Wayne Hu- NeoClassical Probes of the Dark Energy

8/3/2019 Wayne Hu- NeoClassical Probes of the Dark Energy

1/49

in

Wayne Hu

COSMO04 Toronto, September 2004

of the Dark Energy

NeoClassical Probes


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Structural Fidelity

Dark matter simulations approaching the accuracy ofCMB

calculations

WMAP Kravtsov et al (2003)


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Equation of State Constraints

NeoClassical probes statistically competitive already

CMB+SNe+Galaxies+Bias(Lensing)+Ly

Future hinges on controlling systematicsSeljak et al (2004)

-2

-1.8

-1.6

-1.4

-1.2

-1

-0.8

-0.6

0 0.2 0.4 0.6 0.8 1 1.2 1.4

w

z

smooth: w=w0+(1-a)wa+(1-a)2waa

68%

95%


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Dark Energy Observables


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Making Light of the Dark Side Line element:

ds2 = a2[(1 2)d2 (1 + 2)(dD2 + D2Ad)]

where is the conformal time, D comoving distance, DA the

comoving angular diameter distance and the gravitational

potential

Dark components visible in their inuence on the metric elements

a and general relativity considers these the same: consistency

relation for gravity

Light propagates on null geodesics: in the background D = ;

around structures according to lensing by

Matter dilutes with the expansion and (free) falls in the

gravitational potential


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Friedmann and Poisson Equations Friedmann equation:

dln a

d

2

=8G

3a2

[aH(a)]2

implying that the densities of dark components are visible in the

distance-redshift relation (a = (1 + z)

1)

D =

d =

d ln a

aH(a)=

dz

H

Poisson equation:

2 = 4Ga2

implying that the (comoving gauge) density eld of the dark

components is visible in the potential (lensing, motion of tracers).


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Growth Rate Relativistic stresses in the dark energy can prevent clustering. If

only dark matterperturbationsm

m

/m are responsible for

potential perturbations on small scales

d2mdt2

+ 2H(a)dmdt

= 4Gm

(a)m

In a at universe this can be recast into the growth rateG(a)

m/a equation which depends only on the properties of

the dark energy

d2G

d ln a2 +5

2

3

2w(a)DE(a) dGd ln a +

3

2[1 w(a)]DE(a)G = 0

with initial conditions G =const.

Comparison ofdistance and growth tests dark energy smoothness

and/orgeneral relativity


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Fixed Deceleration Epoch


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High-z Energy Densities

WMAP + small scale temperature andpolarization measures

provides self-calibrating standards for the dark energy probes

WMAP: Bennett et al (2003)

Multipole moment (l)

l(l+1)Cl/2

(K2)

Angular Scale

0

0

1000

2000

3000

4000

5000

6000

10

90 2 0.5 0.2

10040 400200 800 1400

ModelWMAP

CBI

ACBAR

TT Cross PowerSpectrum


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Relative heights of the first 3 peaks calibrates sound horizon and

matter radiation equality horizon


l(l+1)Cl/2

(K2)

0

0

1000

2000

3000

4000

5000

6000

10 10040 400200 800 1400

baryons(sound speed)


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Relative heights of the first 3 peaks calibrates sound horizon and

matter radiation equality horizon


l(l+1)Cl/2

(K2)

0

0

1000

2000

3000

4000

5000

6000

10 10040 400200 800 1400

dark matter(horizon, equality)

leading source

of error!


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Cross checked with damping scale (diffusion during horizon time)

andpolarization (rescattering after diffusion): self-calibrated and internally cross-checked



l(l+1)Cl/2

(K2)

0

0

1000

2000

3000

4000

5000

6000

10 10040 400200 800 1400

cross checked


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Standard Ruler

Standard rulerused to measure the angular diameter distance to

recombination (z~1100; currently 2-4%) orany redshift for whichacoustic phenomena observable



l(l+1)Cl/2

(K2)

0

0

1000

2000

3000

4000

5000

6000

10 10040 400200 800 1400

angular scalev. physical scale


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Standard Amplitude

Standard fluctuation: absolute power determines initial fluctuations

in the regime 0.01-0.1 Mpc-1



l(l+1)Cl/2

(K2)

0

0

1000

2000

3000

4000

5000

6000

10 10040 400200 800 1400

k~0.02Mpc-1

k~0.06Mpc-1


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Standard Amplitude

Standard fluctuation:precision mainly limited by reionization which

lowers the peaks as e-2

; self-calibrated bypolarization,cross checkedby CMB lensing in future



l(l+1)Cl/2

(K2)

0

0

1000

2000

3000

4000

5000

6000

10 10040 400200 800 1400

e-2see saturday/astroph

CAPMAP, CBI, DASI


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8(z) Determination of the normalization during the acceleration epoch,

even 8, measures the dark energy with negligible uncertaintyfrom other parameters

Approximate scaling (at, negligible neutrinos: Hu & Jain 2003)

