Dark Energy in the Universehome.fnal.gov/~dodelson/slac.pdf · Dark Energy in the Universe Scott...

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Dark Energy in the Universe Scott Dodelson March 25, 2003

Transcript of Dark Energy in the Universehome.fnal.gov/~dodelson/slac.pdf · Dark Energy in the Universe Scott...

Page 1: Dark Energy in the Universehome.fnal.gov/~dodelson/slac.pdf · Dark Energy in the Universe Scott Dodelson March 25, 2003. Overview Evidence for Dark Energy • Age: Hubble constant

Dark Energy in the Universe

Scott Dodelson

March 25, 2003

Page 2: Dark Energy in the Universehome.fnal.gov/~dodelson/slac.pdf · Dark Energy in the Universe Scott Dodelson March 25, 2003. Overview Evidence for Dark Energy • Age: Hubble constant

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

Page 3: Dark Energy in the Universehome.fnal.gov/~dodelson/slac.pdf · Dark Energy in the Universe Scott Dodelson March 25, 2003. Overview Evidence for Dark Energy • Age: Hubble constant

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

Page 4: Dark Energy in the Universehome.fnal.gov/~dodelson/slac.pdf · Dark Energy in the Universe Scott Dodelson March 25, 2003. Overview Evidence for Dark Energy • Age: Hubble constant

Evidence for Dark Energy

Expansion determined by Einstein Equations for scale factor a. If theuniverse is flat, then

H2 ≡(

da/dt

a

)2

︸ ︷︷ ︸”kinetic energy”

=8πG

3ρ︸ ︷︷ ︸

”potential energy”

and

d2a

dt2︸︷︷︸Acceleration

= −4πGρa

3

1 +new term︷︸︸︷

3w

︸ ︷︷ ︸

Force per mass

with w ≡ P/ρ.

Decceleration unless w < 0.

Page 5: Dark Energy in the Universehome.fnal.gov/~dodelson/slac.pdf · Dark Energy in the Universe Scott Dodelson March 25, 2003. Overview Evidence for Dark Energy • Age: Hubble constant

Evidence for Dark Energy

ρ ∝ a3(1+w) = (1 + z)−3(1+w)

• Matter density scales asa−3 (w = 0)

• Radiation scales as a−4

(w = 1/3)• Cosmological constant is

. . . constant (w = −1)

Page 6: Dark Energy in the Universehome.fnal.gov/~dodelson/slac.pdf · Dark Energy in the Universe Scott Dodelson March 25, 2003. Overview Evidence for Dark Energy • Age: Hubble constant

Evidence for Dark Energy

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

Page 7: Dark Energy in the Universehome.fnal.gov/~dodelson/slac.pdf · Dark Energy in the Universe Scott Dodelson March 25, 2003. Overview Evidence for Dark Energy • Age: Hubble constant

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

• Age of the universe: t =∫∞0

dzH(z)(1+z).

• Luminosity distance:

dL(z) = (1 + z)∫ z

0

dz′

H(z′)

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

∫ z∗0

dzH(z)

• Growth function:

D1(z) =5Ωm

2

H(z)

H0

∫ z

0

dz′ (1 + z′)

(H(z′)/H0)3

Page 8: Dark Energy in the Universehome.fnal.gov/~dodelson/slac.pdf · Dark Energy in the Universe Scott Dodelson March 25, 2003. Overview Evidence for Dark Energy • Age: Hubble constant

Evidence for Dark Energy

Page 9: Dark Energy in the Universehome.fnal.gov/~dodelson/slac.pdf · Dark Energy in the Universe Scott Dodelson March 25, 2003. Overview Evidence for Dark Energy • Age: Hubble constant

Evidence for Dark Energy: dL

Type Ia Supernovae

• Observed flux proportional toL/d2

L. Type Ia SN are stan-dard candles (identical L), sotheir apparent magnitude is ameasure of dL

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

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

Supernova Cosmology Project

Perlmutter, et al. (1998)

effe

ctiv

e m

Bm

ag r

esid

ual

stan

dard

dev

iatio

n

(0.5,0.5) (0, 0)( 1, 0 ) (1, 0)(1.5,–0.5) (2, 0)

(ΩΜ,ΩΛ) = ( 0, 1 )

Flat

(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

-1.5-1.0-0.50.00.51.01.5

0.0 0.2 0.4 0.6 0.8 1.0-6-4-20246

Page 10: Dark Energy in the Universehome.fnal.gov/~dodelson/slac.pdf · Dark Energy in the Universe Scott Dodelson March 25, 2003. Overview Evidence for Dark Energy • Age: Hubble constant

Evidence for Dark Energy: dL

> 50 SN observed by 2 teamsimply ΩΛ 6= 0.

ΩΜ

No Big Bang

1 2 0 1 2 3

expands forever

ΩΛ

Flat Λ = 0

Universe-1

0

1

2

3

2

3

closedopen

90%

68%

99%95%

recollapses eventually

flat

Riess et al. 1999

Page 11: Dark Energy in the Universehome.fnal.gov/~dodelson/slac.pdf · Dark Energy in the Universe Scott Dodelson March 25, 2003. Overview Evidence for Dark Energy • Age: Hubble constant

Evidence for Dark Energy: dL

Systematic Effect?

