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Bモード偏光から探る 初期宇宙と素粒子理論
高橋 史宜 (東北大学)
2014年9月19日 日本物理学会@佐賀大学
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BICEP2 1403.3985
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BICEP2 1403.3985
Too good to be true? Maybe galactic foreground? (cf. Flauger et al 1405.7351)
In any case we will see in the near future.
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もしr = O(10-3‒10-1)だったら いったい何がわかるのか?
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Talk plan 1. CMB Bモードと計量揺らぎ 2. インフレーションとその示唆 3. インフレーション模型 1. RH sneutrino inflation 2. Axion landscape
4. まとめ
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1. CMB Bモードと計量揺らぎ
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Cosmic Microwave Background (宇宙背景輻射)
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CMB光子は
1. エネルギー (あるいは 温度) 2. 偏光
で特徴付けられる。CMB温度および偏光の到来方向異方性はすでに検出。
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CMB temperature sky map
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CMB anisotropy angular power spectrum
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CMB anisotropy angular power spectrum
Cosmological parameters
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CMB polarization
WMAP
CMB photons are polarized!!
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CMB polarization
WMAP
CMB photons are polarized!!
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(Taken from W. Hu’s webpage)
トムソン散乱によって直線偏光は 容易に作られるが、
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(Taken from W. Hu’s webpage)
トムソン散乱によって直線偏光は 容易に作られるが、
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(Taken from W. Hu’s webpage)
宇宙が等方だったら偏光は生じない。 双極子揺らぎでも互いにキャンセルしてダメ。
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(Taken from W. Hu’s webpage)
宇宙が等方だったら偏光は生じない。 双極子揺らぎでも互いにキャンセルしてダメ。
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(Taken from W. Hu’s webpage)
結局、四重極揺らぎによって偏光が生じる。 偏光ベクトルは冷たい方向を結ぶ。(下の例では上下方向)
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(Taken from W. Hu’s webpage)
結局、四重極揺らぎによって偏光が生じる。 偏光ベクトルは冷たい方向を結ぶ。(下の例では上下方向)
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(Taken from Samtleben et al, `07)
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EモードとBモードは偏光ベクトルを 45度回転すると互いに移り合う。
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計量揺らぎ平坦な一様等方宇宙
ds
2 = �dt
2 + a(t)2�ijdxidx
j
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計量揺らぎ平坦な一様等方宇宙
に小さな摂動を加える:
ds
2 = �dt
2 + a(t)2�ijdxidx
j
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計量揺らぎ平坦な一様等方宇宙
に小さな摂動を加える:
ds
2 = �dt
2 + a(t)2�ijdxidx
j
1. Scalar 2. Vector 3. Tensor
線形揺らぎの範囲では以下の3つに分解できる。
inflaton
graviton
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E-mode ONLY BOTH E-mode and B-mode
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E-mode ONLY BOTH E-mode and B-mode
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C
C
C
C
H
H
H H
E-mode ONLY BOTH E-mode and B-mode
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C
C
C
C
H
H
H H
E-mode ONLY BOTH E-mode and B-mode
Rotation by 45 deg.
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BICEP2 found B-mode
Taken from Chinone’s webpage
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2.インフレーションとその示唆
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宇宙初期における加速膨張
Inflation
V �⇥ = H2�
ゆっくり転がるスカラー場 によってインフレーション(Slow-roll inflation)を実現。終了後、軽い自由度に崩壊し、熱い宇宙をつくる(再加熱)。
Linde `82, Albrecht and Steinhardt `82
Guth `81, Sato `80, Starobinsky `80, Kazanas `80, Brout, Englert, Gunzig, `79
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Scalar mode
インフラトンの揺らぎが時間進化に揺らぎを与える。宇宙は膨張しているので、体積の揺らぎ。
Time
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Tensor mode
It is due to fluctuations of graviton itself.
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Observation vs TheoryScalar mode
Tensor mode
V : the inflaton potential
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It’s GUT-scale inflation!
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Large-field inflationThe inflaton excursion exceeds the Planck scale.
φ
During inflation
After inflation
& MP
Lyth bound:Lyth 1997
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GUT-scale, large-field inflation• Inflation model building in sugra/string
• Shift symmetry is likely.
• High reheating temperature: • Thermal leptogenesis is likely. • Baryogenesis, dark matter, unwanted relics. • Symmetry restoration is possible.
• The inflaton mass is about .
• Related to SUSY breaking scale or RH neutrino mass?
• Too large isocurvature perturbations.
• The QCD axion less likely? PQ symmetry restoration?
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3.インフレーション模型
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Various large-field inflation models
Quadratic chaotic inflationLinde `83
-4 -2 2 4
0.5
1.0
1.5
2.0
Natural inflation Freese et al, `90
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Planck, 1303.5802
Predicted values of (ns, r)
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Planck, 1303.5802
Predicted values of (ns, r)
Quadratic chaotic infl
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Planck, 1303.5802
Predicted values of (ns, r)
Quadratic chaotic infl
Natural infl
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Various large-field inflation modelsPolynomial chaotic inflation
(see also Kobayashi, Seto 1403.5055 Kallosh, Linde, Wesphal 1405.0270)
Multi-Natural inflation (MNI)Czerny, FT 1401.5212
Czerny, Higaki FT 1403.0410, 1403.5883
Sub-Planckian decay constants are allowed as hilltop inflation can be realized.
