Scott Dodelson- Dark Energy in the Universe

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Dark Energy in the Universe

Scott Dodelson

March 25, 2003



Overview

Evidence for Dark Energy

• Age: Hubble constant + globular clusters

• Distance vs. redshift: Type Ia Supernovae

• Inventory: CMB (Ω = 1) + Many (Ωm 0.3)

• Growth function: Weak lensing & Cluster counts



Overview

What is it?

• Cosmological constant Λ: Historical edge (Einstein), very unlikely

• Λ = 0; transient energy, eventually will go to zero: Modern favorite,

very unlikely




Expansion determined by Einstein Equations for scale factor a. If the

universe is flat, then

H 2 ≡ da/dt

a 2

”kinetic energy”

=8πG

3

ρ ”potential energy”

and

d2a

dt2

Acceleration

= −4πGρa

3

1 +

new term

3w

Force per mass

with w ≡ P/ρ.

Decceleration unless w < 0.




ρ ∝ a3(1+w) = (1 + z)−3(1+w)

• Matter density scales as

a−3 (w = 0)

• Radiation scales as a−4

(w = 1/3)

• Cosmological constant is

. . . constant (w = −1)




Expansion rate was slower in Λ model ↔ The universe is accelerating!



Evidence for Dark Energy What observables depend on H (z)?

• Age of the universe: t = ∞

0dz

H (z)(1+z).

• Luminosity distance:

dL(z) = (1 + z) z

0dz

H (z)

• Angular diameter distance to recombination: d∗ = 11+z∗

z∗0

dzH (z)

• Growth function:

D1(z) =5Ωm

2

H (z)

H 0

z

0

dz (1 + z)

(H (z)/H 0)3



Evidence for Dark Energy: dL

Type Ia Supernovae

• Observed flux proportional toL/d2

L. Type Ia SN are stan-

dard candles (identical L), so

their apparent magnitude is a

measure of dL

• H (z) smaller in Λ model →dL larger → fainter SN

Calan/Tololo(Hamuy et al, A.J. 1996)

SupernovaCosmologyProject

Perlmutter, et al. (1998)

e f f e c t i v e m B

m a g r e s i d u a l

s t a n d a r d d e v i a t i o n

(0.5,0.5) (0, 0)

( 1, 0 ) (1, 0)(1.5,–0.5) (2, 0)

(ΩΜ,ΩΛ) = ( 0, 1 )

F l a t

(0.28, 0.72)

(0.75, 0.25 ) (1, 0)

(0.5, 0.5 ) (0, 0)

(0, 1 )

(ΩΜ , ΩΛ) =

Λ =

0

redshift z

14

16

18

20

22

24

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

0.0 0.2 0.4 0.6 0.8 1.0

-6

-4

-2

0

2

4

6




> 50 SN observed by 2 teams

imply ΩΛ = 0.

ΩΜ

No Big Bang

1 2 0 1 2 3

e x p a n d s f o r e v e r

Ω Λ

Flat

Λ = 0

Universe-1

0

1

2

3

2

3

c l o s e d o p e n

9 0 %

6 8 %

9 9 %

95 %

reco l la p s e s e v e n t u a l l y

f l a t

Riess et al. 1999




Systematic Effect?

Ordinary dust reddens the im-

age; this is not seen. Gray

dust leads to lower fluxes as

z increases

Riess et al. 1999




Recently SN observed at z = 1.7

a r X i v : a s t r o - p h / 0 1 0 4 4 5 5 v 1 2 7 A p r 2 0 0 1 a r X i v : a s t r o - p h / 0 1 0 4 4 5 5 v 1 2 7 A p r 2 0 0 1

0.1 1.0

z

1.0

0.5

0.0

0.5

Coasting (Ω=0)Grey Dust or EvolutionΩM=0.35, ΩΛ=0.65ΩM=0.35, Ω

Λ=0.0

ΩM=1.0, ΩΛ=0.0

SN 1997ff R e

d d

e n

i n g

Riess et al. 2001




Proposed mission SNAP will ob-

serve thousands of distant SN at

z 1



Evidence for Dark Energy: Inventory

• Hot/cold spots in CMB at z = 1100 are the size of sound horizon.

Apparent size depends on geometry of universe.

• There are many estimates of matter density: all yield Ωm = 0.3.



Evidence for Dark Energy: CMB

Angular size of hot/cold spots distinguishes between open, closed or flat

universe.