Ordinary dust reddens the im-age; this is not seen. Graydust leads to lower fluxes asz increases

Riess et al. 1999

Page 12: Dark Energy in the Universehome.fnal.gov/~dodelson/slac.pdf · Dark Energy in the Universe Scott Dodelson March 25, 2003. Overview Evidence for Dark Energy • Age: Hubble constant

Evidence for Dark Energy: dL

Recently SN observed at z = 1.7

arXiv:astro-ph/0104455 v1 27 Apr 2001 arXiv:astro-ph/0104455 v1 27 Apr 2001

0.1 1.0z

-1.0

-0.5

0.0

0.5

∆(m

-M)

(mag

)

Coasting (Ω=0)Grey Dust or EvolutionΩM=0.35, ΩΛ=0.65ΩM=0.35, ΩΛ=0.0ΩM=1.0, ΩΛ=0.0

SN 1997ff Red

deni

ng

Riess et al. 2001

Page 13: Dark Energy in the Universehome.fnal.gov/~dodelson/slac.pdf · Dark Energy in the Universe Scott Dodelson March 25, 2003. Overview Evidence for Dark Energy • Age: Hubble constant

Evidence for Dark Energy: dL

Proposed mission SNAP will ob-serve thousands of distant SN atz ' 1

Page 14: Dark Energy in the Universehome.fnal.gov/~dodelson/slac.pdf · Dark Energy in the Universe Scott Dodelson March 25, 2003. Overview Evidence for Dark Energy • Age: Hubble constant

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.

Page 15: Dark Energy in the Universehome.fnal.gov/~dodelson/slac.pdf · Dark Energy in the Universe Scott Dodelson March 25, 2003. Overview Evidence for Dark Energy • Age: Hubble constant

Evidence for Dark Energy: CMB

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

Page 16: Dark Energy in the Universehome.fnal.gov/~dodelson/slac.pdf · Dark Energy in the Universe Scott Dodelson March 25, 2003. Overview Evidence for Dark Energy • Age: Hubble constant

Evidence for Dark Energy: CMB

BoomerangDASIMaximaTOCOCBIPythonMSAMViper VSAQMAP

Prior to 2003, ∼ 10 experiments have verified position of first peak. Ouruniverse is flat → Total energy density is equal to the critical density.

Page 17: Dark Energy in the Universehome.fnal.gov/~dodelson/slac.pdf · Dark Energy in the Universe Scott Dodelson March 25, 2003. Overview Evidence for Dark Energy • Age: Hubble constant

Evidence for Dark Energy: CMB

Now WMAP has measured the spec-trum with exquisite precision

Bennett et al. 2003

Page 18: Dark Energy in the Universehome.fnal.gov/~dodelson/slac.pdf · Dark Energy in the Universe Scott Dodelson March 25, 2003. Overview Evidence for Dark Energy • Age: Hubble constant

Evidence for Dark Energy: CMB

• Small scalemodes enter hori-zon earlier; haveundergone moreoscillations.

• Observers todayseee mode ampli-tude at recombi-nation (η∗)

Time →

Page 19: Dark Energy in the Universehome.fnal.gov/~dodelson/slac.pdf · Dark Energy in the Universe Scott Dodelson March 25, 2003. Overview Evidence for Dark Energy • Age: Hubble constant

Evidence for Dark Energy: CMB

• There are manywavevectors ~k whichcontribute to anisotropieson fixed angular scale

• Their amplitudes vary,but their phases (all startwith constant δT : cosinemode) are fixed

• First peak mode haslarge dispersion at re-combination

Time →

Page 20: Dark Energy in the Universehome.fnal.gov/~dodelson/slac.pdf · Dark Energy in the Universe Scott Dodelson March 25, 2003. Overview Evidence for Dark Energy • Age: Hubble constant

Evidence for Dark Energy: CMB

First trough mode hassmall dispersion at re-combination

Time →

Page 21: Dark Energy in the Universehome.fnal.gov/~dodelson/slac.pdf · Dark Energy in the Universe Scott Dodelson March 25, 2003. Overview Evidence for Dark Energy • Age: Hubble constant

Evidence for Dark Energy: CMB

With random phases ...

”First peak” ”First trough”

Inflation sets the phases

Page 22: Dark Energy in the Universehome.fnal.gov/~dodelson/slac.pdf · Dark Energy in the Universe Scott Dodelson March 25, 2003. Overview Evidence for Dark Energy • Age: Hubble constant

Evidence for Dark Energy: CMB

• Structure of peaks andtroughs depends on fre-quency of oscillation anddriving force.

