1 misao sasaki. 2 message of this lecture bing bang universe bing bang universe ・・・ confirmed...
TRANSCRIPT
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
33
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)