Nakayama, FT, Yanagida, 1303.7315
Destri, de Vega, Sanchez [astro-ph/0703417] Nakayama, FT, Yanagida 1303.7315
Czerny, FT, 1401.5212
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Various large-field inflation modelsPolynomial chaotic inflation
(see also Kobayashi, Seto 1403.5055 Kallosh, Linde, Wesphal 1405.0270)
Multi-Natural inflation (MNI)Czerny, FT 1401.5212
Czerny, Higaki FT 1403.0410, 1403.5883
Sub-Planckian decay constants are allowed as hilltop inflation can be realized.
Nakayama, FT, Yanagida, 1303.7315
Destri, de Vega, Sanchez [astro-ph/0703417] Nakayama, FT, Yanagida 1303.7315
Czerny, FT, 1401.5212
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Various large-field inflation modelsPolynomial chaotic inflation
(see also Kobayashi, Seto 1403.5055 Kallosh, Linde, Wesphal 1405.0270)
Multi-Natural inflation (MNI)Czerny, FT 1401.5212
Czerny, Higaki FT 1403.0410, 1403.5883
Sub-Planckian decay constants are allowed as hilltop inflation can be realized.
Nakayama, FT, Yanagida, 1303.7315
Destri, de Vega, Sanchez [astro-ph/0703417] Nakayama, FT, Yanagida 1303.7315
Czerny, FT, 1401.5212
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Chaotic inflation in SUGRA
To have a good control over the inflaton field values greater than the Planck scale, we impose a shift symmetry;
Kawasaki, Yamaguchi, Yanagida, hep-ph/0004243 ,hep-ph/0011104
which is explicitly broken by the superpotential.
even for
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Z2:•One can impose a Z2 symmetry on the inflaton and X.
Z2 or not Z2?
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Z2:•One can impose a Z2 symmetry on the inflaton and X.
Z2 or not Z2?
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Z2:•One can impose a Z2 symmetry on the inflaton and X.
The visible sector particles must be also charged under Z2 for successful reheating.
Z2 or not Z2?
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Z2:•One can impose a Z2 symmetry on the inflaton and X.
The visible sector particles must be also charged under Z2 for successful reheating.
The Z2 might be the matter parity!
Z2 or not Z2?
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The inflaton might be right-handed sneutrino.
(-)(-)Neutrino mass is a low-E consequence of the inflaton!
Murayama, Nakayama, FT, Yanagida,1404.3857
Z2:•One can impose a Z2 symmetry on the inflaton and X.
The visible sector particles must be also charged under Z2 for successful reheating.
The Z2 might be the matter parity!
Z2 or not Z2?
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Sneutrino Chaotic inflationMurayama, Nakayama, FT, Yanagida,1404.3857
We impose an approximate shift symmetry on one of Ni
K = |N1|2 + |N2|2 +1
2(N3 +N†
3 )2 + · · ·
W =1
2MijNiNj + hi↵NiL↵Hu
withMij =
0
@m 0 00 0 M0 M 0
1
A
' =p2ImN3The inflaton is
V =1
2M2'2
All the other directions can be stabilized during inflation.
'
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Natural and Multi-Natural Inflation-Natural inflation Freese, Frieman, Olinto `90
Only large-field inflation is possible, and f is bounded below:
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Aligned Natural Inflation
The effectively large decay constant can be realized by the alignment of two (or more) axion potentials.
• Two axions:
Kim, Nilles, Peloso, hep-ph/0409138Czerny, Higaki, FT 1403.5883, Harigaya and Ibe 1404.3511, Choi, Kim, Yun, 1404.6209, Higaki, FT, 1404.6923, Tye, Won, 1404.6988, Kappl, Krippendorf, Nilles, 1404.7127, Bachlechner et al, 1404.7496, Ben-Dayan, Pedro, Westphal,1404.7773 ,Long, McAllister, McGuirk 1404.7852
If n1/n2 = m1/m2, there is a flat direction; the corresponding decay constant would be infinite.
If n1/n2 ≈ m1/m2, there is a relatively light direction; the corresponding decay constant can be larger than f1 or f2.
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Aligned Natural Inflation
Taken from 1404.6209 by Choi, Kim, Yun
Kim, Nilles, Peloso, hep-ph/0409138
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For a moderately large N (> 5 or so), the effective decay constant can be enhanced w/o hierarchy among the anomaly coefficients.
Aligned Natural Inflation•Multiple axions:
Choi, Kim, Yun, 1404.6209
Prob. dist. was studied in detail for various cases incl. Higaki, FT, 1404.6923
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Higaki, FT 1404.6923
Axion Landscape!For , many axions may form a mini-landscape.
•Eternal inflation takes place in a local minimum.
•A flat direction arises by the alignment mechanism.
•Slow-roll inflation begins after the tunneling event.
•Negative curvature/suppression at large scales if the total e-folding is just 50-60. Linde `95, Freivogel et al `05,
Yamauchi et al `11, Bousso et al `13
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4. まとめ✓宇宙初期にインフレーション(加速膨張期)があり、CMB温度及び偏光揺らぎにその情報が残っている。
✓もし r=O(0.001-0.1)であれば10年(?)以内に分かる。 その場合、 ✓GUTスケールかつLarge-field (super-Planckian) inflation
✓原始重力波直接検出に期待。 ✓どうやってinflaton potentialを制御するのか? ✓インフラトンは何か?右巻きスニュートリノ?アクシオン?
✓一方、もしrが10-3より小さかったらsmall-field inflationである。非常に平らなポテンシャルの頂上近くから始まった。 ✓初期値問題? 対称性の破れと関連?(e.g. B-L Higgs etc.)
See talks by 横山さん、安東さん
See talks by 長谷川さん、松村さん