11

Misao Sasaki

Y TPY UK AW A INS T IT UT E FOR

T HEORET IC AL P HYSICS

22

Message of this lectureMessage of this lecture

• Bing Bang UniverseBing Bang Universe ・・・ ・・・ confirmedconfirmed

・・・ ・・・ probably correctprobably correct

・・・ ・・・ in progressin progress

• Inflationary UniverseInflationary Universe

• Quantum Gravity/CosmologyQuantum Gravity/Cosmology

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Two major theories in modern physicsTwo major theories in modern physics

General RelativityGeneral Relativity

gravity = space-time geometrygravity = space-time geometry

Quantum MechanicsQuantum Mechanics

Unification of the two theories =Unification of the two theories =

most challenging problem in modern physicsmost challenging problem in modern physics

key to origin of the Universekey to origin of the Universe

black holeblack holeexpanding universeexpanding universe

　““vacuum” fluctuationsvacuum” fluctuationsquantum tunnelingquantum tunneling

matter = particle-wave matter = particle-wave complementaritycomplementarity

44

4

8 GG T

c

Gravitation =Gravitation =Geometry of space-timeGeometry of space-time

spacetimespacetimecurvaturecurvature

energy-momentumenergy-momentumdensity of matterdensity of matter

Einstein’s General RelativityEinstein’s General RelativityAlbert Einstein (1915)

G = 6.7×10-11 N m2 /kg2 (gravitational constant)c = 3×108 m/sec (velocity of light)

55Cosmological principleCosmological principle(Copernican principle)(Copernican principle)

Universe looks the same Universe looks the same everywhereeverywhere in in every directionevery direction isotropyisotropyhomogeneityhomogeneity

openopen flatflat closedclosedangle < 180o angle = 180o angle > 180o

homogeneous & isotropic spacehomogeneous & isotropic space

66

Friedmann equationFriedmann equation Friedmann (1922)Friedmann (1922)

Expansion Expansion rate of the rate of the UniverseUniverse

22

8

3

G KH

a

1 0 1

gravitational constant

density

cosmic scale factor

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

G

a

K

daHa

dt

aa

Space expands!Space expands!

77

2 Mpc 2 Mpc

Discovery of “Hubble’s Law”Discovery of “Hubble’s Law”

2 Mpc2 Mpc

70 km/s70 km/s

140 km/s140 km/s

140 km/s140 km/s

1 Mpc = 3 Million light years (Mly)

our our galaxygalaxy

Edwin Hubble (1929)Edwin Hubble (1929)

1 Mpc1 Mpc

galaxies more distant recede fastergalaxies more distant recede faster

expansion rate today:expansion rate today: HH00 = 70 km/s/Mpc = 70 km/s/Mpc

88

30,000 ｋｍ /s

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

Large scale structure of the UniverseLarge scale structure of the Universe

seeing far ＝ seeing past

1Gly1Gly(300Mpc(300Mpc

))

Hubble’s observationHubble’s observation

99

Universe was small in the past.Universe was small in the past.No galaxies, no stars No galaxies, no stars １１ 4 Gyrs4 Gyrs ago agoMatter distributed uniformly in spaceMatter distributed uniformly in space

extremely high temperature, high densityextremely high temperature, high density

Big Bang !Big Bang !Gamov’s fire ball cosmology (1940’s)Gamov’s fire ball cosmology (1940’s)

Birth of the UniverseBirth of the Universe

George GamowGeorge Gamow

1010

Radiation from deep space;Radiation from deep space;from high temperature erafrom high temperature era

of the Universeof the Universe

Discovery of Discovery of CCosmicosmic M MicrowaveicrowaveBBackground ackground (CMB)(CMB)

Wilson and PenziasWilson and Penzias

noise in radio wave fromnoise in radio wave fromall directionsall directions of sky of sky

Penzias & Wilson (1965)Penzias & Wilson (1965)

seeing far = seeing past !seeing far = seeing past !

