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Misao Sasaki

佐々木 節

Y TPYUKAWA INSTITUTE FOR

THEORETICAL PHYSICS

Let's Enjoy Science

20 Oct., 2013

We can now study these questions quantitatively

based on observational data

Era of Precision Cosmology 精密宇宙論の時代

Cosmology Today (現代の宇宙論） • Origin/Birth of the Universe (宇宙の誕生・起源)

Origin of Space-Time and Matter (時空と物質の起源)

• Evolution/Structure of the Universe (宇宙の進化と構造)

Dynamics of Space-Time/Gravity

(時空・重力のダイナミックス)

3 Cosmological principle (宇宙原理)

Universe looks the same everywhere in every direction

isotropy

等方

homogeneity

一様

open flat closed

angle < 180o angle = 180o angle > 180o

homogeneous & isotropic space

Expansion rate

of the Universe

4 Einstein equation for cosmology

= Friedmann equation Friedmann (1922)

2

2

8

3

G KH

a

1 0 1

gravitational constant

density

cosmic scale factor

(open), (flat), (closed) -

G

a

K

daH a

dt

a

Space expands!

宇宙の膨張率

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2 Mpc

Hubble’s Law (ハッブルの法則)

2 Mpc

70 km/s

140 km/s

140 km/s

1 Mpc = 3 Million light years (Mly)

our galaxy

Edwin Hubble (1929)

1 Mpc

galaxies more distant recede faster

expansion rate today: H0 = 70 km/s/Mpc

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30,000 ｋｍ/s

size of observable universe: 10Gly (light velocity ＝ 300,000 km/sec)

Large scale structure of the Universe

宇宙の大規模構造

seeing far ＝ seeing past

遠くを見る＝過去を見る

1Gly (300Mpc)

Hubble’s universe

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Universe was small in the past.

No galaxies, no stars １4 Gyrs ago

Matter distributed uniformly in space

extremely high temperature, high density

Big Bang !

Gamov’s fire ball cosmology (1940’s)

ガモフの「火の玉」宇宙論

Big-Bang Universe

George Gamow

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Radiation from deep space;

from high temperature era

of the Universe

Discovery of Cosmic Microwave

Background (CMB)

Wilson and Penzias

noise in radio wave from

all directions of sky

Penzias & Wilson (1965)

seeing far = seeing past !

宇宙マイクロ波背景放射

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Hot soup of photons and

elementary particles

Nucleosynthesis in the first

3 minutes: 4He, D, 7Li,...

Clear-up/neutralization

at 380,000 yrs after birth

Formation of stars &

galaxies > 1 Gyr after birth

Extremely Brief History of the Universe

big

bang

（光子と素粒子の熱いスープ）

（最初の3分間で元素合成）

（38万年後に晴上り/中性化)

(10億年後から星・銀河形成)

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we see

surface of clouds

Last Scattering Surface （最終散乱面）

If we observe sky at visible frequency band,

we see surface of cosmic clear-up

＝LSS of CMB 宇宙マイクロ波背景放射の最終散乱面

(380,000 yrs old Universe)

at radio frequency (~100 GHz)

(可視光 ~ 500,000 GHz)

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Cosmological Redshift

Cosmic

Expansion

Light once very blue became

redder and redder, even redder than Infra Red,

and became micro (Radio) waves today

l ∝ size of the Universe

l

（宇宙論的赤方偏移）

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Purest

Planck distribution

in nature

“thermal spectrum”

熱平衡分布

CMB Planck distribution (プランク分布）

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accelerated expansion due to vacuum energy

Theory of Inflationary Universe

Before Big Bang ?

Katsuhiko Sato Alan Guth Andrei Linde

インフレーション宇宙理論 （1980～）

真空のエネルギーによる加速膨張

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What is “vacuum” energy?

