powerpoint プレゼンテーション · short calc. 𝜌𝐵∝ −4 𝜌 𝐵,0∼ 0...
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![Page 1: PowerPoint プレゼンテーション · Short Calc. 𝜌𝐵∝ −4 𝜌 𝐵,0∼ 0 2≳10−30G2 At the end of inflation Ω𝐵,𝑓≡ 𝜌B,𝑓 𝜌inf 0 2 𝑓 4𝜌 inf](https://reader033.vdocuments.mx/reader033/viewer/2022043022/5f3e6024685b655aef250a86/html5/thumbnails/1.jpg)
![Page 2: PowerPoint プレゼンテーション · Short Calc. 𝜌𝐵∝ −4 𝜌 𝐵,0∼ 0 2≳10−30G2 At the end of inflation Ω𝐵,𝑓≡ 𝜌B,𝑓 𝜌inf 0 2 𝑓 4𝜌 inf](https://reader033.vdocuments.mx/reader033/viewer/2022043022/5f3e6024685b655aef250a86/html5/thumbnails/2.jpg)
![Page 3: PowerPoint プレゼンテーション · Short Calc. 𝜌𝐵∝ −4 𝜌 𝐵,0∼ 0 2≳10−30G2 At the end of inflation Ω𝐵,𝑓≡ 𝜌B,𝑓 𝜌inf 0 2 𝑓 4𝜌 inf](https://reader033.vdocuments.mx/reader033/viewer/2022043022/5f3e6024685b655aef250a86/html5/thumbnails/3.jpg)
![Page 4: PowerPoint プレゼンテーション · Short Calc. 𝜌𝐵∝ −4 𝜌 𝐵,0∼ 0 2≳10−30G2 At the end of inflation Ω𝐵,𝑓≡ 𝜌B,𝑓 𝜌inf 0 2 𝑓 4𝜌 inf](https://reader033.vdocuments.mx/reader033/viewer/2022043022/5f3e6024685b655aef250a86/html5/thumbnails/4.jpg)
•
• 𝜌inf1/4
≲ 1TeV
• 𝑁𝐻 ≲ 30
![Page 5: PowerPoint プレゼンテーション · Short Calc. 𝜌𝐵∝ −4 𝜌 𝐵,0∼ 0 2≳10−30G2 At the end of inflation Ω𝐵,𝑓≡ 𝜌B,𝑓 𝜌inf 0 2 𝑓 4𝜌 inf](https://reader033.vdocuments.mx/reader033/viewer/2022043022/5f3e6024685b655aef250a86/html5/thumbnails/5.jpg)
![Page 6: PowerPoint プレゼンテーション · Short Calc. 𝜌𝐵∝ −4 𝜌 𝐵,0∼ 0 2≳10−30G2 At the end of inflation Ω𝐵,𝑓≡ 𝜌B,𝑓 𝜌inf 0 2 𝑓 4𝜌 inf](https://reader033.vdocuments.mx/reader033/viewer/2022043022/5f3e6024685b655aef250a86/html5/thumbnails/6.jpg)
1μG
1fG
1pG
![Page 7: PowerPoint プレゼンテーション · Short Calc. 𝜌𝐵∝ −4 𝜌 𝐵,0∼ 0 2≳10−30G2 At the end of inflation Ω𝐵,𝑓≡ 𝜌B,𝑓 𝜌inf 0 2 𝑓 4𝜌 inf](https://reader033.vdocuments.mx/reader033/viewer/2022043022/5f3e6024685b655aef250a86/html5/thumbnails/7.jpg)
1μG
1fG
1pG
![Page 8: PowerPoint プレゼンテーション · Short Calc. 𝜌𝐵∝ −4 𝜌 𝐵,0∼ 0 2≳10−30G2 At the end of inflation Ω𝐵,𝑓≡ 𝜌B,𝑓 𝜌inf 0 2 𝑓 4𝜌 inf](https://reader033.vdocuments.mx/reader033/viewer/2022043022/5f3e6024685b655aef250a86/html5/thumbnails/8.jpg)
1μG
1fG
1pG
![Page 9: PowerPoint プレゼンテーション · Short Calc. 𝜌𝐵∝ −4 𝜌 𝐵,0∼ 0 2≳10−30G2 At the end of inflation Ω𝐵,𝑓≡ 𝜌B,𝑓 𝜌inf 0 2 𝑓 4𝜌 inf](https://reader033.vdocuments.mx/reader033/viewer/2022043022/5f3e6024685b655aef250a86/html5/thumbnails/9.jpg)