1111

Hot soup of photons and Hot soup of photons and elementary particles elementary particles

Nucleosynthesis in the firstNucleosynthesis in the first 3 minutes: 3 minutes: 44He, D, He, D, 77Li,...Li,...

Clear-up (neutralization)Clear-up (neutralization) at 380,000 yrs after birthat 380,000 yrs after birth

Formation of stars &Formation of stars & galaxies > 1 Gyr after birthgalaxies > 1 Gyr after birth

Extremely Brief History of the Extremely Brief History of the UniverseUniverse

bigbigbangbang

1212

ProtonProton

Electron

Clear-up of the UniverseClear-up of the Universe

time 14 Gyr14 Gyr

QSOs galaxy

clear-up

Big BangBig Bang 1 Gyr1 Gyr 10 Gyr10 Gyr

Ionized PlasmaIonized Plasma

⇒ photons are not scattered any more

neutralization of Proton (+) & Electron ( - )

C

M

B

380,000 yrs after big bang380,000 yrs after big bang

1313

we seewe seesurface of cloudssurface of clouds

((LLast ast SScattering cattering SSurfaceurface)

If we observe sky at visible frequency band,If we observe sky at visible frequency band,

we seewe seesurface of surface of cosmic clear-upcosmic clear-up

＝＝ LSSLSS of of CMBCMB(380,000 yrs old Universe)(380,000 yrs old Universe)

at radio frequency at radio frequency (~100 GHz)(~100 GHz)

(~500,000 GHz)(~500,000 GHz)

1414Cosmological Cosmological RedshiftRedshift

CosmicCosmic

ExpansionExpansion

Light once very blue becameLight once very blue became

redder and redder, even redder than Infra Red,redder and redder, even redder than Infra Red,

and became micro (Radio) waves todayand became micro (Radio) waves today

∝ ∝ size of the Universesize of the Universe

1515

PurestPurestPlanck distributionPlanck distribution

in naturein nature

“thermal spectrum”

CMB Planck distributionCMB Planck distribution

1616

accelerated expansion due toaccelerated expansion due to vacuum energyvacuum energy

Theory of Inflationary Universe Theory of Inflationary Universe (1980~) (1980~)

Before Big Bang ?Before Big Bang ?

Katsuhiko Sato Alan Guth Andrei Linde

1717What is What is ““vacuumvacuum”” energy?energy?• false vacuumfalse vacuum

huge energy is produced by expansionhuge energy is produced by expansion

total energy = (energy density) x (volume)total energy = (energy density) x (volume)

energy density remains the same even if energy density remains the same even if space expandsspace expands

absence of any matter, but ‘space’ itself absence of any matter, but ‘space’ itself contains potential energy (vacuum energy)contains potential energy (vacuum energy)

1818

observable size of the Universeobservable size of the Universebaby universebaby universe

xx 10 1030 30 or moreor more

birth of mega-size birth of mega-size universeuniverse

Cosmic InflationCosmic Inflation

looks perfectly looks perfectly

smooth & flatsmooth & flat

explains“homogeneity” & “flatness”

quantum vacuum fluctuations are also stretched to mega scales

and they become seeds for formation of stars and galaxies

1919

Birth of Big Bang UniverseBirth of Big Bang Universe

Whole vacuum energy is converted to heatWhole vacuum energy is converted to heat

birth of matter (quarks, electrons, neutrinos, ...) birth of matter (quarks, electrons, neutrinos, ...) & radiation (photons)& radiation (photons)

cold universecold universe hot universe hot universe

~ 10-34 sec old universe

~ 1028 Kprotonproton = 3 quarks= 3 quarks

2020

Evidence for InflationEvidence for Inflation

• Universe after inflation is extremely Universe after inflation is extremely flat.flat.

