Outtakes - University of Chicagobackground.uchicago.edu/~whu/Presentations/additional.pdf · The...

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

• • Baryon Wiggles P(k)

• LSS Complementarity

• Weak Lensing

• Generalized Dark Matter

• Stress Histories

• Non-Gaussianity

• Neutrino Background Rad.

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)


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

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)

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

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

Complementarity: Achieving Precisionthrough

Large Scale Structure

• Acoustic oscillations in the matter power spectrum

• Isolating classical cosmological parameters

• Weak lensing by large scale structure

• Measuring the growth rate of perturbations

Acoustic Peaks in the Matter• Baryon density & velocity oscillates with CMB

• Baryons decouple at τ / R ~ 1, the end of Compton drag epoch

• Decoupling: δb(drag) ∼ Vb(drag), but not frozen

End of Drag Epoch


Acoustic Peaks in the Matter• Baryon density & velocity oscillates with CMB

• Baryons decouple at τ / R ~ 1, the end of Compton drag epoch

• Decoupling: δb(drag) ∼ Vb(drag), but not frozen

• Continuity: δb = –kVb

• Velocity Overshoot Dominates: δb ∼ Vb(drag) kη >> δb(drag)

• Oscillations π/2 out of phase with CMB

• Infall into potential wells (DC component)

.

End of Drag Epoch Velocity Overshoot + Infall


Features in the Power Spectrum• Features in the linear power spectrum



k (h Mpc-1)

Eisenstein & Hu (1998)

numerical

P(k

) (

arbi

trar

y no

rm.)

0.01 0.1

0.1

1

nonlinearscale




Peacock & Dodds (1994)

k (h Mpc-1)

mv = 0 eVmv = 1 eV

P(k

) (

arbi

trar

y no

rm.)

W. Hu – Feb. 1998 0.01 0.1

0.1

1

nonlinearscale




SDSS BRG

k (h Mpc-1)

mv = 0 eVmv = 1 eV

P(k

) (

arbi

trar

y no

rm.)

W. Hu – Feb. 1998 0.01 0.1

0.1

1

nonlinearscale

Combining Features in LSS + CMB• Consistency check on thermal history and photon–baryon ratio

• Infer physical scale lpeak(CMB) → kpeak(LSS) in Mpc–1

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

k3Pγ(k)

k (Mpc–1)0.05

2

4

6

8

0.1

Pow

er (

arbi

trar

y no

rm.)

ΛCDM



• Measure in redshift survey kpeak(LSS) in h Mpc–1 → h


Pm(k)

k3Pγ(k)

k (Mpc–1)0.05

2

4

6

8

0.1

Pow

er (

arbi

trar

y no

rm.)

h

ΛCDM



• Measure in redshift survey kpeak(LSS) in h Mpc–1 → h• Robust to low redshift physics (e.g. quintessence, GDM)


Pm(k)

k3Pγ(k)

k (Mpc–1)0.05

2

4

6

8

0.1

Pow

er (

arbi

trar

y no

rm.)

h

ΛCDM QCDMwg=–1/2

Eisenstein, Hu, Tegmark (1998)

MAP +P +SDSSH0 ±130 ±23 ±1.2

Ωm ±1.4 ±0.25 ±0.016

Classical Cosmology

SDSS

MAP(P)CMB: ~line of constant

ΩmH02

Ωm+ΩΛ

1.0

ΩΛ

0.2

40

60

80

0 0.4 0.6 0.8

Ωm

H0

0.2

0.4

0.6

0.8

1.0

0

100


MAP +P +SDSSH0 ±130 ±23 ±1.2

Ωm ±1.4 ±0.25 ±0.016

ΩΛ ±1.1 ±0.20 ±0.024

Classical Cosmology

Any other measurement(including H0)breaksdegeneracy

1.0

ΩΛ

0.2

40

60

80

0 0.4 0.6 0.8

Ωm

H0

0.2

0.4

0.6

0.8

1.0

0

100


MAP +P +SDSSH0 ±130 ±23 ±1.2

Ωm ±1.4 ±0.25 ±0.016

ΩΛ ±1.1 ±0.20 ±0.024

Classical Cosmology

MAP

SDSS

SNIa

MAP+SNIa

MAP+SDSS C

ompl

emen

tari

ty

Con

sist

ency

0.2

0.2

0.4

0.6

0.8

1.0

0 0.4 0.6 0.8 1.0Ωm

ΩΛ

Many opportunitiesfor consistency checks!(e.g. high-z SNIa)

