1. 1 Misao Sasaki

2. 2 Message of this lecture Bing Bang Universe Bing Bang Universe ・・・ confirmed ・・・ probably correct ・・・ in progress Inflationary Universe Quantum Gravity/Cosmology Quantum Gravity/Cosmology

3. 3 Two major theories in modern physics General Relativity General Relativity gravity = space-time geometry gravity = space-time geometry Quantum Mechanics Quantum Mechanics Unification of the two theories = most challenging problem in modern physics most challenging problem in modern physics key to origin of the Universe black hole expanding universe “vacuum” fluctuations quantum tunneling matter = particle-wave complementarity complementarity

4. 4 Gravitation = Geometry of space-time spacetimecurvature energy-momentum density of matter Einstein’s General Relativity Albert Einstein (1915) G = 6.7×10 -11 N m 2 /kg 2 (gravitational constant) c = 3×10 8 m/sec (velocity of light)

5. 5 Cosmological principle (Copernican principle) Universe looks the same everywhere in every direction isotropy homogeneity open flatclosed angle < 180 o angle = 180 o angle > 180 o homogeneous & isotropic space

6. 6 Friedmann equation Friedmann (1922) Expansion rate of the Universe a Space expands!

7. 7 2 Mpc Discovery of “Hubble’s Law” 2 Mpc 70 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: H 0 = 70 km/s/Mpc

8. 8 30,000 ｋｍ /s size of observable universe: 10Gly (light velocity ＝ 300,000 km/sec) Large scale structure of the Universe seeing far ＝ seeing past 1Gly(300Mpc) Hubble’s observation

9. 9 Universe was small in the past. No galaxies, no stars １ 4 Gyrs ago Matter distributed uniformly in space extremely high temperature, high density Big Bang ! Gamov’s fire ball cosmology (1940’s) Birth of the Universe George Gamow

10. 10 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 !

11. 11 Hot soup of photons and Hot soup of photons and elementary particles elementary particles Nucleosynthesis in the first Nucleosynthesis in the first 3 minutes: 4 He, D, 7 Li,... 3 minutes: 4 He, D, 7 Li,... Clear-up (neutralization) Clear-up (neutralization) at 380,000 yrs after birth at 380,000 yrs after birth Formation of stars & Formation of stars & galaxies > 1 Gyr after birth galaxies > 1 Gyr after birth Extremely Brief History of the Universe bigbang

12. 12Proton Electron Clear-up of the Universe time 14 Gyr QSOs galaxy clear-up Big Bang 1 Gyr 10 Gyr Ionized Plasma ⇒ photons are not scattered any more neutralization of Proton (+) & Electron ( - ) C M B 380,000 yrs after big bang

13. 13 we see surface of clouds (Last Scattering Surface (Last Scattering Surface) If we observe sky at visible frequency band, we see surface of cosmic clear-up ＝ LSS of CMB (380,000 yrs old Universe) at radio frequency (~100 GHz) (~500,000 GHz)

14. 14 Cosmological Redshift CosmicExpansion Light once very blue became redder and redder, even redder than Infra Red, and became micro (Radio) waves today ∝ size of the Universe ∝ size of the Universe

15. 15Purest Planck distribution in nature “thermal spectrum” CMB Planck distribution CMB Planck distribution

16. 16 accelerated expansion due to vacuum energy Theory of Inflationary Universe (1980~) Before Big Bang ? Katsuhiko Sato Alan Guth Andrei Linde

17. 17 What is “ vacuum ” energy? false vacuum false vacuum huge energy is produced by expansion total energy = (energy density) x (volume) energy density remains the same even if space expands absence of any matter, but ‘space’ itself contains potential energy (vacuum energy)

18. 18 observable size of the Universe baby universe x 10 30 or more birth of mega-size universe Cosmic Inflation looks perfectly smooth & flat explains “homogeneity” & “flatness” quantum vacuum fluctuations are also stretched to mega scales and they become seeds for formation of stars and galaxies

19. 19 Birth of Big Bang Universe Whole vacuum energy is converted to heat birth of matter (quarks, electrons, neutrinos,...) & radiation (photons) cold universe hot universe ~ 10 -34 sec old universe ~ 10 28 K proton = 3 quarks = 3 quarks

20. 20 Evidence for Inflation Universe after inflation is extremely flat. Universe after inflation is extremely flat. Microscopic quantum vacuum fluctuations grow to Microscopic quantum vacuum fluctuations grow to macroscopic density fluctuations to form galaxies. macroscopic density fluctuations to form galaxies. predictions Predictions agree perfectly with observation These fluctuations leave distinguishable imprints on CMB temperature fluctuations

