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1 BIG-BANG! STARS SUPERNOVAE? R-PROCESS COSMIC-RAYS R S N=50) R S N=82) R S N=126) ++ + Actinide AGB STARS S-PROCESS 232 Th (14.05Gy) P 238 U (4.47 Gy) SUPERNOVA-γ PROCESS? 1
2 INFLATION (Grav. Wave, yet to wait) Different Cosmological Models QCD phase transition -What is Ω CDM =? - Cosmological const. is too small and fine tuned! Ω Λ =? Observed Expansing Universe ν-dec, e + e - -annihilation Big-Bang Nucleosynthesis Golden Age of Cosmology Radiation-Dom. Era Observational Signatures at different cosmic epochs ]! Universe is flat & accelerating! Ω B + Ω CDM + Ω Λ = 1 CMB Anisotropies COBE (1992), WMAP (2003, 2006) Matter-Dom. Era Type Ia SNe, Matter Power sec 3 min 10 5 y 1-10 Gy 2
3 Similarity between the Quantum-World and the Universe Land Earth Stars & Galaxy Large Scale Structure Inside the Proton = Microscopic Quantum World City Energy density fluctuates in Quantum Mechanically. Human Energy density (Temperature) of the Universe fluctuates. Nail Horizon = Early Universe Elem. Particle (Quark) Nucleus (Element) Atom DNA Cell Baby Big-Bang Universe expanded, and quantum fluctuation grew! QGP current sea QGP E=mc 2 3
4 vs. SCIENTIFIC GOAL OF THIS LECTURE is to elucidate the tight coupling between the frontline of cosmology and nuclear astrophysics. Einstein Cosmology 1915 Big-Bang Nucleosynthesis 1948 Albert Einstein George Gamow 4
5 Ω Λ, Ω 5
6 Standard Big-Bang Cosmology The Universe is homogeneous and isotropic in a large enough scale. T = K δt < 18 µk 2dF Quasar (Matter) Distribution: Homogeneous Sky Maps of CMB; Isotropic Newtonian Equation Birkoff s Theorem: Gravity due to mass interior to an arbitrary sphere. r(t) M Homogeneous & Isotropic M = 4/3πρr 3 E = 1 2 m mv r Ý 2 GmM r m 1 2 m r Ý = Gm[(4 / 3)πρr 3 ] mv 2 + E r vr Ý r 2 x 1/2mr 2 = 8 3 πgρ + 2 E mr 2 6
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7 [ ] open critical closed 0 NOW t 0 = t U 7
8 General Relativity (1) Weak Gravity (should include Newtonian Gravity), (2) Covariance G µν = R µν 1 2 Rgµν = 8π GT µν +Λg µν R µν = R λ µλν = λ Γ λ λ µν ν Γ µλ + Γ ηλ λ Γ η µν Γ λ µν = 1 { 2 gλβ ν g βµ + µ g βν β g µν } Γ λ η ην Γ µλ 1 g µν = a 2 (t) 1 kr 2 a 2 (t)r 2 a 2 (t)r 2 sin 2 θ ρ T µ ν = p p p Einstein Equation Newtonian Equation G 00 = 8π GT 00 + Λg 00 Hubble parameter H = v/r k = E/m Friedmann Eq. H 2 = 8 3 πgρ + k + Λ a 2 3 Cosmological Constant vr Ý r 2 = 8 3 πgρ + E mr 2 H 2 2 = H Ω γ 0 a 4 + Ω M a 3 + Ω k a 2 +Ω Λ Ω α = ρ α /ρ C ρ C = 3H 02 /8πG a = r = scale factor Deceleration parameter Ω 1 at t = t 0, a 0 = 1 q 0 = (d 2 r/dt 2 )/rh 2 = [Ω CDM /2 Ω Λ ] Ω CDM /2 Ω Λ acceleration! 8
9 Newtonian Orbits: OPEN or CLOSED? Explorer - OPEN Ω < 1 E > 0 ( v > v esc ) Missile - CLOSED Ω > 1 E < 0 ( v < v esc ) k > 0 k < 0 Satellite -MARGINAL Ω = 1 E = 0 ( v = v esc ) k = 0 Escaping Velocity v esc = 11.2 km/s Cosmic Expansion Dark Matter + Dark Energy Affect the expansion of the Universe. Ω CDM Ω Λ accelerating OPEN Flat, but Expand faster! Observable Signature No. 1 History of Hot Big-Bang Expansion decelerating CLOSED CRITICAL Flat! NOW 9
10 Robertson-Walker metric 10
11 Space-space component G 00 = 8π GT 00 +Λg 00 H 2 = 8 3 πgρ + k a 2 + Λ 3 Friedmann Equation H 2 2 = H Ω γ 0 a 4 + Ω M a 3 + Ω k a 2 +Ω Λ Energy Density log ρ Cosmic Expansion History Ω α = ρ α /ρ C, ρ C = 3H 02 /8πG R(t) = a(t) : scale factor Radiation a -4 Λ Matter a -3 Photon Last Scattering Now Cosmic time t [2] Inflationary Scenario Hubble (Causal) Horizon 11
12 Physical Distance Comoving Coordinate Causal Horizon c = velocity of light is constant in any time t & any scale factor R(t). R(t) = SCALE FACTOR 12
13 Metric Expansion R(t) ~ exp(αt) (Inf.) ~ t 1/2 (RD) ~ t 2/3 (MD) Energy Density ρ(t) ~ const. (Inf.) ~ T 4 (RD) ~ T 3 (MD) 13
