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Dark Energy

J. Frieman: Overview 30

A. Kim: Supernovae 30

B. Jain: Weak Lensing 30

M. White: Baryon Acoustic Oscillations 30

P5, SLAC, Feb. 22, 2008

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Progress since last P5 ReportBEPAC recommends JDEM as highest-priority

for NASAs Beyond Einstein program: joint AO

expected 2008DES recommended for CD2/3a approval

LSST successful Conceptual Design Review

ESA Cosmic Visions Program: DUNE, SPACEConcept Advisory Team studying possible

merger

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3

What is causing cosmic acceleration?

Dark Energy:

Gravity:

Key Experimental Questions:

1. Is DE observationally distinguishable from a cosmologicalconstant, for which w =1?

2. Can we distinguish between gravity and dark energy?

Combine distance with structure-growth probes

3. Does dark energy evolve: w=w(z)?

G"= 8#G[T

"(matter)+ T

"(dark energy)]

DE equation of state : w = Tii /T0

0< $1/ 3

G"+ f(g

") = 8#GT

"(matter)

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4

Probe dark energy through the history of the expansion rate:

and the growth of large-scale structure:

Four Primary Probes (DETF):

Weak Lensingcosmic shear Distance r(z)+growth

Supernovae Distance

Baryon Acoustic Oscillations Distance+H(z)

Cluster counting Distance+growth

What is the nature of Dark Energy?

H2 (z)

H02

="m

(1+ z)3+"

DEexp 3 (1+ w(z))dln(1+ z)#[ ] + 1$"m $"DE( ) 1+ z( )

2

"# a( )#

r(z) = Fdz

H z( )"#

$%

&

'(

dV

dzd)=

r2(z)

H(z)

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5

Probe dark energy through the history of the expansion rate:

and the growth of large-scale structure:

Four Primary Probes (DETF):

Weak Lensingcosmic shear Distance r(z)+growth

Supernovae Distance

Baryon Acoustic Oscillations Distance+H(z)

Cluster counting Distance+growth

What is the nature of Dark Energy?

H2 (z)

H02

="m

(1+ z)3+"

DEexp 3 (1+ w(z))dln(1+ z)#[ ] + 1$"m $"DE( ) 1+ z( )

2

"# a( )#

r(z) = Fdz

H z( )"#

$%

&

'(

dV

dzd)=

r2(z)

H(z)

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Model Assumptions

Most current data analyses assume a simplified, two-

parameter class of models:

Future experiments aim to constrain (at least) 4-

parameter models:

Higher-dimensional EOS parametrizations possible

Other descriptions possible (e.g., kinematic)

"m,"

DE,w(z) # either : "

m,"

DE(w = $1)

or : "m, w (constant), flat : "

m+"

DE=1

"m,"

DE,w(a)= w

0+ w

a (1# a

)

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Current

Constraints onConstantDark

Energy Equation

of State

2-parameter model:

Data consistent with

w=10.1

Allen et al 07

w, "m

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Current

Constraints onConstantDark

Energy Equation

of State

2-parameter model:

Data consistent with

w=10.1

Allen et al 07

Kowalski et al 08

w, "m

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Curvature and Dark Energy

WMAP3+

SDSS+2dF+SN

w(z)=constant

3-parametermodel:

Spergel etal 07

w, "m

, "k

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Much weaker

current

constraints on

Time-varying

Dark Energy

3-parameter model

marginalized overm

Kowalski et al 08 Assumes flat Universe

w(z) = w0 + wa (1" a)+ ...

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Dark Energy Task Force Report (2006)

Defined Figure of Merit to compare expts andmethods:

Highlighted 4 probes: SN, WL, BAO, CL

Envisioned staged program of experiments:

Stage II: on-going or funded as of 2006Stage III: intermediate in scale + time

Stage IV: longer-term, larger scale

LSST, JDEM

FoM" 1

#(w0)#(wa )

"3

"10

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Much weaker

current

constraints on

Time-varying

Dark Energy

3-parameter model

marginalized overm

Kowalski et al 08

w(z) = w0 + wa (1" a)

``Stage III

``Stage IV

Theoretical

prejudice

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Growth of Large-

scale Structure

Robustness of the

paradigm recommends

its use as a Dark

Energy probe

Price:additional

cosmological and

structure formation

parameters

Bonus:additional

structure formation

parameters

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Expansion History vs. Perturbation Growth

Growth ofPerturbations

probesH(z)

and gravitymodifications

Linder

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Expansion History vs. Perturbation Growth

Growth ofPerturbations

probesH(z)

and gravitymodifications

Linder

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Probing Dark Energy

Primary Techniques identified by the

Dark Energy Task Force report:

Supernovae

Galaxy Clusters

Weak Lensing

Baryon Acoustic Oscillations

Multiple Techniques needed: complementary in systematics

and in science reach

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Caveat:

Representative list,

not guaranteed to be

complete or accurate

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Type Ia SN

Peak Brightness

as calibratedStandard Candle

Peak brightness

correlates with

decline rate

Variety of algorithms

for modeling these

correlations

After correction,~ 0.15 mag(~7% distance error)

Lumino

sity

Time

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2007

Wood-Vasey etal 07

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Large-scale Correlations of

SDSS Luminous Red Galaxies

Acoustic series in

P(k) becomes a

single peak in (r)

Pure CDM model

has no peak

Eisenstein, etal

05

Redshift-

space

Correlation

Function

Baryon

Acoustic

Oscillations

seen in

Large-scale

Structure

"(r) =

#(r

x)#(r

x+

r

r)

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Cold Dark

Matter Models

Power Spectrum

of the Mass

Density

" k( ) = d3# x $ eir

k$r

x"%x( )

%

" k1( )" k2( ) =

2#( )3

P k1( )"

3r

k1+

r

k2( )

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22Tegmark etal 06

SDSS

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Weak lensing: shear and mass

Jain

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Cosmic Shear Correlations

Shear

Amplitude

VIRMOS-Descart Survey

Signal

Noise+systematics

2x10-4

10-4

0

,()

0.6Mpc/h 6Mpc/h 30Mpc/h

CDM

55 sq deg

z= 0.8

Van

Waerbeke

etal 05

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Clusters and Dark Energy

MohrVolume Growth

(geometry)

Number of clusters above observable mass threshold

Dark Energy

equation of state

dN(z)

dzd"=

dV

dz d"n z( )

Requirements1.Understand formation of darkmatter halos

2.Cleanly select massive dark matterhalos (galaxy clusters) over a range

of redshifts3.Redshift estimates for each cluster

4.Observable proxy O that can beused as cluster mass estimate:

p(O|M,z)

Primary systematic:

Uncertainty in bias & scatter ofmass-observable relation

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Clusters form hierarchically

z = 7 z = 5 z = 3

z = 1 z = 0.5 z = 0

5 Mpc

dark matterdark matter

timetime

Kravtsov

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Theoretical Abundance of Dark Matter Halos

Warren et al 05

Warren etal

n(z) = (dn /dlnM)dlnMMmin

"

#

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Cluster Selection

4 Techniques for Cluster Selection:

Optical galaxy concentration

Weak Lensing

Sunyaev-Zeldovich effect (SZE)

X-ray

Cross-compare selection to controlsystematic errors

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Photometric Redshifts

Measure relative flux in

multiple filters:

track the 4000 A break

Precision is sufficient

for Dark Energy probes,

providederror distributions

well measured.

Need deep spectroscopic galaxy

samples to calibrate

Redshifted Elliptical galaxy spectrum

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Photometric Redshifts

Measure relative flux in

multiple filters:

track the 4000 A break

Precision is sufficient

for Dark Energy probes,

providederror distributions

well measured.

Need deep spectroscopic galaxy

samples to calibrate

Redshifted Elliptical galaxy spectrum

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Cluster Mass Estimates

4 Techniques for Cluster Mass Estimation:

Optical galaxy concentration

Weak Lensing

Sunyaev-Zeldovich effect (SZE)

X-ray

Cross-compare these techniques to

reduce systematic errors

Additional cross-checks:

shape of mass function; cluster

correlations

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Calibrating the Cluster Mass-

Observable Relation

Weak Lensing by

stacked SDSS Clusters

insensitive toprojection effects

Calibrate mass-

richness

Johnston, Sheldon, etal 07

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Current Constraints: X-ray clusters

Mantz, et al 2007

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Systematic Errors

Supernovae: uncertainties in dust and SN colors;

selection biases; ``hidden luminosity evolution;

limited low-z sample for training & anchoring

BAO: redshift distortions; galaxy bias; non-

linearities; selection biases

Weak Lensing: additive and multiplicative shear

errors; photo-z systematics; small-scale non-linearity

& baryonic efffects

Clusters: scatter & bias in mass-observable relation;

uncertainty in observable selection function; small-

scale non-linearity & baryonic effects

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Conclusions

Excellent prospects for increasing the precision on DarkEnergy parameters from a sequence of increasingly complex

and ambitious experiments over the next 5-15 years

Exploiting complementarity of multiple probes will be key:

we dont know what the ultimate systematic errorfloors for

each method will be. Combine geometric with structure-

growth probes to help distinguish modified gravity from dark

energy.

What parameter precision is needed to stimulate theoretical

progress? It depends in large part on what the answer is.