2 2 G M 0 0-5 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)] 0.5 5 10 0 1 η / M G µν F µν(b) + 1 8 eϵµνρσ f I (ab) F (a) µν F ρσ (b)
1. 2. 3. 2
1. (1960 3K 3
( 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
( Hubble ) (1929) 1000 1929 年 観測 2001 速度 (km/s) 500 0 0 1 2 距離 (Mpc) Mpc = 326 万光年 5
( Lemaître ) (1927) ( Hoyle ) ( Gamov ) ( 1946 ) 6
1 He4 ( He3 D Li7 ) 2p +2n 4 He He4 Y= He3 D Li7 ( Li7 ) ( / ) X 10 10 7
( Penzias) ( Wilson ) (1965) [ 1978 ] COBE ( 1993 ) T=2.73K (mm) (MJy/sr) error bars are multiplied by 400 400 8
38 ( ) COBE [ 2006 ] WMAP ( 2003~) Planck ( 2013~) http://www.esa.int http://map.gsfc.nasa.gov 9
1 137 10
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
2. = ρv da dt = 8 G V 3 a a exp(h inf t) H inf = 8 G V /3: inflation ( ) 10-36 10 26 V = 12 φ
... the vacuum stays at the metastable state for a long time, the Universe begins to expand exponentially... (A. Guth) 13
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
Guth-Sato (old inflation) potential = (Slow-Roll inflation) (New inflation) (chaotic inflation) scalar field 15
(Linde Albrecht-Steinhardt 1982) potential scalar field (Linde 1983) potential V = 1 2 m2 2 Mp scalar field V = 1 4 4 16
(t, x) = (t) + (t, x) H inf 2 17
(graviton) ( ) h ij (t, z) = h + h 0 h h + 0 0 0 0 i (t z) e h +, GH inf 2 ( X ) 18
+ ( ) a ψ ( ) δρ ( = a a = 1 a da dt dt d = H inf =(4or 3) a a 19
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
( 38 ) ( + ) T(n )=,m a m Y m (n ) a m a m = mm C 21
http://www.esa.int WMAP Planck n s =0.96 ± 0.01 4 Inflation inflation 2 4/3 2/3 n s 22
( ) ( ) 4 23
E E ( + mode x mode ) B E B 24
BB jack χ PTE = 0.99 0 50 100 150 200 0 50 200 100 250 150 300 200 100 150 PTE = 0.99 100 0.1 3. BICEP2実験 150 200 250 300 0 50 250 300 0.01 250 300 0 50 0.1 50 100 150 200 0.1 0 100 250150 300200 1000 15050 200 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 50 50 Eモード 1.8 55 55 0 60 60 65 65 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 50 50 0.3 55 55 0 µk BICEP2: B signal 0 Right ascension [deg.] µk BICEP2: E signal Declination [deg.] Declination [deg.] BICEP2実験 60 60 65 65 50 50 50 50 0.3 0 0 0 Right ascension [deg.] Right ascension [deg.] 50 50 50 BICEP2 (2014) 50 50 25
BICEP2 (2014) BICEP2 10 2 BICEP2 BICEP1 10 1 QUAD QUIET Q QUIET W CBI Boomerang DASI WMAP CAPMAP Inflation 1 Planck l(l+1)c l BB /2π [µk 2 ] 10 0 10 1 10 2 10 3 r=0.2 lensing 10 1 10 2 10 3 Multipole Planck (2014) 26
Strarobinsky 35..... in a maximum symmetrical quantum state before the beginning of the classical Friedman expansion..... the spectrum of long-wave, background gravitational radiation is calculated..... 27
BICEP2 h ρinf h GH inf G 1/2 inf H inf : inflation G : BICEP2 1/4 inf 10 16 GeV High-scale Lyth H inḟ Hinf & M p 28 H 2 inf
Chaotic inflation V ( V~m2 φ 2 ) m ( M p ) φ Mp V = f( + ) +ic (C : ) m =0 m =0 29
Chaotic Inflation chaotic inflation : V/m 2 M 2 100 1 0-10 -5 0 / M p 5 10 0 0.5 / 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
1 ( 10-36 ) 31
Backup 32