14 Good bye (Inflation) DIS-CONNEXTED Hello (RD/MD) - SCENARIO HORIZON-in Quantum Fluctuation Causally Connected HORIZON PROBLEM, SOLVED! Exponential Expansion of CURVED-SPACE FLATNESS PROBLEM, SOLVED! 1 = Ω M + Ω Λ 14
15 [3] COSMIC EXPANSION AGE : RED-SHIFT Z : MATTER DOMINATED EPOCH : 1 = Ω γ /a 4 + Ω /a 3 + Ω M /a + Ω Λ Ω /a 3 + Ω M /a + Ω Λ z Ω M Ω Λ The COSMIC (UNIVERSE) AGE could NOT be SHORTER than the GALACTIC AGE! 15
16 AGE of GLOBULAR CLUSTER 16
17 Galactic AGE > Globular Cluster AGE 17
18 Dark Energy (Cosmological const.) can make the COSMIC AGE LONGER! 13.7 Gyr (WMAP-CMB) 18
19 Ω Λ, Ω Ω Λ Ω 19
20 Today: Ω tot = At t = 1 sec: Ω tot (nucleosynthesis) = Type Ia Supernova Redshift-Magnitude Relation 20
21 Latest CMB Results Fluctuations of Cosmic Microwave Background Anisotropies Spergel et al. 2003, ApJS, 148, 175. WMAP determined all cosmological parameters? t 0 Model dependent! = /- 0.2 Gyr Only 4.4% baryons are known. What is Ω m or Ω Λ? A. Penzias & R. Wilson discovered CBR in J. Smoot & R. Mathar discovered CMB Anisotropies in R. Wilson A. Penzias CBR is a direct evidence of Hot Big-Bang! J. Smoot CMB Anisotropies opens a door for Physical Cosmology! Planck: T = 2.7 K T = K δt/t = of oder
22 Cosmic Microwave Background Anisotropies WMAP-3 Two-point (direction) Correlation Function: C = δt/t(n) δt/t(n+θ) Temperature Fluctuations, expanded in terms of spherical harmonics: δt T = l 2 C l a lm m a lm Y lm (θ,φ) l= 2 l= 4 Cosmological Parameter Dependence Angle (deg) smaller Larger Ω Λ Larger Ω CDM Larger Ω B CMB Anisotropies Multipole l Dark Matter potential Ω CDM Baryon Mass Ω B Tγ Photon Pressure 22
23 Sachs-Wolfe Effect & ν-free Ftreaming Effect Acoustic Oscillation Finite mass of neutrinos make the decay of curvature rapidly. Ψ - CDM Massive Dodelson et al.,1996, ApJ, 467, 10) 45 Larger Ω Λ Universal expansion becomes faster! Ω Λ = 0 Physical fluctuation lngth scale λ k -1 looks smaller in angular scale θ l -1 for observer! Ω Λ =
24 MASS of the GALAXY Galaxy = stars MACHO = massive astronomical Compact halo objects Almost ALL luminous stars MACHO MASS of the CLUSTER? CLUSTER = 10 ~ 1000 galaxies 24
25 Hot X-Ray Gas Asymptotic Value = Universal Gas Fraction f U = Ω b /Ω M h 50 3/2 Ω b h 1002 ~ 0.04 (WMAP) Ω M ~ 0.35 h 100-1/2 MASS of the Rich Clusters and Large Scale Structure Asymptotic Value represents Universal Mass Ω M ~
26 HOW MASSIVE IS THE UNIVERSE? 26
27 27
Big Bang Planck Big Bang 1 43 Planck Planck quantum gravity Planck Grand Unified Theories: GUTs X X W X 1 15 ev 197 Glashow Georgi 1 14 GeV 1 2
12 Big Bang 12.1 Big Bang Big Bang 12.1 1-5 1 32 K 1 19 GeV 1-4 time after the Big Bang [ s ] 1-3 1-2 1-1 1 1 1 1 2 inflationary epoch gravity strong electromagnetic weak 1 27 K 1 14 GeV 1 15 K 1 2 GeV
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20 11 1 KEK 2 (cosmological perturbation theory) CMB R. Durrer, The theory of CMB Anisotropies, astro-ph/0109522; A. Liddle and D. Lyth, Cosmological Inflation and Large-Scale Structure (Cambridge University
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1 ( ) Einstein, Robertson-Walker metric, R µν R 2 g µν + Λg µν = 8πG c 4 T µν, (1) ( ds 2 = c 2 dt 2 + a(t) 2 dr 2 ) + 1 Kr 2 r2 dω 2, (2) (ȧ ) 2 H 2
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Title ブラックホールと重力波天文学 Author(s) 長峯, 健太郎 Citation 高大連携物理教育セミナー報告書. 28 Issue Date Text Version publisher URL DO
Title ブラックホールと重力波天文学 Author(s) 長峯, 健太郎 Citation 高大連携物理教育セミナー報告書. 28 Issue Date 2017-03 Text Version publisher URL http://hdl.handle.net/11094/60516 DOI rights Osaka University Knowledge Archive : OUKA
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有限質量をもつ娘粒子へ崩壊する 暗黒物質モデルとその観測的制限 名古屋大学大学院理学研究科理論天体物理学研究室 (AT 研 ) 修士 2 年 青山尚平 共同研究者 : 市來淨與 新田大輔 杉山直 今回の発表結果は下記の研究成果に基づくものです S.A., K.Ichiki, D.Nitta and N.Sugiyama, ArXiv(2011) [1106.1984] 目次 1. Introduction
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