understanding the properties of dark energy in the universehuterer/talks/pitt_2003.pdf · ¥ high...

Understanding the Properties of

Dark Energy in the Universe

Dragan Huterer

Case Western Reserve University

Understanding the Properties of Dark Energy in the Universe – p.1/37

The Cosmic Food Pyramid

??

Radiation (

)Luminous Matter (

)

Baryonic Matter (

)

Dark Matter (

)

Dark Energy (

)


Type Ia Supernovae

-20 0 20 40 60-15

-16

-17

-18

-19

-20

-20 0 20 40 60-15

-16

-17

-18

-19

-20

B Band

as measured

light-curve timescale “stretch-factor” corrected

days

MB

– 5

log(

h/65

)

days

MB

– 5

log(

h/65

)

Calan/Tololo SNe Ia

Kim, et al. (1997)


Discovering SNe Ia

SupernovaDiscovery

(as seen from Hubble SpaceTelescope)

Difference

(as seen fromtelescopes on Earth)

3 Weeks Before

Supernova 1998baSupernova Cosmology Project

(Perlmutter, et al., 1998)


Recent Supernova data

Supernova Cosmology Project

=0.3,

=0.7 =0.3,

=0.0 =1.0,

=0.0

m-M

(m

ag)

High-Z SN Search Team

0.01 0.10 1.00z

(m-

M)

(mag

)

! "$# ! "$% & '

() * +


Parameterizing Dark Energy

"% & % & ) '

) ' , % &% &

' "# ( ' "% & ( ' (flat)

' ( '

'

# % & % & '


Parameterizing Dark Energy

"% & % & ) '

) ' , % &% &

' "# ( ' "% & ( ' (flat)

' ( '

'

# % & % & '

may be varying:

* ( ' ' ( '


Current Supernova Constraints


Fine-Tuning Problems I: “Why Now ?”

DE is important only at

, since

% & #

"% &"#

( '

and )

100

105

1010

1015

1+z

10-60

10-40

10-20

100

1020

ρ (G

eV4 )

ρΛ

ρRAD

ρM

Λ dominates


Fine-Tuning Problems II: “Why so small ?”

Refers to the vacuum energy, .

(recall

)

( ) ' () '

50 – 120 orders of magnitude discrepancy!


A candidate: Quintessence

V

φ

100

102

104

106

108

1010

1012

z+1

-1.2

-0.8

-0.4

0.0

0.4

0.8

1.2

Equ

atio

n-of

-sta

te (

wQ

)

KE dominates

Q frozen

Q joins tracker sol.

100

102

104

106

108

1010

1012

z+1

10-50

10-40

10-30

10-20

10-10

ρ (G

eV4 )

Peebles & Ratra 1987, Caldwell, Dave & Steinhardt 1998


Classical Tests

0.0 0.1 1.0 10.0 100.0 1000.0z

0.0

1.0

2.0

3.0

4.0

-dr/dw

r(z) w=-0.4

w=-1.0

0 1 2 3z

0

0.2

0.4

dV

/dΩ

dz

w=-0.4

-0.6

-0.8

-1.0

0.11.010.0z

0.1

1

δ(z)

/δ(to

day)

w=−1

w=−1/3


Wish List

Goals:Measure

" % &,

Measure '

– equivalently, % & 'Measure any clustering of DE

Difficulties:

DE may cluster at scales


Cosmological Tests of Dark Energy

Matter density

Vacuum density constant

CURRENT SN 1a

SNAP

Tegmark 2001


Weak Gravitational Lensing


Current Data and Constraints

0 0.5 1Ω

M

0.5

1

1.5

σ8

Refregier 2003, Bacon et al. 2003


Weak Lensing and DE

1 10 100 1000 10000l

10−10

10−8

10−6

10−4

10−2

l(l+1

)Plκ /(

2π)

ΩX=0.70, w=−1.0ΩX=0.70, w=−0.5ΩX=0.65, w=−1.0

linear

Hu 1999, Huterer 2002, Refregier et al. 2003


Weak Lensing and DE

1 10 100 1000 10000l

10−10

10−8

10−6

10−4

10−2

l(l+1

)Plκ /(

2π)