8(z) 5.6 105bh

2

0.0241/3

mh

2

0.140.563

(3.12h)(n1)/2

h

0.72

0.693G(z)

0.76,

, bh2, mh2, n all well determined; eventually to 1%precision

h =mh2/m (1 DE)

1/2 measures dark energy density

G measures dark energy dependent growth rate


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Reionization

Biggest surprise ofWMAP: early reionization from temperature

polarization cross correlation (central value

=0.17)

Kogut et al (2003)


0

(l+1)C

l

/2

(K

2)

-1

0

1

2

3

10 10040 400200 800 1400

TE Cross PowerSpectrumReionization


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Leveraging the CMB

Standard fluctuation: large scale - ISW effect; correlation with

large-scale structure; clustering of dark energy; low multipoleanomalies? polarization



l(l+1)Cl/2

(K2)

0

0

1000

2000

3000

4000

5000

6000

10 10040 400200 800 1400


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Standard Deviants[H0 w(z = 0.4)]

[8 dark energy]


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Dark Energy Sensitivity

Fixed distance to recombinationDA(z~1100)

Fixed initial fluctuationG(z~1100) Constant w=wDE; (DE adjusted - one parameter family of curves)

DA/DA

G/G

H-1/H-1

wDE=1/3

0.1

0

0.1

0.2

-0.2

-0.1

1z


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Other cosmological test, e.g. volume, SNIa distance constructed

as linear combinations

deceleration

epoch measures

Hubble constant

DA/DA

(H0DA)/H0DA

H0/H

0G/G

H-1/H-1

wDE=1/3

0.1

0

0.1

0.2

-0.2

-0.1

1z


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Amplitude of Fluctuations

Recent determinations:

compilation: Refrigier (2003)


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Three parameterdark energy model: w(z=0)=w0; wa=-dw/da; DE

wa sensitivity; (fixed w0 = -1; DE adjusted)

deceleration

epoch measures

Hubble constant

DA/DA

(H0DA)/H0DA

H0/H

0G/G

H-1/H-1

wa=1/2; w0=0

0.1

0

0.1

0.2

-0.2

-0.1

1z


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Pivot Redshift

Any deviation from w=-1 rules out a cosmological constant

Seljak et al (2004)

-2

-1.8

-1.6

-1.4

-1.2

-1

-0.8

-0.6

0 0.2 0.4 0.6 0.8 1 1.2 1.4

w

z

smooth: w=w0+(1-a)wa+(1-a)2waa

68%

95%

Equation of state best measured at z~0.2-0.4 = Hubble constant


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Three parameter dark energy model: w(z=0)=w0; wa=-dw/da; DE

H0 fixed (orDE); remaining w0-wa degeneracy Note: degeneracy does notpreclude ruling out (w(z)-1 at somez)

deceleration

epoch measures

Hubble constant

DA/DA

(H0DA)/H0DA

G/G

H-1/H-1

wa=1/2; w0=-0.15

0.1

0

0.01

0.02

-0.02

-0.01

1z


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Rings of Power


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Local Test: H0 Locally DA = z/H0, and the observed powerspectrum

is isotropic in h Mpc-1

space Template matching the features yields the Hubble constant

Eisenstein, Hu & Tegmark (1998)k(Mpc1)

0.05

2

4

6

8

0.1

Power

h

Observed

h Mpc-1

CMB provided


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Cosmological Distances

Modesperpendicular to line of sight measure angular diameter

distance

Cooray, Hu, Huterer, Joffre (2001)k(Mpc1)

0.05

2

4

6

8

0.1

Power

Observed

l DA-1

CMB provided

DA


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Cosmological Distances

Modesparallel to line of sight measure the Hubble parameter

Eisenstein (2003); Seo & Eisenstein (2003) [also Blake & Glazebrook 2003; Linder 2003; Matsubara & Szalay 2002]

k(Mpc1)0.05

2

4

6

8

0.1

Power

Observed

H/z

CMB provided

H


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0.02

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.04 0.06 0.08 0.10 0.12 0.14

k (Mpc-1)

k

(Mpc-1)

0.02 0.04 0.06 0.08 0.10 0.12 0.14

k (Mpc-1)

Hu & Haiman (2003)

Information density in k-space sets requirements for the redshifts

Purely angular limit corresponds to a low-pass k||redshift survey inthe fundamental mode set by redshift resolution

Projected Power

(a)DA (b) H

angular

Limber

limit


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Galaxies and Halos

Recent progress in the assignment ofgalaxies to halos and halo

substructure reduces galaxy bias largely to a counting problemKravtsov et al (2003)SDSS: Zehavi et al (2004)


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Gravitational Lensing


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Lensing Observables

Correlation ofshear distortion of background images: cosmic shear

Cross correlation between foreground lens tracers and shear:galaxy-galaxy lensing

cosmic

shear

galaxy-galaxy lensing


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Halos and Shear


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Lensing Tomography

Divide sample byphotometric redshifts

Cross correlate samples

Order of magnitude increase in precision even afterCMB breaksdegeneracies

Hu (1999)