BoomerangDASIMaximaTOCOCBIPythonMSAMViper VSAQMAP

Prior to 2003, ∼ 10 experiments have verified position of first peak. Our

universe is flat → Total energy density is equal to the critical density.




Now WMAP has measured the spec-

trum with exquisite precision

Bennett et al. 2003




• Small scale

modes enter hori-

zon earlier; haveundergone more

oscillations.

• Observers today

seee mode ampli-

tude at recombi-nation (η∗)

Time →




• There are many

wavevectors k which

contribute to anisotropies

on fixed angular scale• Their amplitudes vary,

but their phases (all start

with constant δT : cosine

mode) are fixed

• First peak mode haslarge dispersion at re-

combinationTime →




First trough mode has

small dispersion at re-

combination

Time →




With random phases ...

”First peak” ”First trough”

Inflation sets the phases




• Structure of peaks andtroughs depends on fre-

quency of oscillation and

driving force.

• The CMB is very sensi-

tive to Ωmh2




The CMB plus a mild con-

straint on Hubble constant im-

plies dark energy.

Spergel et al. 2003



Evidence for Dark Energy: Ωm

• Direct counting givesΩm = 0.3

• Also: Large scale struc-

ture, velocities, Clusters

. . . All give Ωm = 0.3

Mass-to-Light Ratio vs. Scale

H0 = 100

Ω = 1

Ω = 0.3

1000

100

Rich Clusters (med)

Morgan Groups (med)

Hickson Groups (med)

CFA Groups (med)

X-ray Groups

The Local Group

M101, M31, Milky Way

Cor Bor Supercluster

Spirals (med)

Ellipticals (med)

Shapley Supercluster

Cosmic Virial Theorem

Least Action Method

Virgo Infall (range)

Bulk Flows (range)

M / L B ( M / L )

10

1

0.01 0.1 1

R (Mpc)

Sp

E

10

Bahcall et al. 2000




All data agree

SN

CMB

CMB+HST

ALL

Lewis & Bridle 2002



Evidence for Dark Energy: Growth function

• Less growth in a Λ uni-verse

• Clustering was compara-

ble at z ∼ 0.5−1 to now

• Roughly same number of

clusters




How can we measure mass?

Gravitational Lensing!




What can be done with lensing?

• cluster masses

• galaxy-galaxy

• lensing by lss• lensing of cmb

SDSS: Fischer et al. 2000




Wittman et al. 2000

• In 2000, four groups detected

weak lensing of distant galaxies

by large scale structure

• Lensing by LSS today is where

CMB was eight years ago




• Tomography: Can see

how structure grows with

redshift• Growth sensitive to dark

energy and neutrino

mass

• Accelerator ν experi-

ments will teach us aboutdark energy

Abazajian & Dodelson, 2003



Niels closed the conversation with

one of those stories he liked to tell on

such occasions: “One of our neigh-

bors in Tisvilde once fixed a horse-

shoe over the door to his house.

When a common friend asked him,

‘But are you really superstitious?

Do you honestly believe that this

horseshoe will bring you luck?’ he

replied, ‘Of course not; but they say it

works even if you don’t believe in it.’”

Heisenberg 1927



What is it?

Why now? Now is the only

time when ρΛ ambient den-

sity. Need fine tuning initially

to one part in 10128 to get

present value.



What is it?

Quintessence

• True value of Λ = 0

• Some other form of energy non-

zero today, will eventually relax

to true vacuum.

• Most popular incarnation: single

scalar field with V (φ)



What is it? My (Favorite) Quintessence Model

Exponential potential leads to ρφ

tracking ambient density. Use

instead V (φ) = e−λφ [1 +

A sin(νφ)]

10−11

10−10

10−9

10−8

10−7

10−6

10−5

10−4

10−3

10−2

10−1

100

a

0−2

0−1

100

101

102

λ = 4.0, A = 0.98, ν = 0.51

Ωφ

φ

Dodelson, Stewart, & Kaplinghat (2001)



Conclusions

• Several pieces of independent evidence for dark energy: Type Ia su-

pernovae and Cosmic Inventory. Efforts to hunt down systematics and

increase statistics are ongoing.

• Another class of evidence growth function (gravitational lensing, clus-

ters) will play a key role in near future

• Modern Cosmology encompasses not only smooth universe, but also

structure. Need to learn about dark energy, weak lensing, polarization,

inflation, galaxy surveys, velocities, clusters, . . .

Scott Dodelson- Dark Energy in the Universe

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