Gravitational Lensing by LSS

• Shearing of galaxy images reliably detected in clusters

• Main systematic effects are instrumental rather than astrophysical

Colley, Turner, & Tyson (1996)

Cluster (Strong) Lensing: 0024+1654

Statistics of Weak Lensing by LSS

• Efficient PM simulations to build statistics• Tiling of hundreds of independent

simulations

6° × 6° FOV; 2' Res.; 245–75 h–1Mpc box; 480–145 h–1kpc mesh; 2–70 109 M

Convergence Shear

White & Hu (1999)

lenses

“tiling”

sources obs.

Weak Lensing: Power Spectrum

• Convergence power spectrum

• Sub-degree scale power fromnon-linear regime (l >100)

2563

5123

shot noise

linear

PD96

10–5

10–4

Pow

er

~

White & Hu (1999)




• Mean power matches densityscaling prediction (PD96)

2563

5123

shot noise

linear

PD96

vs PD96

0.6

1

1.4

10–5

10–4

Rat

ioPo

wer

~

White & Hu (1999)





• Sample variance near Gaussian until l~1000

2563

5123

2563

5123

Gaussian

shot noise

linear

PD96

vs PD96

0.1

0.3

0.6

1

1.4

10–5

10–4

Rat

ioPo

wer

Sam

plin

g E

rror

s

~

White & Hu (1999)





• Sample variance near Gaussian until l~1000

• Shot noise from intrinsicellipticities takes over forl >1000 (γrms=0.4; 2×105deg–1)

• Gaussian approximationreasonable for estimationpurposes

2563

5123

2563

5123

Gaussian

shot noise

linear

PD96

vs shot noise

vs PD96

1

1.2

1.4

0.1

0.3

0.6

1

1.4

10–5

10–4

1000100

Rat

ioR

atio

Pow

erSa

mpl

ing

Err

ors

l

~

~

White & Hu (1999)

Weak Lensing: Power Spectrum & Cosmological Parameters

• Potentially as precise as the CMB

• Systematic effects are under control at the sub% level in shear

• The Good News: Depends on most (8) cosmological parameters





• The Bad News: Depends on most (8) cosmological parameters

Degeneracies!• Solutions:

Large sky coverageTomography on source distributionCombination with CMB measurementsNongaussianity

Blandford et al. (1991); Miralda-Escude (1991); Kaiser (1992)





• The Bad News: Depends on most (8) cosmological parameters

Degeneracies!• Solutions:

Large sky coverageTomography on source distributionCombination with CMB measurementsNongaussianity


• Large sky coverage

• Comparable precision to CMB per area of sky

11D CDM Space

σ(Ωmh2)σ(Ωbh2)σ(mν)σ(ΩΛ)σ(ΩK)σ(ns)σ(lnA)σ(zs)σ(τ)σ(T/S)σ(Yp)

WL√fsky

0.0240.00920.290.0790.0960.0660.280.047––(0.02)

MAP(T)

0.0290.00290.771.00.290.11.21(1)0.630.45(0.02)

Planck(T+P)

0.00270.00020.250.110.0300.0090.045(1)0.0040.0120.01

Hu & Tegmark (1999)


• Divide sample by photometric redshifts

• Cross correlate samples

• Order of magnitude increase in precision, e.g. ΩΛ

Hu (1999)

1

1

2

2

D0 0.5

0.1

1

2

3

0.2

0.3

1 1.5 2.0

g i(D

) n

i(D

)

(a) Galaxy Distribution

(b) Lensing Efficiency

22

11

12

100 1000 104

10–5

10–4

l

Pow

er


• Combine with CMB

• Degeneracy breaking even with1° FOV (acheivable today)

• Order of magnitude gains for> 10° FOV

• Opportunity to probe the detailed nature of darkenergy

Hu & Tegmark (1999)

ΩΛ ΩΚ

mν

zs

0.01 0.1 1

1

10

10–5 10–4 10–3fsky:

ΩΛ

ΩΚ mν

zs

Θdeg1

1

10

10 100

(a) Weak Lensing + MAP

(b) Weak Lensing + Planckim

prov

emen

t ove

r C

MB

Weak Lensing: Skewness

• Skewness of the convergence

• Sensitive to Ωm, ΩG (Bernardeau et al. 1997, Hui 1999; Jain, Seljak & White 1999)

