationAxion Isocurvature

Hidden 1st peak

Weighing Neutrinos• Massive neutrinos suppress power strongly on small scales

[∆P/P ≈–8Ων/Ωm]: well modeled by [ceff2=wg, cvis

2=wg, wg: 1/3→1]

• Degenerate with other effects [tilt n, Ωmh2...]

• CMB signal small but breaks degeneracies

• 2σ Detection: 0.3eV [Map (pol) + SDSS]

Power Suppression Complementarity

k (h Mpc-1)

mv = 0 eVmv = 1 eV

P(k

)

0.01 –0.01 0.0

0.6

0.8

1.0

1.2

1.4

0.01 0.02 0.030.1

0.1

1 SDSS

Ωνh2 = mν/94eV

n

SDSSonly

MAP only

Joint

Hu, Eisenstein, & Tegmark (1998); Eisenstein, Hu & Tegmark (1998)

Cosmology and the

Neutrino Anomalies

10-3

10-2

10-1

100

sin22θ

10-11

10-10

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

101

102

103

∆m2 (

eV2 )

Solar

Solarνe−νµ, τ

νe−νµ limit

νµ−ντ limit

BBNLimit

νµ−νs

νe−νs

νe- νµ,τ

LSNDνµ- νe

Atmosνµ−ντ

Solarνe- νµ,τ,s

Hata (1998)

CosmologicallyExcluded

Cosmology and the

Neutrino Anomalies

10-3

10-2

10-1

100

sin22θ

10-11

10-10

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

101

102

103

∆m2 (

eV2 )

Solar

Solarνe−νµ, τ

νe−νµ limit

νµ−ντ limit

BBNLimit

νµ−νs

νe−νs

νe- νµ,τ

LSNDνµ- νe

Atmosνµ−ντ

Solarνe- νµ,τ,s

Hata (1998)Hu, Eisenstein & Tegmark (1998)

Detectable inRedshift Surveys


Cosmology and the

Neutrino Anomalies

10-3

10-2

10-1

100

sin22θ

10-11

10-10

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

101

102

103

∆m2 (

eV2 )

Solar

Solarνe−νµ, τ

νe−νµ limit

νµ−ντ limit

BBNLimit

νµ−νs

νe−νs

νe- νµ,τ

LSNDνµ- νe

Atmosνµ−ντ

Solarνe- νµ,τ,s

Hata (1998)Hu, Eisenstein & Tegmark (1998)Hu & Tegmark (1998)

Detectable inWeak Lensing

Detectable inRedshift Surveys


10-8 10-6 10-4 10-2 1

0.2

0.4

0.01

0.1

1

a

aeq

wddm

ζ

Φ

∆T/T

Decaying Dark Matter• Example: relativistic matter goes non-

relativistic, decays back into radiation

• Model decay and decay products as a single component of dark matter

• Novel consequences: scale–invariant curvature perturbation from scale–invariant isocurvature perturbations

10 100 1000l

20

40

60

80

100

∆T (µ

K)

100

104

103P

(k)

0.01 0.1 1k (h Mpc-1)

Hu (1998)

τ=3yrsτ=5yrsτ=8yrs

m=5keV

Testing Λ• If wg<0, GDM has no effect on

acoustic dynamics → (kpeaks, heights)independent of wg, Ωg, ceff, cvis

• CMB sensitive to GDM/Λ mainly through angular diameter distance [dA =f(wg,Ωg...)]

Hu, Eisenstein, Tegmark & White (1998)

MAP(no pol with pol)

Ωg

wg

0

–0.5

–1.00.2 0.4 0.6 0.8 1.0

l (rescaled to dA)

Pow

er (

×10-1

0 )

ceff2=1=–1/6=–1/3=–2/3=–1

wg

10 100 1000

2

4

6

8

degeneracy




• Galaxy surveys determines h

• CMB determines Ωmh2 → Ωm

• Flatness Ωg = 1 – Ωm


SDSSOnly


MAP+ SDSS

Ωg

wg

0

–0.5

–1.00.2 0.4 0.6 0.8 1.0

l (rescaled to dA)

Pow

er (

×10-1

0 )

ceff2=1=–1/6=–1/3=–2/3=–1

wg

10 100 1000

2

4

6

8

degeneracy







• SNIa determines luminosity distance [dL =f(wg,Ωg)]


SDSSOnly

SNIaOnly


MAP+ SNIa

MAP+ SDSS

Con

sist

ency

Ωg

wg

0

–0.5

–1.00.2 0.4 0.6 0.8 1.0

Com

plem

etar

ity

l (rescaled to dA)

Pow

er (

×10-1

0 )

ceff2=1=–1/6=–1/3=–2/3=–1

wg

10 100 1000

2

4

6

8

degeneracy

SN data July 1998







• SNIa determines luminosity distance [dL =f(wg,Ωg)]

Garnavich et al (1998); Riess et al (1998); Perlmutter et al (1998)Ωg

wg

0

–0.5

–1.00.2 0.4 0.6 0.8 1.0

l (rescaled to dA)

Pow

er (

×10-1

0 )

ceff2=1=–1/6=–1/3=–2/3=–1

wg

10 100 1000

2

4

6

8

degeneracy


Is the Missing Energy a Scalar Field?