• Microscopic Microscopic quantum vacuum fluctuationsquantum vacuum fluctuations grow to grow to macroscopic density fluctuations to form macroscopic density fluctuations to form galaxies.galaxies.

predictionspredictions

Predictions agree perfectly with observationPredictions agree perfectly with observation

These fluctuations leaveThese fluctuations leave distinguishable distinguishable imprints on CMB temperature fluctuations imprints on CMB temperature fluctuations

2121Map of 380,000 yrs old UniverseMap of 380,000 yrs old Universe(Last Scattering Surface) by WMAP satellite(Last Scattering Surface) by WMAP satellite

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

Temperature is highly uniformTemperature is highly uniform

510TT

TempTemperature erature TT is slightly is slightly higher inhigher in Red regions,Red regions,

while it is slightlywhile it is slightly lower in Blue regionslower in Blue regions

If we magnify fluctuations by If we magnify fluctuations by 100,000100,000 times times

2222CMB anisotropy power CMB anisotropy power spectrumspectrum

This tells us a lot about the past and present of the UniverseThis tells us a lot about the past and present of the Universe

theorytheory

WMAP dataWMAP data

2323

Expansion of the UniverseExpansion of the Universe

22

8

3

G KH

a Matter DE ··· Friedmann eqnFriedmann eqn.

best-fit modelbest-fit model(flat: K=0)(flat: K=0)

no dark energyno dark energymodelmodel

(flat: K=0)(flat: K=0)

no dark energyno dark energymodelmodel

(closed: K>0)(closed: K>0)

““dark” energydark” energy

accelerated accelerated expansionexpansion

2424Content of the Universe Content of the Universe todaytoday

Dark EnergyDark Energy ~ “vacuum” energy~ “vacuum” energy

accelerated expansionaccelerated expansionof the Universeof the Universe

Dark MatterDark Matter

large scale structurelarge scale structureof the Universeof the Universe

AtomsAtoms

stars, visible objectsstars, visible objects

96% of the Universe is unknown!96% of the Universe is unknown!

2525

future of future of ＣＭＢ ＣＭＢ observationobservation

WMAPPLANCK (simulation)

much finer CMB map much finer CMB map

much better understanding much better understanding

of the Universe of the Universebut these are indirect evidence of inflationbut these are indirect evidence of inflation

2626

GWs

End of InflationEnd of Inflation(10(10-34-34 sec old) sec old)

clear-up of Universeclear-up of Universe(350,000 yrs old)(350,000 yrs old)

EM wavesEM waves

Proof of Quantum Gravity !

Direct evidence?Direct evidence?• vacuum vacuum fluctuations of spacetimefluctuations of spacetime grow to macroscopic grow to macroscopic gravitational waves gravitational waves which propagate until todaywhich propagate until today

Gravitational Waves = “final” frontier of Astronomy

2727

Hawking-Penrose singularity theorem (1970)Hawking-Penrose singularity theorem (1970)

physical laws break down at singularity!

beginning of the Universe

= space-time singularity?

General Relativity is inapplicable

Universe has a finite pastUniverse has a finite past

Universe before inflation?Universe before inflation?

PenroseHawking

2828

Quantum Quantum CosmologyCosmology

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

Quantum theory of Space-timeQuantum theory of Space-time

Quantum GravityQuantum Gravity

Quantum mechanics of cosmic scale factor: a(t)Quantum mechanics of cosmic scale factor: a(t)

• quantum approach to the birth of the Universequantum approach to the birth of the Universe

• first step toward full quantum gravityfirst step toward full quantum gravity

2929

particle cannot particle cannot penetrate the barrierpenetrate the barrier

quantum theoryquantum theory

““probability wave” of a particleprobability wave” of a particle

probability wave probability wave permeates through permeates through

the barrier the barrier

classical theoryclassical theory

Tunneling Tunneling - characteristic of quantum theory -- characteristic of quantum theory -