• The CMB is very sensi-tive to Ωmh2

Page 23: Dark Energy in the Universehome.fnal.gov/~dodelson/slac.pdf · Dark Energy in the Universe Scott Dodelson March 25, 2003. Overview Evidence for Dark Energy • Age: Hubble constant

Evidence for Dark Energy: CMB

The CMB plus a mild con-straint on Hubble constant im-plies dark energy.

Spergel et al. 2003

Page 24: Dark Energy in the Universehome.fnal.gov/~dodelson/slac.pdf · Dark Energy in the Universe Scott Dodelson March 25, 2003. Overview Evidence for Dark Energy • Age: Hubble constant

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

Page 25: Dark Energy in the Universehome.fnal.gov/~dodelson/slac.pdf · Dark Energy in the Universe Scott Dodelson March 25, 2003. Overview Evidence for Dark Energy • Age: Hubble constant

Evidence for Dark Energy

All data agree

SNCMBCMB+HSTALL

Lewis & Bridle 2002

Page 26: Dark Energy in the Universehome.fnal.gov/~dodelson/slac.pdf · Dark Energy in the Universe Scott Dodelson March 25, 2003. Overview Evidence for Dark Energy • Age: Hubble constant

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 ofclusters

Page 27: Dark Energy in the Universehome.fnal.gov/~dodelson/slac.pdf · Dark Energy in the Universe Scott Dodelson March 25, 2003. Overview Evidence for Dark Energy • Age: Hubble constant

Evidence for Dark Energy: Growth function

How can we measure mass?

Gravitational Lensing!

Page 28: Dark Energy in the Universehome.fnal.gov/~dodelson/slac.pdf · Dark Energy in the Universe Scott Dodelson March 25, 2003. Overview Evidence for Dark Energy • Age: Hubble constant

Evidence for Dark Energy: Growth function

What can be done with lensing?

• cluster masses• galaxy-galaxy• lensing by lss• lensing of cmb

SDSS: Fischer et al. 2000

Page 29: Dark Energy in the Universehome.fnal.gov/~dodelson/slac.pdf · Dark Energy in the Universe Scott Dodelson March 25, 2003. Overview Evidence for Dark Energy • Age: Hubble constant

Evidence for Dark Energy: Growth functionWittman et al. 2000

• In 2000, four groups detectedweak lensing of distant galaxiesby large scale structure

• Lensing by LSS today is whereCMB was eight years ago

Page 30: Dark Energy in the Universehome.fnal.gov/~dodelson/slac.pdf · Dark Energy in the Universe Scott Dodelson March 25, 2003. Overview Evidence for Dark Energy • Age: Hubble constant

Evidence for Dark Energy: Growth function

• Tomography: Can seehow structure grows withredshift

• Growth sensitive to darkenergy and neutrinomass

• Accelerator ν experi-ments will teach us aboutdark energy

Abazajian & Dodelson, 2003

Page 31: Dark Energy in the Universehome.fnal.gov/~dodelson/slac.pdf · Dark Energy in the Universe Scott Dodelson March 25, 2003. Overview Evidence for Dark Energy • Age: Hubble constant

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

Page 32: Dark Energy in the Universehome.fnal.gov/~dodelson/slac.pdf · Dark Energy in the Universe Scott Dodelson March 25, 2003. Overview Evidence for Dark Energy • Age: Hubble constant

What is it?

Why now? Now is the onlytime when ρΛ ' ambient den-sity. Need fine tuning initiallyto one part in 10128 to getpresent value.

Page 33: Dark Energy in the Universehome.fnal.gov/~dodelson/slac.pdf · Dark Energy in the Universe Scott Dodelson March 25, 2003. Overview Evidence for Dark Energy • Age: Hubble constant

What is it?

Quintessence

• True value of Λ = 0

• Some other form of energy non-zero today, will eventually relaxto true vacuum.

• Most popular incarnation: singlescalar field with V (φ)

Page 34: Dark Energy in the Universehome.fnal.gov/~dodelson/slac.pdf · Dark Energy in the Universe Scott Dodelson March 25, 2003. Overview Evidence for Dark Energy • Age: Hubble constant

What is it? My (Favorite) Quintessence Model

Exponential potential leads to ρφ

tracking ambient density. Useinstead 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

10−2

10−1

100

101

102

λ = 4.0, A = 0.98, ν = 0.51

Ωφ

φ

Dodelson, Stewart, & Kaplinghat (2001)

Page 35: Dark Energy in the Universehome.fnal.gov/~dodelson/slac.pdf · Dark Energy in the Universe Scott Dodelson March 25, 2003. Overview Evidence for Dark Energy • Age: Hubble constant

Conclusions

• Several pieces of independent evidence for dark energy: Type Ia su-pernovae and Cosmic Inventory. Efforts to hunt down systematics andincrease 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 alsostructure. Need to learn about dark energy, weak lensing, polarization,inflation, galaxy surveys, velocities, clusters, . . .

Page 36: Dark Energy in the Universehome.fnal.gov/~dodelson/slac.pdf · Dark Energy in the Universe Scott Dodelson March 25, 2003. Overview Evidence for Dark Energy • Age: Hubble constant