1μG
1fG
1pG
![Page 10: PowerPoint プレゼンテーション · Short Calc. 𝜌𝐵∝ −4 𝜌 𝐵,0∼ 0 2≳10−30G2 At the end of inflation Ω𝐵,𝑓≡ 𝜌B,𝑓 𝜌inf 0 2 𝑓 4𝜌 inf](https://reader033.vdocuments.mx/reader033/viewer/2022043022/5f3e6024685b655aef250a86/html5/thumbnails/10.jpg)
• 𝐵0 ≳ 10−16G
• 𝐿𝑐 ≳ 1Mpc
• in Void region
![Page 11: PowerPoint プレゼンテーション · Short Calc. 𝜌𝐵∝ −4 𝜌 𝐵,0∼ 0 2≳10−30G2 At the end of inflation Ω𝐵,𝑓≡ 𝜌B,𝑓 𝜌inf 0 2 𝑓 4𝜌 inf](https://reader033.vdocuments.mx/reader033/viewer/2022043022/5f3e6024685b655aef250a86/html5/thumbnails/11.jpg)
![Page 12: PowerPoint プレゼンテーション · Short Calc. 𝜌𝐵∝ −4 𝜌 𝐵,0∼ 0 2≳10−30G2 At the end of inflation Ω𝐵,𝑓≡ 𝜌B,𝑓 𝜌inf 0 2 𝑓 4𝜌 inf](https://reader033.vdocuments.mx/reader033/viewer/2022043022/5f3e6024685b655aef250a86/html5/thumbnails/12.jpg)
![Page 13: PowerPoint プレゼンテーション · Short Calc. 𝜌𝐵∝ −4 𝜌 𝐵,0∼ 0 2≳10−30G2 At the end of inflation Ω𝐵,𝑓≡ 𝜌B,𝑓 𝜌inf 0 2 𝑓 4𝜌 inf](https://reader033.vdocuments.mx/reader033/viewer/2022043022/5f3e6024685b655aef250a86/html5/thumbnails/13.jpg)
I𝟐 𝑭𝝁𝝂𝑭𝝁𝝂(𝝓)
𝑭𝝁𝝂 𝑭𝝁𝝂
+ 𝝓
𝑴
Model examples
+𝜉𝑅𝐴𝜇𝐴𝜇
+𝑒2𝜙2𝐴𝜇𝐴𝜇
𝐴𝜇 ≃ 𝑍𝜇inf𝑠𝑖𝑛2𝜃𝑤
![Page 14: PowerPoint プレゼンテーション · Short Calc. 𝜌𝐵∝ −4 𝜌 𝐵,0∼ 0 2≳10−30G2 At the end of inflation Ω𝐵,𝑓≡ 𝜌B,𝑓 𝜌inf 0 2 𝑓 4𝜌 inf](https://reader033.vdocuments.mx/reader033/viewer/2022043022/5f3e6024685b655aef250a86/html5/thumbnails/14.jpg)
I𝟐 𝑭𝝁𝝂𝑭𝝁𝝂(𝝓)
𝑭𝝁𝝂 𝑭𝝁𝝂
+ 𝝓
𝑴
Model examples
+𝜉𝑅𝐴𝜇𝐴𝜇
+𝑒2𝜙2𝐴𝜇𝐴𝜇
𝐴𝜇 ≃ 𝑍𝜇inf𝑠𝑖𝑛2𝜃𝑤
![Page 15: PowerPoint プレゼンテーション · Short Calc. 𝜌𝐵∝ −4 𝜌 𝐵,0∼ 0 2≳10−30G2 At the end of inflation Ω𝐵,𝑓≡ 𝜌B,𝑓 𝜌inf 0 2 𝑓 4𝜌 inf](https://reader033.vdocuments.mx/reader033/viewer/2022043022/5f3e6024685b655aef250a86/html5/thumbnails/15.jpg)
(?)
• 𝟏𝟎−𝟏𝟓𝐆
•
![Page 16: PowerPoint プレゼンテーション · Short Calc. 𝜌𝐵∝ −4 𝜌 𝐵,0∼ 0 2≳10−30G2 At the end of inflation Ω𝐵,𝑓≡ 𝜌B,𝑓 𝜌inf 0 2 𝑓 4𝜌 inf](https://reader033.vdocuments.mx/reader033/viewer/2022043022/5f3e6024685b655aef250a86/html5/thumbnails/16.jpg)
![Page 17: PowerPoint プレゼンテーション · Short Calc. 𝜌𝐵∝ −4 𝜌 𝐵,0∼ 0 2≳10−30G2 At the end of inflation Ω𝐵,𝑓≡ 𝜌B,𝑓 𝜌inf 0 2 𝑓 4𝜌 inf](https://reader033.vdocuments.mx/reader033/viewer/2022043022/5f3e6024685b655aef250a86/html5/thumbnails/17.jpg)
Short Calc.