• But depends on:degree of non-linearityshape of power spectrum

• Hierarchical scaling ansatzonly applies on deeply-nonlinear, shot noiselimited scales (<1')

• Severely limited by samplevariance (>1')

σ=10'

σ (arcmin)

σ=5'

2563

5123

convergence–0.05 0

0

0

10–1

1

101

50

100

150

10 20 30

0.05 0.1

ratio biasscalingS 3

PDF

6° × 6°

White & Hu (1999)

Hu & Eisenstein (1998)

Vector Perturbations

Stress Free Anisotropic StressH(±1) >> (p/ρcr)Π(±1) H(±1) (p/ρcr)Π(±1)

Pure Decay Decay from arbitrary initial conditions

Stress Integral Defects

<~

Einstein EquationsGµν=8πGTµν

FRW Background+

Linear Perturbations

Tensor Perturbations

Scalar Perturbations

Stress Free Anisotropic StressHT

(±2) >> (p/ρcr)Π(±2) HT

(±2) (p/ρcr)Π(±2)

Free GravityWaves tCDM (matter)

Stress Integral tCDM (radiation) Defects

<~

Stress Freeζ >> S, SΠ

Clustered

Smooth

2 Componentw1,w2

2,3 ComponentwC = w1wS = w1,w2

const.backgrd.integral

ζ =Φ =

ζ =

Φ =

backgrd.ODE backgrd.ODE

All AdiabaticModels exceptOCDM

ΛCDMOCDMHCDMstrCDMφCDMQCDM

GDMφQCDMΛHCDMOHCDMQHCDM

wC = 0, wS = –1,–1/3(integral) ΛOCDM

Anisotropicζ SΠζ >> S

ζ > SΠ

cC2 > 0

ζ =Φ =

ζ =

Φ =

const.iterativesoln.

ζ < SΠ ζ =

Φ =const.stressintegral

SΕ >> SΠ ζ =

Φ =SΕ-integralζ,SΕ-integral

stressintegral homog.ODE

General ζ =

Φ =

stressintegral Green'sintegral

Perturbative All Adiabatic Models (ν)

Π–decayingmode Defects iDDM

Constant Entropy

Two Componentw1,w2 PIB Axion iDDM

GeneralWKB ks>>1

Two Componentw1,w2, k >>ky Adiabatic Acoustic Peaks

One Component QCDM,GDM (w<0)

Sonic/Entropic

σ = constw1,w2, k >>ky PIB

σ−generationHeat Conduction All ModelsSmooth Formation QCDM, GDM CDMv

Sonic/Aniso-tropic

ViscousDamping All Models

CollisionlessDamping All Models (ν)

Scalar Stressζ S, SΠ <~

<~ S=SS

SonicEntropicS=SΕ

MixedSΠ

,SΕ ,SS

Sonic/Entropic/Anisotropic

IsocurvatureScaling Seeds Traditional Defect Models

Isocurvature Seeds General Defect Models

Part III:Determining

the Properties of the Dark Sector

• Inconsistent precision measures?

• Generalized dark matter

• Examples:

massive neutrinos, scalar fields, decaying dark matter, neutrino background radiation

Inconsistent Precision Measures ?• Expect precision results from CMB, galaxy surveys, SNIa, weak lensing...

• May turn out inconsistent with even the large adiabatic CDM parameter space (11–15 parameters)

Inconsistent Precision Measures ?

What If

• Expect precision results from CMB, galaxy surveys, SNIa, weak lensing...

• May turn out inconsistent with even the large adiabatic CDM parameter space (11–15 parameters)

• CMB shows sub–degree scale structure, but not necessarily the peaksof adiabatic CDM

• Nature of the initial fluctuations isocurvature vs. adiabaticinflation vs. ordinary causal mechanisms

• Clustering properties of matterscale & time dependent biasgravity on large scalesdark matter properties

Beyond Cold Dark Matter

• Parameter estimation and likelihood analysis is only as good as the model space considered

• Even if we do live in CDM space one should observationally prove dark matter is CDM

and missing energy is Λ or scalar field quintessence

• Need to parameterize the possibilities continuously from CDM to more exotic possibilities