• false vacuum (偽の真空)

huge energy is produced by expansion

total energy = (energy density) x (volume)

energy density remains the same even if

space expands

空間が膨張してもエネルギー密度は一定

absence of any matter, but ‘space’ itself

contains potential energy (vacuum energy)

物質のない「空間」が潜在的エネルギーを持つ

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observable size of the Universe 観測可能な宇宙のサイズ

baby universe

x 1030 or more

birth of mega-size

universe

Cosmic Inflation

looks perfectly

smooth & flat

explains

“homogeneity” & “flatness” 一様性と平坦性を説明

quantum vacuum fluctuations are also stretched to mega scales

and they become seeds for formation of stars and galaxies

真空の量子揺らぎも巨大サイズに引き伸ばされ星や銀河の種になる

（宇宙のインフレーション）

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Birth of Big Bang Universe

Whole vacuum energy is converted to heat 真空のエネルギーがすべて熱になる

birth of matter 物質の誕生

(quarks, electrons, neutrinos, ... & photons)

cold universe hot universe

~ 10-34 sec old universe ~ 1028 K

(ビッグバン宇宙の誕生）

strongest phase transition in the history of the Universe

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Predictions of Inflation

• Microscopic quantum vacuum fluctuations grow to

macroscopic density fluctuations to form galaxies.

（真空の量子揺らぎが密度揺らぎに成長し銀河になる）

(インフレーション宇宙論の予言）

Predictions agree perfectly with observation

• These fluctuations leave distinguishable imprints

on CMB temperature fluctuations

（この量子揺らぎはＣＭＢ揺らぎに特徴的痕跡を残す）

• Universe after inflation is extremely flat.

（インフレーション後の宇宙は極めて平坦）

18 Map of 380,000 yrs old Universe

(Last Scattering Surface) by Planck satellite

If the Universe were100 yrs old, this was 1 day old Universe

Temperature is highly uniform

510T

T

Temperature T is slightly higher in Red regions,

while it is slightly lower in Blue regions

If we magnify fluctuations by 100,000 times

(2013)

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CMB angular power spectrum

Agreement with theory tells us much about the Universe

theory

Planck 2013 data

温度揺らぎの角度パワースペクトル

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Content of the Universe today

Dark Energy (暗黒エネルギー)

~ “vacuum” energy

accelerated expansion

of the Universe

Dark Matter (暗黒物質)

large scale structure

of the Universe

Atoms (原子・通常の物質)

stars, visible objects

96% of the Universe is unknown!

現在の宇宙の構成要素

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Quantum Cosmology （量子宇宙論）

Quantum gravity is still in its infancy Superstring theory, M-theory, loop quantum gravity, ....

Need Quantum Gravity

（量子重力理論が必要）

Universe before Inflation? （インフレーション以前？）

Quantum mechanics of cosmic scale factor: a(t)

宇宙の大きさ a(t) を量子力学で取扱う

• quantum approach to the birth of the Universe

（宇宙誕生の量子論的理解） • first step toward full quantum gravity

（完全な量子重力理論への第一歩）

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At scale L ~ 10-33cm, energy fluctuations become so large

that even spacetime geometry is no longer smooth at all.

Planck Scale

Planck length: PlanckL = -3310 cm

Planck energy: Planck

2E = /c-510 g

PlanckE 810 kcal or 500 kw hour

(~ power consumed by a family / month)

J.A. Wheeler

23 World of Quantum Gravity

The whole Universe was in quantum state

when its size was ~10-33 cm

black holes and worm holes are violently created and annihilated

at scales ~ 10-33 cm (Planck scale)

Existence of the Universe is probabilistic

宇宙の存在自身が確率的

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Summary: from “nothing” to “something”

• Universe might have been born out of “nothing”.

• The baby Universe was perhaps of Planck size (10-33 cm).

• nucleosynthesis, photon decoupling, star/galaxy formation,

solar system, birth of life, ....

• inflation by vacuum energy to gigantic size. Then the

vacuum energy was converted to matter and radiation.

“無”から“有”へ

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Message of this lecture

• Big Bang Universe ・・・ confirmed

・・・ probably correct

・・・ in progress

• Inflationary Universe

• Quantum Gravity/Cosmology