𝜌𝐵 ∝ 𝑎−4 𝜌𝐵,0 ∼ 𝐵02 ≳ 10−30G2
At the end of inflation
Ω𝐵,𝑓 ≡𝜌B,𝑓
𝜌inf≃
𝐵02
𝑎𝑓4𝜌inf
≈ 10−19
⇒ MF had tiny energy fraction
Instant Reheating
![Page 18: PowerPoint プレゼンテーション · Short Calc. 𝜌𝐵∝ −4 𝜌 𝐵,0∼ 0 2≳10−30G2 At the end of inflation Ω𝐵,𝑓≡ 𝜌B,𝑓 𝜌inf 0 2 𝑓 4𝜌 inf](https://reader033.vdocuments.mx/reader033/viewer/2022043022/5f3e6024685b655aef250a86/html5/thumbnails/18.jpg)
𝐸𝑘𝐵𝑘
=𝜕𝜂𝐴𝑘
𝑘𝐴𝑘∼
1
𝑘𝜂= 𝑒𝑁𝑘
Ratio between EF and MF
Ω𝐸,𝑓 ≈ 10−19𝑒2𝑁𝑘 ≫ 1
EF dominates during inflation.
Right before inflation end
![Page 19: PowerPoint プレゼンテーション · Short Calc. 𝜌𝐵∝ −4 𝜌 𝐵,0∼ 0 2≳10−30G2 At the end of inflation Ω𝐵,𝑓≡ 𝜌B,𝑓 𝜌inf 0 2 𝑓 4𝜌 inf](https://reader033.vdocuments.mx/reader033/viewer/2022043022/5f3e6024685b655aef250a86/html5/thumbnails/19.jpg)
𝑩𝟎 𝟏𝐌𝐩𝐜 ≲ 𝟏𝟎−𝟑𝟐𝐆
𝐼 𝜙 𝐹𝐹
𝜌inf1/4
= 1015GeV
![Page 20: PowerPoint プレゼンテーション · Short Calc. 𝜌𝐵∝ −4 𝜌 𝐵,0∼ 0 2≳10−30G2 At the end of inflation Ω𝐵,𝑓≡ 𝜌B,𝑓 𝜌inf 0 2 𝑓 4𝜌 inf](https://reader033.vdocuments.mx/reader033/viewer/2022043022/5f3e6024685b655aef250a86/html5/thumbnails/20.jpg)
![Page 21: PowerPoint プレゼンテーション · Short Calc. 𝜌𝐵∝ −4 𝜌 𝐵,0∼ 0 2≳10−30G2 At the end of inflation Ω𝐵,𝑓≡ 𝜌B,𝑓 𝜌inf 0 2 𝑓 4𝜌 inf](https://reader033.vdocuments.mx/reader033/viewer/2022043022/5f3e6024685b655aef250a86/html5/thumbnails/21.jpg)
𝜌inf1/4
< 6 × 1011GeVB0
10−15G
−2
![Page 22: PowerPoint プレゼンテーション · Short Calc. 𝜌𝐵∝ −4 𝜌 𝐵,0∼ 0 2≳10−30G2 At the end of inflation Ω𝐵,𝑓≡ 𝜌B,𝑓 𝜌inf 0 2 𝑓 4𝜌 inf](https://reader033.vdocuments.mx/reader033/viewer/2022043022/5f3e6024685b655aef250a86/html5/thumbnails/22.jpg)
Usually we assume,
Ω𝐸,𝑓 ≈ 10−19𝑒2𝑁𝑘
𝑁1Mpc ≈ 50 + ln𝜌inf1/4
1015GeV
Short Calc. 2
![Page 23: PowerPoint プレゼンテーション · Short Calc. 𝜌𝐵∝ −4 𝜌 𝐵,0∼ 0 2≳10−30G2 At the end of inflation Ω𝐵,𝑓≡ 𝜌B,𝑓 𝜌inf 0 2 𝑓 4𝜌 inf](https://reader033.vdocuments.mx/reader033/viewer/2022043022/5f3e6024685b655aef250a86/html5/thumbnails/23.jpg)
Ω𝐸,𝑓 ≈ 10−19𝑒2𝑁𝑘
In Low Energy,
𝑁1Mpc ≈ 23 + ln𝜌inf1/4
1TeV
Short Calc. 2
