PowerPoint プレゼンテーション · Short Calc. 𝜌𝐵∝ −4 𝜌 𝐵,0∼ 0...
Transcript of PowerPoint プレゼンテーション · Short Calc. 𝜌𝐵∝ −4 𝜌 𝐵,0∼ 0...
•
• 𝜌inf1/4
≲ 1TeV
• 𝑁𝐻 ≲ 30
1μG
1fG
1pG
1μG
1fG
1pG
1μG
1fG
1pG
1μG
1fG
1pG
• 𝐵0 ≳ 10−16G
• 𝐿𝑐 ≳ 1Mpc
• in Void region
I𝟐 𝑭𝝁𝝂𝑭𝝁𝝂(𝝓)
𝑭𝝁𝝂 𝑭𝝁𝝂
+ 𝝓
𝑴
Model examples
+𝜉𝑅𝐴𝜇𝐴𝜇
+𝑒2𝜙2𝐴𝜇𝐴𝜇
𝐴𝜇 ≃ 𝑍𝜇inf𝑠𝑖𝑛2𝜃𝑤
I𝟐 𝑭𝝁𝝂𝑭𝝁𝝂(𝝓)
𝑭𝝁𝝂 𝑭𝝁𝝂
+ 𝝓
𝑴
Model examples
+𝜉𝑅𝐴𝜇𝐴𝜇
+𝑒2𝜙2𝐴𝜇𝐴𝜇
𝐴𝜇 ≃ 𝑍𝜇inf𝑠𝑖𝑛2𝜃𝑤
(?)
• 𝟏𝟎−𝟏𝟓𝐆
•
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
𝐸𝑘𝐵𝑘
=𝜕𝜂𝐴𝑘
𝑘𝐴𝑘∼
1
𝑘𝜂= 𝑒𝑁𝑘
Ratio between EF and MF
Ω𝐸,𝑓 ≈ 10−19𝑒2𝑁𝑘 ≫ 1
EF dominates during inflation.
Right before inflation end
𝑩𝟎 𝟏𝐌𝐩𝐜 ≲ 𝟏𝟎−𝟑𝟐𝐆
𝐼 𝜙 𝐹𝐹
𝜌inf1/4
= 1015GeV
𝜌inf1/4
< 6 × 1011GeVB0
10−15G
−2
Usually we assume,
Ω𝐸,𝑓 ≈ 10−19𝑒2𝑁𝑘
𝑁1Mpc ≈ 50 + ln𝜌inf1/4
1015GeV
Short Calc. 2
Ω𝐸,𝑓 ≈ 10−19𝑒2𝑁𝑘
In Low Energy,
𝑁1Mpc ≈ 23 + ln𝜌inf1/4
1TeV
Short Calc. 2
Ω𝐸,𝑓 < 1 𝜌inf1/4
≲ 1TeV
𝑁Mpc ,
𝟏𝟎−𝟏𝟒𝐆
𝑁Mpc ,
𝟏𝟎−𝟏𝟒𝐆
𝑁Mpc ,
I𝟐 𝑭𝝁𝝂𝑭𝝁𝝂 :(𝝓) 𝜙
𝜙 𝑁Mpc
𝜁𝒌𝐸𝑀 ≃
𝑑𝑁
𝜖 𝜌inf𝜌𝒌𝐸𝑀
Isocurvature pert. ⇒ Adiabatic pert.
Non-gaussianity: 𝜌𝒌𝐸𝑀 ∼ 𝐴𝑘′𝐴𝑘−𝑘′
𝒫𝒌𝐸𝑀, 𝑓NL
EM, 𝜏𝑁𝐿𝐸𝑀 ≤ Planck result
𝜁𝒌𝐸𝑀 ≃
𝑑𝑁
𝜖 𝜌inf𝜌𝒌𝐸𝑀 ∝
𝜌inf𝜖
Low energy ⇒ Small Curvature Pert.(?)
~𝐻4 ∝ 𝜌inf2
In single slow-roll case,
𝒫𝜁 =1
24𝜋2𝑀𝑃𝑙4
𝜌inf
𝜖≈ 10−9
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• 𝝐