Generalized Dark Matter

•An extention of X-matter (Chiba, Sugiyama & Nakamura 1997) basedon gauge invariant variables (Kodama & Sasaki 1984)


• Arbitrary Stress–Energy Tensor Tµν 16 Components

• Local Lorentz Invariance → Symmetric Tµν 10 Components

Hu (1998)




• Energy–Momentum Conservation 4 Constraints 1 Pressure 5 Anisotropic stresses

Hu (1998)





• Linear Perturbations scalar, vector, tensor 1 Pressure (scalar)1 Scalar anisotropic stress

2 vorticities 2 Vector anisotropic stress2 gravity wave pol. 2 Tensor anisotropic stress

• Homogeneity & Isotropy + Gravitational 1 Background pressureInstability 1 Pressure fluctuation

1 Scalar anisotropic stress fluctuation

Hu (1998)





• Linear Perturbations scalar, vector, tensor 1 Pressure (scalar)1 Scalar anisotropic stress

2 vorticities 2 Vector anisotropic stress2 gravity wave pol. 2 Tensor anisotropic stress

• Homogeneity & Isotropy + Gravitational 1 Background pressureInstability 1 Pressure fluctuation

1 Scalar anisotropic stress fluctuation

• Model as Equations of State

• Gauge Invariance w =p/ρ 1 Equation of State ceff2 =(δp/δρ)

comov1 Sound Speed

cvis2 = (viscosity coefficient) 1 Anisotropic StressHu (1998)

Dark Components

Prototypes:• Cold dark matter 0 0 0

(WIMPs)

• Hot dark matter 1/3→0(light neutrinos)

• Cosmological constant –1 arbitrary arbitrary(vacuum energy)

equation of state

wg

sound speed

ceff2viscosity

cvis2

Dark Components

Prototypes:• Cold dark matter 0 0 0

(WIMPs)

• Hot dark matter 1/3→0(light neutrinos)

• Cosmological constant –1 arbitrary arbitrary(vacuum energy)

Exotica:• Quintessence variable 1 0

(slowly-rolling scalar field)

• Decaying dark matter 1/3→0→1/3(massive neutrinos)

• Radiation backgrounds 1/3 1/3 0→1/3(rapidly-rolling scalar field, NBR)

equation of state

wg

sound speed

ceff2viscosity

cvis2

Exotic Dark Matter: Examples

• Two examples

(1) Dark Energy (accelerating component)

(2) Relativistic Dark Matter

(a) alternate model for the seeds of fluctuations

(b) neutrino background radiation (number, anisotropies?)

Determining the Accelerating Component

• Is a cosmological constant responsible for the acceleration?

σ(wg)=0.13 (MAP+SDSS)σ(wg)=0.13 (MAP+SN Ia)σ(wg)=0.03 (Planck+SDSS)σ(wg)=0.03 (Planck+SN Ia)

• If not (–1<wg <0), is a scalarfield responsible?

sound speed constrained if wg > –1/2


SDSS

SNIa

MAP(P)

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

Relativistic Dark Matter: Model

• Defining Elements:Additional species of dark matter: relativistic ideal fluid ρy

Scale-invariant isocurvature fluctuationsδρy = –(δργ + δρν + δρc) ; k3Py(k) = const.

Adiabatic relation in the usual components: δγ = δν = 4δc/3

• Phenomenological Consequences:Scale–invariant series of

Acoustic Peaks Correct CMB/LSS power

(∆T/T = –Φ/3)

• Early–Universe Pedigree:Scalar field rapidly

rolling in quartic potentialGravitationally produced

during inflation a (× 10−5)

(a) Perfect Fluid

(b) Massless Particles

δc

δcδy /f

δy /f

δγ

δγ

0 1 2

–2

–1

0

1

2

–3

–2

–1

0

1

3 4

ampl

itude

Hu & Peebles (1999)

Relativistic Dark Matter: Consequences

• Differs from ΛCDMby ~10% to l=200

• Peak heights oppositeto ΛCDM for Ωbh2

for Ωmh2

• Large scale structuresensitive to rel. darkmatter dynamics:c2vis = 0 vs 1/3

k (h Mpc−1)

l

P(k

)∆T

(µK

)

0.01

10 100 1000

101

102

20

40

60

80

100

103

104

0.1

Ωbh2=0.012 Ωbh2=0.02Massless Particles (Ωbh2=0.012)

set A

Approximate χ2/ν

Model All A B2.62.72.5

1.52.01.2

1.31.31.4ΛCDM

σ8= 0.84; 0.86 (Ωm=0.35; h=0.8)

