Dark Energy and the Homogeneous Universe

Lam HuiColumbia University

許林

暗能量及宇宙整體之膨脹

This is a series of 3 talks.

Today: Dark energy and the homogeneous

universe

July 11: Dark matter and the large scale

structure of the universe

July 18: Inflation and the early universe

Outline Basic concepts: a homogeneous, isotropic and expanding universe.Measurements: how do we measure the universe’s expansion history?Dynamics: what determines the expansion rate?Dark energy: a surprising recent finding.

There is by now much evidence for homogeneity and isotropy.There is also firm evidence for an expanding universe.

Blandton & Hogg

scale ∼ 1023

cm

scale ∼ 1023

cm

Hubble deep field

scale ∼ 1024

cm

CfA survey

scale ∼ 1025

cm

Sloan Digital Sky Survey scale ∼ 1026

cm

Ned Wright

There is by now much evidence for homogeneity and isotropy. There is also firm evidence for an expanding universe.

There is by now much evidence for homogeneity and isotropy. There is also firm evidence for an expanding universe.But how should we think about it?

Frequently Asked Questions:1. What is the universe expanding into?

2. Where is the center of expansion?

3. Is our galaxy itself expanding?

Frequently Asked Questions:1. What is the universe expanding into? Nothing.2. Where is the center of expansion? Everywhere and nowhere.3. Is our galaxy itself expanding? No.

A B

C

A B

C

Therefore:

dAC = 2 dAB dAC = 2 dAB

∆dAC

∆t= 2

∆dAB

∆t

Hubble law: Velocity ∝ Distance

SupernovaDiscovery

(as seen from Hubble SpaceTelescope)

Difference

(as seen fromtelescopes on Earth)

3 Weeks Before

Supernova 1998baSupernova Cosmology Project

(Perlmutter, et al., 1998)

Supernova 超新星as standard candle

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

Supernova Cosmology Project

effe

ctiv

e m

B(0.5,0.5) (0, 0)

( 1, 0 ) (1, 0)(1.5,–0.5) (2, 0)

(ΩΜ,ΩΛ) =

( 0, 1 )

Fla

t

Λ =

0

redshift z

14

16

18

20

22

24

26

0.02 0.05 0.1 0.2 0.5 1.00.02 0.05 0.1 0.2 0.5 1.0

Perlmutter, et al. (1998)

FA

INT

ER

(F

art

her)

(F

urt

her

back in

tim

e)

MORE REDSHIFT (More total expansion of universe since the supernova explosion)

In flat universe: ΩM = 0.28 [± 0.085 statistical] [± 0.05 systematic]

Prob. of fit to Λ = 0 universe: 1%

See also Riess et al. 98

Slope = Distance/Velocity = 10 billion years

Age of Universe

Dynamics: what determines the expansion rate and how it changes with time?

R

1

2mv

2−

GMm

R= E

For simplicity set E = 0 :1

2v

2 =GM

R

Secondary school physics:

Apply to the expanding universe:

R

1

2v2

=GM

R, but remember :M =

4π

3R3ρ

1

2v2

=GM

Rwhere M =

4π

3R3ρImportant equation:

Example 1 - ordinary matterρ ∝

3

4πR3(M = constant) =⇒ v2 ∝

1

R

Therefore : v ↓⇐⇒ R ↑

Example 2 - cosmological constant ρ = constant =⇒ v2 ∝ R2

Therefore : v ↑⇐⇒ R ↑ Acceleration!ρ drops slower than

1

R2Dark Energy:i.e. ρ ∝ R−3(1+w)

with w < −1/3

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

Supernova Cosmology Project

effe

ctiv

e m

B(0.5,0.5) (0, 0)

( 1, 0 ) (1, 0)(1.5,–0.5) (2, 0)

(ΩΜ,ΩΛ) =

( 0, 1 )

Fla

t

Λ =

0

redshift z

14

16

18

20

22

24

26

0.02 0.05 0.1 0.2 0.5 1.00.02 0.05 0.1 0.2 0.5 1.0

Perlmutter, et al. (1998)

FA

INT

ER

(F

art

her)

(F

urt

her

back in

tim

e)

MORE REDSHIFT (More total expansion of universe since the supernova explosion)

In flat universe: ΩM = 0.28 [± 0.085 statistical] [± 0.05 systematic]

Prob. of fit to Λ = 0 universe: 1%

See also Riess et al. 98

0.0 0.5 1.0 1.5 2.0ΩM

0.0

0.5

1.0

1.5

2.0Ω

Λ

ESSENCE+SNLS+gold(ΩM,ΩΛ) = (0.27,0.73)

ΩTotal=1

Wood-Vasey et al. 07

70% dark energy, 30% matter

0.0 0.2 0.4 0.6 0.8 1.0ΩM

−2.0

−1.5

−1.0

−0.5

0.0w

ESSENCE+SNLS+goldBAO

SNeIa+BAO(ΩM,w) = (0.27,−1)

ESSENCE+SNLS+goldBAO

SNeIa+BAO(ΩM,w) = (0.27,−1)

Wood-Vasey et al. 07

Dark energy ρ ∝ R−0.6 to R1.2

What is dark energy?

1. Vacuum energy (Einstein’s cosmological constant)

2. Scalar field (Bose Einstein condensate)

3. Modified gravity (Einstein was wrong!)

What is dark energy?

1. Vacuum energy (Einstein’s cosmological constant)

2. Scalar field (Bose Einstein condensate)

3. Modified gravity (Einstein was wrong!)

Observed value too small.

Required mass too small.

No compelling theory.

LH & Greene 06

ΩΛ(grow)

ΩΛ(geom)

0.66 0.70 0.74 0.78 0.820.66

0.70

0.74

0.78

0.82

w(grow) w(geom)

−2.5 −2 −1.5 −1

−2.5

−2

−1.5

−1

Wang, LH, May & Haiman 07See also Li & Chu, Li, Chan & Chu 06

Summary- Basic concepts of a homogeneous, isotropic and expanding universe.

- Surprisingly, our current expansion appears to be accelerating. Explaining it, and measuring it precisely, is a major goal of cosmology today.

Let there be light. Genesis 1:3