Dark Energy and the Homogeneous Universe 暗能量及宇宙整體之膨脹

Home , Dark energy, Homogeneity (physics)

Lam Hui 許林 Columbia University 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. scale ∼ 1023 cm

Blandton & Hogg scale ∼ 1024 cm

Hubble deep ﬁeld scale ∼ 1025 cm

CfA survey 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. C C

A B A B

dAC = 2 dAB

∆d ∆d AC = 2 AB Therefore: ∆t ∆t

Hubble law: Velocity ∝ Distance Supernova 1998ba Supernova Cosmology Project (Perlmutter, et al., 1998)

(as seen from Hubble Space Telescope)

3 Weeks Supernova Before Discovery

(as seen from telescopes on Earth)

Difference

Supernova 超新星as standard candle

FAINTER (Farther) (Further back in time) Perlmutter, et al. (1998) (ΩΜ,ΩΛ) = 26 ( 0, 1 ) (0.5,0.5) (0, 0) ( 1, 0 ) (1, 0) 24 (1.5,–0.5) (2, 0) Supernova Cosmology Flat Project Λ = 0 22 B m 20 Calan/Tololo (Hamuy et al, A.J. 1996)

effective 18

14 0.02 0.05 0.1 0.2 0.5 1.0

redshift z MORE REDSHIFT (More total expansion of universe since the supernova explosion) See also Riess et al. 98

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

Prob. of fit to Λ = 0 universe: 1% Age of Universe

Slope = Distance/Velocity = 10 billion years Dynamics: what determines the expansion rate and how it changes with time?

Secondary school physics: 1 GMm mv2 − = E 2 R 1 GM For simplicity set E = 0 : v2 = 2 R Apply to the expanding universe:

1 GM 4π v2 = , but remember : M = R3ρ 2 R 3 1 GM 4π v2 = where M = R3ρ Important equation: 2 R 3 Example 1 - ordinary matter 3 2 1 ρ ∝ (M = constant) =⇒ v ∝ 4πR3 R

Therefore : v ↓⇐⇒ R ↑

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

Therefore : v ↑⇐⇒ R ↑ Acceleration! 1 ρ drops slower than Dark Energy: R2 − w i.e. ρ ∝ R 3(1+ ) with w < −1/3

effective 18

14 0.02 0.05 0.1 0.2 0.5 1.0

redshift z MORE REDSHIFT (More total expansion of universe since the supernova explosion) See also Riess et al. 98

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

Prob. of fit to Λ = 0 universe: 1% Wood-Vasey et al. 07

2.0 ESSENCE+SNLS+gold

(ΩM,ΩΛ) = (0.27,0.73) Ω =1 1.5 Total

Λ 1.0 Ω

0.5

0.0 0.0 0.5 1.0 1.5 2.0 ΩM 70% dark energy, 30% matter Wood-Vasey et al. 07

0.0 ESSENCE+SNLS+gold BAO SNeIa+BAO −0.5 (ΩM,w) = (0.27,−1)

w −1.0

−1.5

−2.0 0.0 0.2 0.4 0.6 0.8 1.0 ΩM 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) Observed value too small. 2. Scalar ﬁeld (Bose Einstein condensate) Required mass too small. 3. Modiﬁed gravity (Einstein was wrong!) No compelling theory.

LH & Greene 06 0.82 −1

0.78 −1.5 (geom) (geom) Λ 0.74 Ω

w −2

0.70 −2.5

0.66 0.66 0.70 0.74 0.78 0.82 −2.5 −2 −1.5 −1 (grow) Ω(grow) w Λ Wang, LH, May & Haiman 07 See 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