Hu & Peebles (1999)

Detecting the Neutrino Background Radiation

• Neutrino number Nν or temperature Tν alters the matter–radiation ratio

• Degenerate with matter density Ωmh2

• Break degeneracy with NBR anisotropies

10

5

0

–5

Nν

MAPno polpol

SDSS

Ignoring Anisotropies


Ωmh2

ρm/ρr fixedMAP+SDSS

Anisotropies in the Neutrino Background Radiation

• Neutrino quadrupole anisotropies alter Ψand drive acoustic oscillations

• Anisotropies well modeled by GDM viscosity cvis2 =1/3 but largely degenerate

• Detectability: 1σ, MAP (pol); 3.5σ, MAP+SDSS; 7.2σ, Planck (pol); 8.7σ, Planck+SDSS

0 0.2 0.4 0.6

10

5

0

–5

Ωmh2

Nν

10

5

0

–5N

ν

MAPno polpol

SDSS

SDSS

ρm/ρr fixedMAP+SDSS

Ignoring Anisotropies

Employing Anisotropies

l

Pow

er

2

10 100

4

8

NeutrinosGDM cvis2 = 1/3GDM cvis2 = 0

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

?CMB Anisotropy

Measurements

LSS+High-z

CMB Polarization

% LevelClassical

Cosmological Parameters

+Origin of Fluctuations

(inflation?)

ClusteringProperties of Matter

Nature ofDark Matter Bias

Cosmological Parameters

+Origin and Evolution

of Fluctuations(inflation?)

Gravity WavesVorticity

DensityPerturbations

LSS+

High-z

Originand

Evolution of Structure(defects?)

Cosmological Model

CMBPolarization

CMBPol

Gravity?

?∆T

/T

∆T/T

l

k

k

l

P(k

) P(k

)

Recent Work on Isolating Secondary Anisotropies

• Subarcminute Power SpectrumVishniac Effect; Kinetic SZ Effect;

Patchy Reionization Hu (1999)Bruscoli et al. (1999)

SZ in Clusters Komatsu & Kitayama (1999)

SZ in Radio Galaxies Yamada, Sugiyama, Silk (1999)

• PolarizationWeak Lensing

Zaldarriaga & Seljak (1999)Guzik, Seljak & Zaldarriaga (1999)

Secondary Scattering Hu (1999); Weller (1999)

• Frequency spectrumSZ Effect

Bouchet & Gispert (1999); Tegmark et al. (1999)Cooray, Hu & Tegmark (2000)

• Temperature non-Gaussianity

Weak Lensing & Secondaries 3pt function (bispectrum)Goldberg & Spergel (1999), Seljak & Zaldarriaga (1999),Cooray & Hu (1999)

Weak Lensing: 4pt function (trispectrum) Zaldarriaga (1999)

spot ellipticity & correlationVan Waerbeke,Bernardeau & Benabed (1999)

SZ Effect: hydro-simulationsda Silva et al. (1999); Refrigier et al.

(1999), Seljak, Burwell, Pen (2000); Press-Schechter Aghanim & Forni (1999);

• Polarization non-GaussianityHu (2000)

Spectrum

•FIRAS Spectrum

•Perfect Blackbody

frequency (cm–1)

Bν

(× 1

0–5 )

GHz

error × 50

5

0

2

4

6

8

10

12

10 15 20

200 400 600

Thermalization

•Compton upscattering: y–distortion

•Redistribution: µ-distortion

y–distortion

µ-distortion

p/Tinit

∆T / T

init

0.1

0

–0.1

–0.2

10–3 10–2 10–1 1 101 102

Nucleosynthesis

•Light element abundance depends on baryon/photon ratio

•Existence and temperature of CMB originally predicted (Gamow 1948) by light elements + visible baryons

•With the CMB photon number density fixed by the temperature light elements imply dark baryons

Burles, Nollett, Turner (1999)

Recombination

•Hung up by Lyα opacity (2γ forbidden transition + redshifting)

•Frozen out with a finite residual ionization fraction

Saha

2-levelioni

zatio

n fr

actio

n

scale factor a

redshift z

10–4

10–3

10–2

10–1

1

10–3

103104 102

10–2

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