ΩX=0.70, w=−1.0ΩX=0.70, w=−0.5ΩX=0.65, w=−1.0

linear

0 1 2 3 4 5z

0

0.2

0.4

0.6

0.8

n(z)

0 0.2 0.4 0.6 0.8 1ΩM

−1.0

−0.8

−0.6

−0.4

−0.2

0.0

w

1 redshift bin2 bins10 bins

Hu 1999, Huterer 2002, Refregier et al. 2003


Deeper and Wider

25 26 27 28 29depth (R−band mag)

0.00

0.01

0.02

0.03

0.04

0.05

σ(w)

σ(ΩX)

10 100 1000 10000sky coverage (deg

2)

0.00

0.02

0.04

0.06

0.08

0.10

σ(w)

σ(ΩX)

Huterer 2002


Number Counts

0 0.5 1 1.5 2z

102

103

104

105

dN/d

z (

4000

deg

2 )

ΩM

=1, ΩDE

=0

ΩM

=0.3, ΩDE

=0.7, w=-1

w=-0.8


Number Counts

Count clusters using X-ray, SZ, weaklensing...

Mass-observable relation

Haiman, Mohr & Holder 2001, Majumdar & Mohr 2003


Cosmic Microwave Background Anisotropies

Bennett et al. 2003 (WMAP collaboration)


CMB Sensitivity to Dark Energy

Peak locations are sensitive to dark energy (but not much):

1 10 100 1000 10000

l

0

1000

2000

3000

4000

5000

6000

7000

l(l+

1)C

l / (2

π) (

µK2 )

w = -1.0w = -0.5

Same as measurement of

with

fixed

End up constraining:

(Planck:

to

%)

Huterer & Turner 2001, Frieman et al. 2003


SNe plus CMB

constant ' '

0 0.5 1 1.5 2 2.5z

MAX

0.1

0.2

0.3

0.4

0.5

0.6

σ w

SNeSNe + σΩ

M= 0.03

SNe + σΩM= 0.01

SNe + Planck SNe + Planck + σΩ

M= 0.01

0 0.5 1 1.5 2 2.5z

MAX

0.2

0.4

0.6

0.8

1

1.2

1.4

σ dw/d

z

SNeSNe + σΩ

M= 0.03

SNe + σΩM= 0.01

SNe + PlanckSNe + Planck + σΩ

M= 0.01

Frieman, Huterer, Linder & Turner 2003


CMB-LSS cross-correlation



−0.1 0.0 0.1 0.2 0.3⟨XT⟩/σXσT

0

50

100

150

Num

ber

of R

ealiz

atio

ns ΩΛ = 0.0ΩΛ = 0.5ΩΛ = 0.8

Boughn, Crittenden & Turok 1997



−0.1 0.0 0.1 0.2 0.3⟨XT⟩/σXσT

0

50

100

150

Num

ber

of R

ealiz

atio

ns ΩΛ = 0.0ΩΛ = 0.5ΩΛ = 0.8

-0.5

0

0.5

1

1.5

2

wgT

(θ)

[µK

]

z ~ 0.57 z ~ 0.49

1 10

θ (degrees)

-1

-0.5

0

0.5

1

1.5 z ~ 0.43

1 10

z ~ 0.35

Boughn, Crittenden & Turok 1997, Scranton et al. 2003Understanding the Properties of Dark Energy in the Universe – p.23/37

Strong Gravitational Lensing


Strong Lensing Statistics

Required input:

Cosmology (

, , )Luminosity function (galaxies)or mass function (all halos)

Density profile of lenses

e.g. SIS:

or generalized NFW:

Magnification bias

1 1.2 1.4 1.6 1.8 2β

10-6

10-5

10-4

10-3

10-2

τ

Kochanek 1993, 1996, Cooray & Huterer 1999, Chae 2003,Davis, Huterer & Krauss 2003, Kuhlen, Keeton & Madau 2003


Strong Lensing Statistics

Required input:

Cosmology (

, , )Luminosity function (galaxies)or mass function (all halos)

Density profile of lenses

e.g. SIS:

or generalized NFW:

Magnification bias

0.5 0.75 1 1.25 1.5 1.75 2β

1012

1013

1014

Mc /

(h-1

Msu

n)68% CL 95% CL

Huterer & Ma 2003


Beyond

' '

' (

-1 -0.9 -0.8 -0.7 -0.6 -0.5w0

-1.0

-0.5

0.0

0.5

1.0

w’


Beyond

' '

' (

-1 -0.9 -0.8 -0.7 -0.6 -0.5w0

-1.0

-0.5

0.0

0.5

1.0

w’

Principal Components of

0 0.5 1 1.5z

-0.5

0

0.5

e i(z)

1

2

3

4

49

50

Huterer & Starkman 2003


Reconstruction of

( ' ( "$# ( ' ' '

"$# ( ' '

0 0.2 0.4 0.6 0.8 1z

−1.0

−0.8

−0.6

−0.4

−0.2

0.0

w(z

)

Huterer and Turner 1999; Chiba and Nakamura 1999, Weller & Albrecht 2002


Requirements• Measure Ω and Λ• Measure w and w(z)

M

SCIENCE

• Sufficient (~2000) numbers of SNe Ia

• ...distributed in redshift

• ...out to z < 1.7

STATISTICAL REQUIREMENTS

Identified & proposed systematics:

• Measurements to eliminate / bound each one to +/-0.02mag

SYSTEMATICS REQUIREMENTS

SATELLITE / INSTRUMENTATION REQUIREMENTS

DATA SET REQUIREMENTS

• Discoveries 3.8 mag before max.• Spectroscopy with S/N=10 at 15 Å bins.• Near-IR spectroscopy to 1.7 µm.

•••

• ~2-meter mirror• 1-square degree imager• 3-channel spectrograph

(0.3 µm to 1.7 µm)

Derived requirements: • High Earth orbit • ~5 Mb/sec bandwidth

•••


SuperNova/Acceleration Probe


Mirror and Focal Plane


SNAP SuperNovaAcceleration Probe

~2500 SNe Ia


SNAP predicted constraints

No Big Bang

1 2 0 1 2 3

expands forever

-1

0

1

2

3

2

3

closed

recollapses eventually

Supernovae

CMB Boomerang

Maxima

Clusters

mass density

vacu

um

en

erg

y d

en

sity

(co

smo

log

ica

l co

nst

an

t)

open

flat

SNAP Target Statistical Uncertainty

network of cosmic strings w = –1/3

range of "Quintessence"

models

cosmological constant w = –1

90%95%

99%

68%

0.0

0.0 0.2 0.4 0.6 0.8 1.0

–0.2

–0.4

–0.6

–0.8

–1.0

ΩΜ = 1 − Ωu

equa

tion

of

stat

e w

= p

u /

ρu

Unknown Component,Ωu, of Energy Density

Flat Universe Constant w

Supernova Cosmology Project Perlmutter et al. (1998)

SNAP Satellite Target Statistical Uncertainty

Dark Energy


Weak Lensing with SNAP

0 0.1 0.2 0.3 0.4 0.5

ΩM

-1

-0.9

-0.8

-0.7

-0.6

-0.5

w

SNe

WL (PS)

WL (PS+BS)

SNe + WL (PS+BS)

-1.2 -1.1 -1 -0.9 -0.8w

0

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

dw

/dz

SNeWL (PS)

WL (PS+BS)

SNe + WL (PS+BS)


1

NASA-DOE

Joint Dark Energy Mission

Paul Hertz / NASA

Robin Staffin / DOE

Endorsed by

Raymond L. Orbach Edward J. Weiler

Director of the Office of Science Associate Administrator for Space Science

Department of Energy NASA

September 24, 2003 September 25, 2003Understanding the Properties of Dark Energy in the Universe – p.36/37

Conclusions

Dark energy makes up

of energy density in the universe.It is smooth and has negative pressure.

We describe it via

and .

It affects cosmology by modifying the expansion rate

at recent times (

).

SNe Ia, weak lensing and number counts are most promising probes;variety of other methods can help.

Bright prospects with future wide-field surveys (SNAP, LSST, SPT,...)

But to understand DE, major insights will be needed from theorists.This will be especially hard if

!


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