1

1

2

2

D

0 0.5

0.1

1

2

3

0.2

0.3

1 1.5 2.0

gi(D)

ni(D)

(a) Galaxy Distribution

(b) Lensing Efficiency

22

11

12

100 1000 104

105

104

l

Power

25 deg2, zmed=1


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Galaxy-Shear Power Spectra

Auto and cross power spectra ofgalaxy density and shear

in multiple redshift bins

g1g1

11

12

22g12

g11

g22

g21

g2g2

100

10-4

0.001

0.01

0.1

1000

l

l2Cl/2

Hu & Jain (2003)[also geometric constraints: Jain & Taylor (2003); Bernstein & Jain (2003); Zhang, Hui, Stebbins (2003); Knox & Song (2003)]

shear-shear

cross correlation

and B modes

check systematics

Hoekstra et al (2002); Guzik & Seljak (2001)


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Mass-Observable Relation

With bias determined, galaxy spectrum measures mass spectrum

Use galaxy-galaxy lensing to determine relation with halos orbias

0.001

0.01

0.1

1

10

1011 1012 1013 1014 1015

Mh (h-1M)

M*

0

dnh

dlnMhN(Mh)

ms

As

Mth

lnM

z=0


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Cluster Abundance


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Counting Halos

Massive haloslargely avoidN(Mh)problem ofmultiple objects

0.001

0.01

0.1

1

10

1011 1012 1013 1014 1015

Mh (h-1M)

M*0

dnhdln Mh N(Mh)

ms

As

Mth

lnM

z=0


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Counting Halos for Dark Energy Number density of massive halos extremely sensitive to the growth of structure and hence the dark energy

Potentially %-levelprecision in dark energy equation of state

Haiman, Holder & Mohr (2001)

M Ob bl R l i


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Mass-Observable Relation

Relationship between halos of given mass and observables setsmass threshold and scatteraround threshold

Leading uncertainty in interpreting abundance; self-calibration?

0.001

0.01

0.1

1

10

1011 1012 1013 1014 1015

Mh (h-1M)

M*

0

dnh

dlnMhN(Mh)

ms

As

Mth

lnM

z=0

Pierpaoli, Scott & White (2001); Seljak (2002); Levine, Schultz & White (2002)


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Dark Energy Clustering

ISW Eff


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ISW Effect

Ifdark energy is smooth, gravitational potential decays with expansion

Photon receives a blueshift falling in without compensating redshift

Doubled by metric effect of stretching the wavelength

Sachs & Wolfe (1967); Kofman & Starobinski (1985)

ISW Eff t


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ISW Effect

ISW effect hidden in the temperature power spectrum byprimaryanisotropy and cosmic variance

[plot: Hu & Scranton (2004)]

10-12

10-11

10-10

10-9

l(l+1)Cl

/2

10 100

l

total

ISW

w=-0.8

ISW G l C l ti


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ISW Galaxy Correlation

A 2-3detection of the ISW effect through galaxy correlations

Boughn & Crittenden (2003); Nolte et al (2003); Fosalba & Gaztanaga (2003); Fosalba et al (2003);

Afshordi et al (2003)

0 10 20 30

(degrees)

- 0.4

- 0.2

0

0.2

0.4

(TOT

cntss

-1

K)

Boughn & Crittenden (2003)

D k E S th


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Dark Energy Smoothness

Ultimately can test the dark energy smoothness to ~3% on 1 Gpc

Hu & Scranton (2004)

(

s

)/s

0.011 10

0.03

0.10

ce0 (Gpc)

total

z10

fsky=1

S


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Summary NeoClassical probes based on the evolution ofstructure

CMB xes deceleration epoch observables: expansion rate, energydensities, growth rate, absolute amplitude, volume elements

General relativity predicts a consistency relation between

deviations in distances and growth due to dark energy

Leading dark energy distance observable is H0 or equivalentlyw(z 0.4)

Leading growth observable 8 measures dark energy (and

neutrinos)

Many NeoClassical tests can measure the evolution ofw but all

will require a control oversystematic errors at the 1%

Promising probes are beginning to bear fruit: cluster abundance,

cosmic shear, galaxy clustering, galaxy galaxy lensing,

D k E S iti it


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H0 fixed (orDE); remaining wDE-Tspatial curvature degeneracy

Growth rate breaks the degeneracy anywhere in the accelerationregime

deceleration

epoch measures

Hubble constant

DA/DA

(H0DA)/H0DA

G/G

H-1/H-1

0.1

0

0.01

0.02

-0.02

-0.01

1z

wDE=0.05; T=-0.0033

K i th Hi h Fi d


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Keeping the High-z Fixed

CMB fixes energy densities, expansion rate and distances to deceleration epoch fixed

Example: constant w=wDE models require compensating shiftsin DE and h

-1

0.7

0.6

0.5

-0.8 -0.6 -0.4

wDE

DE

h

Wayne Hu- NeoClassical Probes of the Dark Energy

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