• Scalar Fields have maximal sound speed [ceff =1, speed of light]

• CMB+LSS → Lower limit on ceff>0.6 at wg=–1/6[2.7σ: MAP+SDSS; 7.7σ: Planck+SDSS]

[in 10d parameter space, including bias, tensors]

• Strong constraints for wg > –1/2

Large Scale Structure CMB Anisotropies

k (h Mpc–1) l

P(k

)

Pow

er (

×10-1

0 )

wg=–1/6 wg=–1/6ceff2=0 ceff2=0

1/6 1/6

11scalar

fields scalar fields

0.001 0.01 0.1 10 100 1000

104

103

102

4

6

2

Polarization from Thomson Scattering

• Thomson scattering of anisotropic radiation → linear polarization

• Polarization aligned with cold lobe of the quadrupole anisotropy

QuadrupoleAnisotropy

Thomson Scattering

e—

Linear Polarization

ε’

ε’

ε

Perturbations & Their Quadrupoles

m=0

v

Scalars:

hot

hot

cold

m=1

vv

Vectors:m=2

Tensors:

Hu & White (1997)

• Orientation of quadrupole relative to wave (k) determines pattern

• Scalars (density) m=0 • Vectors (vorticity) m=±1 • Tensors (gravity waves) m=±2

Polarization Patterns

π/20

0

π/2

ππ 3π/2 2π

θ

l=2, m=0

E, B

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 Patterns

Global ParityFlip

E

B

LocalAxes

Principal PolarizationKamionkowski, Kosowski, Stebbins (1997)Zaldarriaga & Seljak (1997)Hu & White (1997)

• Global view: behavior under parity

• Local view: alignment of principle vs. polarization axes

Patterns and Perturbation Types

Kamionkowski, Kosowski, Stebbins (1997); Zaldarriaga & Seljak (1997); Hu & White (1997)

• Amplitude modulated by plane wave → Principle axis

• Direction detemined by perturbation type → Polarization axis

Scal

ars

Vec

tors

Ten

sors

π/2

0 π/4 π/2

π/2

φ

θ

10 100l

0.5

1.0

0.5

1.0

0.5

1.0

Polarization Pattern Multipole Power

B/E=0

B/E=6

B/E=8/13

Polarization Raw Sensitivity

10

2

0.1

0.2

0.3

0.4

4

6

100 1000

10

l

∆T (

µK)

SDSS: Improving Parameter Estimation

Eisenstein, Hu & Tegmark (1998)

h 1.3Ωm 1.4ΩΛ 1.1ΩK 0.31

0.0120.0160.0240.011

0.23

0.25

0.20

0.057

100% 75% 50% 25% 0%

Relative Errors

MAP(no pol)

MAP(pol)

MAP+SDSS(pol, 0.2hMpc-1)

Classical Cosmology

Supernovae Type Ia

Ωg

wg

0

–0.5

–1.00.2 0.4 0.6 0.8

68%95

%99%

July 1998

Garnavich et al. (1998); Riess et al. (1998); Perlmutter et al. (1998)Figure: Hu, Eisenstein, Tegmark, White (1998)

MAP(P)

SDSS

SN

Ωg0.2 0.4 0.6 0.8 1.0

ProjectionSupernovae Type Ia, CMB & LSS

Hu, Eisenstein, Tegmark, White (1998)

wg

0

–0.5

–1.0

SDSS: Improving 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)

Secondary Anisotropies

• Temperature and polarization anisotropies imprinted in the CMB after z=1000

• Rescattering Effects

• Linear Doppler Effect (cancelled)

• Modulated Doppler Effects (non–linear)

• by linear density perturbations → Ostriker–Vishniac Effect

• by ionization fraction → Inhomogeneous Reionization

• by clusters → thermal & kinetic Sunyaev–Zel'dovich Effects

• Gravitational Effects

• Gravitational Redshifts

• by cessation of linear growth → Integrated Sachs–Wolfe Effect

• by non–linear growth → Rees–Sciama Effect

• Gravitational Lensing

Cancellation of the Linear Effect

overdensity

e— velocity redshifted γ

blueshifted γ

Observer

Cancellation

Last Scattering Surface

Modulated Doppler Effect

overdensity,ionization patch,cluster...

e— velocity unscattered γ

blueshifted γ

Observer

Last Scattering Surface

Ostriker–Vishniac Effect

Ostriker–Vishniac

Primary

Doppler

Hu & White (1996)

Patchy ReionizationAghanim et al (1996)

Gruzinov & Hu (1998)

Knox, Scocciomarro & Dodelson (1998)

Thermal SZ Effect

Persi et al. (1995) Atrio–Barandela & Muecket (1998)

Rees–Sciama Effect Gravitational Lensing

Seljak (1996a,b)

Residual Foreground Effects

10

1

0.1

100

10

1

100

10

10 100 1000

1

0.01

100

total

totalincreased noisesynchrotron

totalincreased noisesynchrotron

x2

x2

x2

Temperature

E-polarization

B-polarization

dustsynchrotronfree-free

increased noisepoint sources

% d

egra

datio

n

l

1

1

10 100 1000

totaldustincreased noisepoint sources

totaldustincreased noisesynchrotron

totaldustincreased noisesynchrotron

x2

x2

x2

Temperature

E-polarization

B-polarization

l

MAP Planck

Foregrounds & Parameter Estimation

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

Features in the Transfer Function• Features in the linear transfer function

• Break at sound horizon

• Oscillations at small scales; washed out by nonlinearities

T(k)

T(k

) / T

BB

KS8

6(k)

EH98

k (h Mpc-1)

Ωm=0.3, h=0.5, Ωb/Ω0=0.3

0.01

1.0

0.9

0.7

0.6

0.5

0.1

Eisenstein & Hu (1998)

PD94

S95

BBKS86

Outtakes - University of Chicagobackground.uchicago.edu/~whu/Presentations/outtakes.pdf · Doppler...

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