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1 2 2 G M ϕ / M G 0 L SUGRA = 1 2 er + eg ij Dµ φ i Dµ φ j 1 2 eg2 D (a) D +ieg ij χ j σ µ Dµ χ i + eϵ µνρσ ψ µ σ ν Dρ ψ σ 1 4 ef (ab) R F (a) [ ] + i 2 e λ (a) σ µ Dµ λ (a) + λ (a) σ µ Dµ λ (a) 1 2 f (ab) I D [ µ eλ (a) σ µ λ (b)] η / M G µν F µν(b) eϵµνρσ f I (ab) F (a) µν F ρσ (b)
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3 1. (1960 3K 3
4 ( Friedmann ) (1922) a(t) da dt 2 + K = 8 G 3 K < 0 a 2 a : : K : G : K > 0 K = 0 K=0 : K=1 : K=-1 : t 4
5 ( Hubble ) (1929) 年 観測 2001 速度 (km/s) 距離 (Mpc) Mpc = 326 万光年 5
6 ( Lemaître ) (1927) ( Hoyle ) ( Gamov ) ( 1946 ) 6
7 1 He4 ( He3 D Li7 ) 2p +2n 4 He He4 Y= He3 D Li7 ( Li7 ) ( / ) X
8 ( Penzias) ( Wilson ) (1965) [ 1978 ] COBE ( 1993 ) T=2.73K (mm) (MJy/sr) error bars are multiplied by
9 38 ( ) COBE [ 2006 ] WMAP ( 2003~) Planck ( 2013~) 9
10
11 38 A B T 10 5 T 現在の地平線 宇宙の 2 点 A B は過去において因果関係がない A B 2 11
12 2. = ρv da dt = 8 G V 3 a a exp(h inf t) H inf = 8 G V /3: inflation ( ) V = 12 φ
13 ... the vacuum stays at the metastable state for a long time, the Universe begins to expand exponentially... (A. Guth) 13
14 A B 2 インフレーション前 再結合時 現在 A A 宇宙背景輻射 地平線の大きさ B 観測者 インフレーションによる膨張 B w inflation) AB (w/o inflation) inflation 14
15 Guth-Sato (old inflation) potential = (Slow-Roll inflation) (New inflation) (chaotic inflation) scalar field 15
16 (Linde Albrecht-Steinhardt 1982) potential scalar field (Linde 1983) potential V = 1 2 m2 2 Mp scalar field V =
17 (t, x) = (t) + (t, x) H inf 2 17
18 (graviton) ( ) h ij (t, z) = h + h 0 h h i (t z) e h +, GH inf 2 ( X ) 18
19 + ( ) a ψ ( ) δρ ( = a a = 1 a da dt dt d = H inf =(4or 3) a a 19
20 1 m : 4 = 1 3 m m : k = d3 xe ik x (x ) x k k =(2 ) 3 3 (k k ) P (k) P (k) k n s n s 1 ns : 20
21 ( 38 ) ( + ) T(n )=,m a m Y m (n ) a m a m = mm C 21
22 WMAP Planck n s =0.96 ± Inflation inflation 2 4/3 2/3 n s 22
23 ( ) ( ) 4 23
24 E E ( + mode x mode ) B E B 24
25 BB jack χ PTE = PTE = BICEP2実験 Multipole F IG. 2. B ICEP 2 power spectrum results for signal (black points) and temporal-split jack F IG. 2. B ICEP power results signal (black points) power spectrum results for signal (black points) and temporal-split jackknife (blue The red curves show the and lensed- CDM expectations in 2the case spectrum of BB anpoints). r = 0.2for spectrum is also shown. Thetemporal-split error barstheory arejack th e case of BB an r = 0.2 spectrum is also shown. The error bars are(pte) the standard ofofthe lensed- CDM+noise simulations. Thethe expectations in the case of andeviations r = value 0.2 spectrum is also2 statistic shown. is The error are given (asbars evaluated probability to exceed thebb observed a simple 2 statistic is given evaluated against the simulations). the very differentisof y-axis scales for the (PTE) the observed value of a simple 2 statistic given (as spectrum. evaluated probability to(asexceed (PTE) the observed of Note aadditional simple jackknife spectra (other than BB). See thevalue text for discussion the BB her than BB). See the text for additional discussion of the BB spectrum. jackknife spectra (other than BB). See the text for additional discussion of the BB spectrum. 南極でCMBの偏光を計る BICEP2: E signal 2014年3月にBモードを発見と報告BICEP2: E signal Simulation: E fromelensed ΛCDM+noise BICEP2: signal Inflation起源 1.7µK 1.7µK 1.7µK 1.7µK Eモード BICEP2: B signal 1.8 BICEP2: signal Simulation: B fromblensed ΛCDM+noise BICEP2: B signal 0.3µK Bモード 0.3µK 0.3µK 0.3µK 0.3µK µk BICEP2: B signal 0 Right ascension [deg.] µk BICEP2: E signal Declination [deg.] Declination [deg.] BICEP2実験 Right ascension [deg.] Right ascension [deg.] BICEP2 (2014)
26 BICEP2 (2014) BICEP BICEP2 BICEP QUAD QUIET Q QUIET W CBI Boomerang DASI WMAP CAPMAP Inflation 1 Planck l(l+1)c l BB /2π [µk 2 ] r=0.2 lensing Multipole Planck (2014) 26
27 Strarobinsky in a maximum symmetrical quantum state before the beginning of the classical Friedman expansion..... the spectrum of long-wave, background gravitational radiation is calculated
28 BICEP2 h ρinf h GH inf G 1/2 inf H inf : inflation G : BICEP2 1/4 inf GeV High-scale Lyth H inḟ Hinf & M p 28 H 2 inf
29 Chaotic inflation V ( V~m2 φ 2 ) m ( M p ) φ Mp V = f( + ) +ic (C : ) m =0 m =0 29
30 Chaotic Inflation chaotic inflation : V/m 2 M / M p / M p chaotic inflation = 1 2 Im Kawasaki, Yamaguchi, Yanagida (2000) V = 1 2 m2 2 V f>5m p Natural inflation V = 4 1 cos f f 30
31 1 ( ) 31
32 Backup 32
中央大学セミナー.ppt
String Gas Cosmology References Brandenberger & Vafa, Superstrings in the early universe, Nucl.Phys.B316(1988) 391. Tseytlin & Vafa, Elements of string cosmology, Nucl.Phys.B372 (1992) 443. Brandenberger,
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A 1. Boltzmann Planck u(ν, T )dν = 8πh ν 3 c 3 kt 1 dν h 6.63 10 34 J s Planck k 1.38 10 23 J K 1 Boltzmann u(ν, T ) T ν e hν c = 3 10 8 m s 1 2. Planck λ = c/ν Rayleigh-Jeans u(ν, T )dν = 8πν2 kt dν c
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1 6 6.1 (??) (P = ρ rad /3) ρ rad T 4 d(ρv ) + PdV = 0 (6.1) dρ rad ρ rad + 4 da a = 0 (6.2) dt T + da a = 0 T 1 a (6.3) ( ) n ρ m = n (m + 12 ) m v2 = n (m + 32 ) T, P = nt (6.4) (6.1) d [(nm + 32 ] )a
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