•

• 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

•

•

• 𝝐