Cosmology of the (QCD) axion coupled with hidden photons C Dark - - PowerPoint PPT Presentation

Cosmology of the (QCD) axion coupled with hidden photons

北嶋直弥

素粒子物理学の進展２０１８

（C研）

V = m2

aF 2 a

 1 − cos ✓ a Fa ◆ ≈ 1 2m2

aa2

Dark matter 調和振動子 = 冷たい暗黒物質

アクシオン ̶ 暗黒物質の候補の１つ

残存量：

ma ' 6 ⇥ 10−6 eV ✓1012 GeV Fa ◆

質量： Ωah2 = 0.18θ2

i

✓ Fa 1012 GeV ◆1.19

本当？

高次元の理論 （超弦理論など） ４次元時空 String axions +

ストリングアクシオン “String Axiverse” どうやって見つける？

Contents Part 1 - アクシオン暗黒物質の存在量 Part 2 - アクシオンによる重力波生成

アクシオンと電磁場の相互作用

credit: ICEPP

Laγγ = 1 4gaγγaFµν ˜ F µν = −gaγγa ~ E · ~ B

宇宙初期にどんな影響を及ぼすか？

Axion-Hidden photon coupling and axion abundance

NK, T. Sekiguchi, F . Takahashi, arXiv:1711.06590

∆L = −gφγ0 4 φFHµν ˜ F µν

H

≡ − βH 4fa φFHµν ˜ F µν

H

Axion-Hidden (dark) photon interaction

FHµν = @µAHν − @νAHµ, ˜ F µν

H

= ✏µνρσFHρσ/2√−g Hidden U(1) gauge field n.b. βH >> 1 is possible in some cases (e.g. clockwork/aligned axion model) L = 1 2∂µφ∂µφ − V (φ) − 1 4FHµνF µν

H − βH

4fa φFHµν ˜ F µν

H

axion + hidden U(1) gauge field

Evolution equations

¨ φ + 3H ˙ φ r2φ a2 + ∂V ∂φ = βH fa EH · BH (FH,0i = −EH,i, FH,ij = ✏ijkBH,k)

• Axion equation of motion
• Maxwell equations

˙ BH = r ⇥ EH ˙ EH + HEH = 1 a2 r ⇥ BH βH afa ( ˙ φBH + rφ ⇥ EH) r · BH = 0, r · EH = βH afa rφ · BH

a : scale factor H : Hubble parameter (in flat-FRW Universe)

V (φ) = m2

af 2 a

 1 − cos ✓ φ fa ◆

backreaction photon production

Tachyonic growth of gauge fields

AH = X

λ=±

Z d3k (2π)3 eik·xελ(k) ⇥ Aλ

H(k)aλ(k) + Aλ∗ H (k)a†(−k)

⇤ k a < βH ˙ φ fa Aλ

H(k) →

1 √ 2k eπ|ξ| p 2π|ξ| , with ξ ≡ βH ˙ φ 2faH ゲージ場を円偏光モードで展開 ¨ A(±)

H (k) + H ˙

A(±)

H (k) +

✓k2 a2 ⌥ k a βH ˙ φ fa ◆ A(±)

H (k) = 0

（空間的一様なアクシオン場を仮定）

10-30 10-25 10-20 10-15 10-10 10-5 100 10-2 10-1 100 101 102

PE+ PE- PB+ PB-

10-20 10-18 10-16 10-14 10-12 10-10 10-8 8 9 10 11 12 13 N

plus minus axion

axion EM+ EM-

k/m

evolution of energy density power spectrum

Tachyonic growth of gauge fields

• cf. Magnetic field generation in the early universe

¨ φ + 3H ˙ φ r2φ a2 + ∂V ∂φ = βH fa EH · BH ˙ BH = r ⇥ EH ˙ EH + HEH = 1 a2 r ⇥ BH βH afa ( ˙ φBH + rφ ⇥ EH)

https://en.wikipedia.org/wiki/Finite-difference_time-domain_method

Lattice AED (axion electrodynamics)

Dissipation or overdamping

γ’ γ’

• 1. dissipation
• 2. overdamping

axion energy is dissipated by gauge field production axion abundance is suppressed

• nset of oscillation is delayed

by strong backreaction axion abundance is enhanced large friction by produced photons energy dissipation into hidden photons

10-4 10-3 10-2 10-1 100 101 2 4 6 8 10 12 14 16 18 20 comoving number density [ma Fa

2]

scale factor axion gauge field (B)

evolution of the comoving number density

• dissipation

βH = 20 suppressed

evolution of the comoving number density

• overdamping

10-4 10-3 10-2 10-1 100 101 2 4 6 8 10 12 14 16 18 20 comoving number density [ma Fa

2]

scale factor axion gauge field (B)

βH = 400 enhanced

suppression/enhancement factor

10-3 10-2 10-1 100 101 1 10 100 1000 axion number ratio n/nβH=0 βH

axion abundance can be suppressed ~ 0.01

Gravitational wave forest from axiverse

NK, J. Soda, Y. Urakawa, arXiv:1807.07037

(Dilute instanton gas approximation)

Axion potential (for ALP)

Potential with plateau region Cosine-type potential : (some classes of ) string axion

V (φ) = m2f 2 2 tanh2(φ/f) 1 + c tanh2(φ/f)

Soda, Urakawa, 1710.00305

String axion (with α-attractor type potential)

自己相互作用 ̶> パラメター共鳴 場の揺らぎが指数関数的に成長

δφ/δφi

φ

一様モード 場の揺らぎ (k/m=0.1)

“Frapping” resonance

V (φ)

Vk(δφ)

• scillon

O(1) overdensity

ds = −dt2 + a2(t)(δij + hij)dxidxj

Gravitational wave emission

tensor metric perturbation (GW) TT projection tensor evolution equation (Einstein equation) for gravitational waves ΩGW(k) = 1 ρcr dρGW d ln k , ρGW = 1 32πGh˙ hij ˙ hiji Density spectrum of GW ¨ hij + 3H ˙ hij r2hij a2 = 16πGΠTT

ij

ΠTT

ij

= − 1 a2 P lm

ij ∂iφ∂jφ

with

LISA 10−15 eV

1 eV

1 MeV

1 µeV

10-18 10-16 10-14 10-12 10-10 10-8 10-6 10-10 10-8 10-6 10-4 10-2 100 102 104 ΩGWh2 f [Hz]

SKA DECIGO ET c = 5 and φi = 3 (upper), 2 (lower)

重力波フォレスト

Ωφh2 = 1.5 ⇣ m 10−14 eV ⌘1/2 ✓ m Hosc ◆3/2 ✓ φosc 1016 GeV ◆2

axion abundance :

10-20 10-18 10-16 10-14 10-12 10-10 10-8 10-6 10-15 10-14 10-13 10-12 10-11 10-10 10-9 10-8 ΩGWh2 f [Hz]

1016 GeV

1015 GeV

c = 5 and φi = 3 (left), 2 (right)

Axion = dark matter

SKA

アクシオン-ダークフォトン相互作用を仮定 アクシオンのエネルギーがダークフォトンに散逸 —> アクシオン存在量は減る アクシオンの振動がダークフォトンに妨げられる —> アクシオン存在量は増える Plateau typeのポテンシャルをもつアクシオンは重力波を予言 「重力波フォレスト」