Ω𝐸,𝑓 < 1 𝜌inf1/4
≲ 1TeV
![Page 24: PowerPoint プレゼンテーション · Short Calc. 𝜌𝐵∝ −4 𝜌 𝐵,0∼ 0 2≳10−30G2 At the end of inflation Ω𝐵,𝑓≡ 𝜌B,𝑓 𝜌inf 0 2 𝑓 4𝜌 inf](https://reader033.vdocuments.mx/reader033/viewer/2022043022/5f3e6024685b655aef250a86/html5/thumbnails/24.jpg)
𝑁Mpc ,
𝟏𝟎−𝟏𝟒𝐆
![Page 25: PowerPoint プレゼンテーション · Short Calc. 𝜌𝐵∝ −4 𝜌 𝐵,0∼ 0 2≳10−30G2 At the end of inflation Ω𝐵,𝑓≡ 𝜌B,𝑓 𝜌inf 0 2 𝑓 4𝜌 inf](https://reader033.vdocuments.mx/reader033/viewer/2022043022/5f3e6024685b655aef250a86/html5/thumbnails/25.jpg)
𝑁Mpc ,
𝟏𝟎−𝟏𝟒𝐆
![Page 26: PowerPoint プレゼンテーション · Short Calc. 𝜌𝐵∝ −4 𝜌 𝐵,0∼ 0 2≳10−30G2 At the end of inflation Ω𝐵,𝑓≡ 𝜌B,𝑓 𝜌inf 0 2 𝑓 4𝜌 inf](https://reader033.vdocuments.mx/reader033/viewer/2022043022/5f3e6024685b655aef250a86/html5/thumbnails/26.jpg)
𝑁Mpc ,
I𝟐 𝑭𝝁𝝂𝑭𝝁𝝂 :(𝝓) 𝜙
𝜙 𝑁Mpc
![Page 27: PowerPoint プレゼンテーション · Short Calc. 𝜌𝐵∝ −4 𝜌 𝐵,0∼ 0 2≳10−30G2 At the end of inflation Ω𝐵,𝑓≡ 𝜌B,𝑓 𝜌inf 0 2 𝑓 4𝜌 inf](https://reader033.vdocuments.mx/reader033/viewer/2022043022/5f3e6024685b655aef250a86/html5/thumbnails/27.jpg)
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𝜁𝒌𝐸𝑀 ≃
𝑑𝑁
𝜖 𝜌inf𝜌𝒌𝐸𝑀
Isocurvature pert. ⇒ Adiabatic pert.
Non-gaussianity: 𝜌𝒌𝐸𝑀 ∼ 𝐴𝑘′𝐴𝑘−𝑘′
𝒫𝒌𝐸𝑀, 𝑓NL
EM, 𝜏𝑁𝐿𝐸𝑀 ≤ Planck result
![Page 30: PowerPoint プレゼンテーション · Short Calc. 𝜌𝐵∝ −4 𝜌 𝐵,0∼ 0 2≳10−30G2 At the end of inflation Ω𝐵,𝑓≡ 𝜌B,𝑓 𝜌inf 0 2 𝑓 4𝜌 inf](https://reader033.vdocuments.mx/reader033/viewer/2022043022/5f3e6024685b655aef250a86/html5/thumbnails/30.jpg)
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𝜁𝒌𝐸𝑀 ≃
𝑑𝑁
𝜖 𝜌inf𝜌𝒌𝐸𝑀 ∝
𝜌inf𝜖
Low energy ⇒ Small Curvature Pert.(?)
~𝐻4 ∝ 𝜌inf2
In single slow-roll case,
𝒫𝜁 =1
24𝜋2𝑀𝑃𝑙4
𝜌inf
𝜖≈ 10−9
![Page 33: PowerPoint プレゼンテーション · Short Calc. 𝜌𝐵∝ −4 𝜌 𝐵,0∼ 0 2≳10−30G2 At the end of inflation Ω𝐵,𝑓≡ 𝜌B,𝑓 𝜌inf 0 2 𝑓 4𝜌 inf](https://reader033.vdocuments.mx/reader033/viewer/2022043022/5f3e6024685b655aef250a86/html5/thumbnails/33.jpg)
•
•
• 𝝐
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