21. 21 Map of 380,000 yrs old Universe (Last Scattering Surface) by WMAP satellite this If the Universe were100 yrs old, this was 1 day old Universe Temperature is highly uniform Temperature T is slightly higher in Red regions, while it is slightly lower in Blue regions If we magnify fluctuations by 100,000 times

22. 22 CMB anisotropy power spectrum This tells us a lot about the past and present of the Universe theory WMAP data

23. 23 Expansion of the Universe Friedmann eqn ··· Friedmann eqn. best-fit model (flat: K=0) no dark energy model (flat: K=0) no dark energy model (closed: K>0) “dark” energy accelerated expansion

24. 24 Content of the Universe today Dark Energy ~ “vacuum” energy ~ “vacuum” energy accelerated expansion of the Universe Dark Matter large scale structure of the Universe Atoms stars, visible objects 96% of the Universe is unknown!

25. 25 future of ＣＭＢ observation WMAP PLANCK (simulation) much finer CMB map much better understanding of the Universe but these are indirect evidence of inflation

26. 26 GWs End of Inflation (10 -34 sec old) clear-up of Universe (350,000 yrs old) EM waves Proof of Quantum Gravity ! Direct evidence? vacuum fluctuations of spacetime grow to macroscopic vacuum fluctuations of spacetime grow to macroscopic gravitational waves which propagate until today gravitational waves which propagate until today Gravitational Waves = “final” frontier of Astronomy

27. 27 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 past Universe before inflation? Penrose Hawking

28. 28 Quantum Cosmology Quantum gravity is still in its infancy Superstring theory, M-theory, loop quantum gravity,.... Quantum theory of Space-time Quantum Gravity Quantum mechanics of cosmic scale factor: a(t) quantum approach to the birth of the Universe quantum approach to the birth of the Universe first step toward full quantum gravity first step toward full quantum gravity

29. 29 particle cannot penetrate the barrier quantum theory “probability wave” of a particle probability wave permeates through the barrier classical theory Tunneling - characteristic of quantum theory -

30. 30 vacuum fluctuations vacuum is not a quiet empty space of nothing vacuum is not a quiet empty space of nothing elementary particles are randomly created and annihilated elementary particles are randomly created and annihilated at microscopic scales at microscopic scales Planck Constant L E smaller the size L, larger the energy E - characteristic of quantum field theory -

31. 31 At scale L ~ 10 -33 cm, energy fluctuations become so large that even spacetime geometry is no longer smooth at all. Planck Scale Planck length: Planck energy: (~ power consumed by a family / month)

32. 32 World of Quantum Gravity the whole Universe was in quantum state when its size was ~10 -33 cm 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) at scales ~ 10 -33 cm (Planck scale) Universe (=spacetime) itself is probabilistic J.A. Wheeler

33. 33 de Sitter spacetime solution of Einstein equation filled with vacuum energy (cosmological constant) t minimum radius of the Universe barrier in the motion of radius of the Universe R contraction expansion R min time R E E R can become smaller than R min in quantum theory

34. 34 Creation of the Universe from “nothing” born through quantum tunneling from R=0 （ nothing ） Vilenkin (1982), Hawking, Vilenkin (1982), Hawking, … barrier against “motion” of the Universe Vilenkin quantum tunneling Radius barrier height classical de Sitter solution quantum solution

35. 35 Summary: from “nothing” to “something” Universe might have been born out of “nothing”. Universe might have been born out of “nothing”. The baby Universe was perhaps of Planck size (10 -33 cm). The baby Universe was perhaps of Planck size (10 -33 cm). nucleosynthesis, photon decoupling, star/galaxy formation, nucleosynthesis, photon decoupling, star/galaxy formation, solar system, birth of life,.... inflation by vacuum energy to gigantic size. Then the inflation by vacuum energy to gigantic size. Then the vacuum energy was converted to matter and radiation. vacuum energy was converted to matter and radiation. (research still at primitive stage) (testing theory against observation)

36. 36 Future of the Universe? if expands forever if expands forever expansion rate decreases indefinitely expansion rate decreases indefinitely Thermal death (empty space with dead stars & galaxies) Thermal death (empty space with dead stars & galaxies) expansion rate increases indefinitely expansion rate increases indefinitely Big Rip (everything will be ripped apart) Big Rip (everything will be ripped apart) expands at a constant rate expands at a constant rate Steady state (realization of “inflationary universe”) Steady state (realization of “inflationary universe”) End of the Universe? Beginning of a new Universe? if expansion stops if expansion stops Universe eventually starts to contract Universe eventually starts to contract Big Crunch (everything will be crushed to a single point) Big Crunch (everything will be crushed to a single point)