3030

vacuum fluctuationsvacuum fluctuations• vacuum is vacuum is not a quiet empty spacenot a quiet empty space of nothing of nothing• elementary particles are elementary particles are randomly created and annihilatedrandomly created and annihilated at microscopic scalesat microscopic scales

263 10 J m c

cE

L

Planck Planck

ConstantConstant

smaller the size L L , larger the energy EE

- characteristic of quantum field theory -

3131

At scale L ~ 10At scale L ~ 10-33-33cm, energy fluctuations become so large cm, energy fluctuations become so large that even spacetime geometry is no longer smooth at all.that even spacetime geometry is no longer smooth at all.

Planck ScalePlanck Scale

Planck length: Planck length: PlanckL = -3310 cm

Planck energy: Planck energy: Planck2E = /c-510 g

PlanckE 810 kcal or 500 kw hour

(~ power consumed by a family / month)(~ power consumed by a family / month)

3232World of Quantum World of Quantum GravityGravity

• the whole Universe was in quantum state the whole Universe was in quantum state when its size was ~10when its size was ~10-33 -33 cmcm

black holes and worm holes are violently created and annihilatedblack holes and worm holes are violently created and annihilated

at scales ~ 10at scales ~ 10-33 -33 cm (Planck scale)cm (Planck scale)

Universe (=spacetime) itself is probabilistic

J.A. Wheeler

3333de Sitter spacetimede Sitter spacetimesolution of Einstein equation filled with solution of Einstein equation filled with

vacuum energy (cosmological constant) vacuum energy (cosmological constant)

t

minimum radiusminimum radius of the Universeof the Universe

barrier barrier in the motion ofin the motion of radius of the Universeradius of the Universe

R contractioncontraction expansionexpansion

Rmintimetime

RREE

EE

RR can become smaller than can become smaller than RRminmin in quantum theory in quantum theory

3434Creation of the Universe from Creation of the Universe from “nothing”“nothing”

born throughborn through quantum tunneling from R=0 quantum tunneling from R=0 （（ nothingnothing ））Vilenkin (1982), Hawking,Vilenkin (1982), Hawking, …

barrier against “motion” of the Universebarrier against “motion” of the Universe

Vilenkin

quantum quantum tunnelingtunneling

RadiusRadius

barrier heightbarrier height

classical de Sitter classical de Sitter solutionsolutionquantum solutionquantum solution

3535Summary: Summary: from “nothing” to from “nothing” to “something”“something”• Universe might have been born out of Universe might have been born out of “nothing”.“nothing”.

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

• nucleosynthesis, photon decoupling, star/galaxy formation,nucleosynthesis, photon decoupling, star/galaxy formation,solar system, birth of life, ....solar system, birth of life, ....

• inflationinflation by by vacuum energyvacuum energy to gigantic size. Then the to gigantic size. Then the vacuum energy was vacuum energy was converted to matter and radiationconverted to matter and radiation..

(research still at primitive stage)(research still at primitive stage)

(testing theory against observation)(testing theory against observation)

3636Future of the Future of the Universe?Universe?• if expands foreverif expands forever

expansion rate decreases indefinitely expansion rate decreases indefinitely

Thermal death Thermal death (empty space with dead stars & galaxies)(empty space with dead stars & galaxies)

　　　　 expansion rate increases indefinitelyexpansion rate increases indefinitely

　　　 　　　 Big Rip Big Rip (everything will be ripped apart)(everything will be ripped apart)

　 　 expands at a constant rateexpands at a constant rate

　　　　　　　　 Steady state Steady state (realization of “inflationary universe”)(realization of “inflationary universe”)

End of the Universe? Beginning of a new Universe?End of the Universe? Beginning of a new Universe?

• if expansion stopsif expansion stops

Universe eventually starts to contractUniverse eventually starts to contract

Big Crunch Big Crunch (everything will be crushed to a single (everything will be crushed to a single point)point)