Cosmological evolution ofaxion and hidden sector
Dec. 20 2017 @Osaka Univ.
"Axion physics and dark matter cosmology"

Fumi Takahashi(Tohoku)

Kitajima, Sekiguchi, FT, 1711.06590

Kawasaki, FT, Yamada,1511.05030,1708.06047

1. Introduction
The QCD axion is a plausible candidate for physics
beyond the standard model:
See talk by Jihn E Kim• Dynamically solves the strong CP problem
Peccei, Quinn ̀77, Weinberg ̀78, Wilczek ̀78• Explains the observed dark matter
Preskill, Wise, Wilczek ̀83, Abbott, Sikivie, ̀83, Dine, Fischler, ̀83- Cold and long-lived DM with the correct abundance
See talk by NagamineT ⌧ ⇤QCD

T⇤QCD✓iaa/fa

1. Introduction
See talks by Giannotti, Yoshimura,Spector, Yamamoto, Sasao, Busker,
Iwasaki, Taguchi, Semertzidis

1. Introduction
See talks by Giannotti, Yoshimura,Spector, Yamamoto, Sasao, Busker,Iwasaki, Taguchi, Semertzidis

1. Introduction
See talks by Giannotti, Yoshimura,Spector, Yamamoto, Sasao, Busker,Iwasaki, Taguchi, Semertzidis

The axion-mediated dipole-dipole potential:

V (r) =

2gAee((~ 1 · ~ 2 )216⇡me3(~ 1 · ~n)(~ 2 · ~n)) /r3

The sign was recently corrected.
Daido and FT, 1704.00155

1. Introduction
See talks by Giannotti, Yoshimura,Spector, Yamamoto, Sasao, Busker,
Iwasaki, Taguchi, Semertzidis

Does the QCD axion couple only to the SM?

The axion-mediated dipole-dipole potential:

V (r) =

2gAee((~ 1 · ~ 2 )216⇡me3(~ 1 · ~n)(~ 2 · ~n)) /r3

The sign was recently corrected.
Daido and FT, 1704.001551. Introduction
In this talk, I discuss a scenario where axion is theportal to a hidden sector.

Standard Model

Hidden Sector

Axion

1. Introduction
In this talk, I discuss a scenario where axion is theportal to a hidden sector.

Standard Model

Hidden Sector

Axion

U(1)H

1) Case with moderately large coupling to U(1)H2) Case of U(1)H w/ monopoles2. Axion coupled to hidden photons

Kitajima, Sekiguchi, FT, 1711.06590

Coupling to hidden photons
The relevant part of the Lagrangian is1
L = rµ rµ21µ⌫FHµ⌫ FH
4QCD (T )
H



1cos✓

fa

◆µ⌫FHµ⌫ F̃H .+ (coupling to SM)

4fa: axion, AH , FH : hidden photon and ﬁeld strength
QCD (T ) =0

1 + (T /Tc )b2
4=(7.6⇥10GeV),0Tc = 0.16 GeV, b = 8.2

P S. Borsanyi et al,1606.07494↵H c 0H =2⇡
N.B.

Hwith

E0c 0 =N

(The ratio of the anomaly
coeﬃcients)

can be larger than unity in the clockwork axion.

[Alignment/clockwork]: Kim, Nilles, Peloso, hep-ph/0409138, Choi, Kim, Yun, 1404.6209, Choi and Im 1511.00132, Kaplan
and Rattazzi, 1511.01827. Giudice and McCullough 1610.07962,[Clockwork QCD axion]: Higaki, Jeong, Kitajima, FT, 1512.05295, 1603.02090, Farina, Pappadopulo, Rompineve, and Tesi,1611.09855.

Coupling to hidden photons
Equations of motion:¨ + 2H ˙

r2+a2 @V@ÄH + r ⇥ (r ⇥ AH ) =r · ȦH =Hfa=
HfahHȦH · (r ⇥ AH ),2fa a˙ (r ⇥ AH )(r ) · (r ⇥ AH ),i(r ) ⇥ ȦH ,Overdot is a derivative
w.r.t. conformal time

Coupling to hidden photons
Equations of motion:¨ + 2H ˙

r2+a2 @V@ÄH + r ⇥ (r ⇥ AH ) =r · ȦH =H

fa

=
H

fahH
ȦH · (r ⇥ AH ),2fa a

˙ (r ⇥ AH )i(r ) ⇥ ȦH ,Overdot is a derivative(r ) · (r ⇥ AH ),w.r.t. conformal time

For spatially homogeneous axion,

ÄHk,± + k k ⌥Hfa˙!

AHk,± = 0

Tachyonic instability exists if k <± : helicity

˙|
H |/fa !

Garretson, G. B. Field, and S. M. Carroll, hep-ph/9209238

The eﬀect was studied in a context of natural inﬂation (warm inﬂation, non-Gaussianity, reheating),
magnetogenesis, and relaxion.

Eﬀects on the axion dynamics
So, if coupling is moderately large, the QCD
axion produces hidden photons eﬃciently, andthe abundance may be reduced.
0⌦aEﬀects on the axion dynamics
The axion DM is produced as coherent oscillations[misalignment mechanism].
Preskill, Wise, Wilczek ̀83, Abbott, Sikivie, ̀83, Dine, Fischler, ̀83⌦a h22' 0.11 ✓i C(✓i )✓fa
5 ⇥ 1011 GeV

Anharmonic eﬀect◆1.184

CDMBae, Huh, Kim ̀08, Visinelli and Gondolo ̀08

T ⌧ ⇤QCD

T⇤QCD✓ia/faEﬀects on the axion dynamics“Axion window”

10 GeV . fa . 10
812GeVPreskill, Wise, Wilczek ̀83, Abbott, Sikivie ̀83, Dine, Fischler ̀83
Mayle et al ̀88, Raﬀelt and Seckel ̀88, Turner 88.

If fa = O(1016 ) GeV , the axion abundance exceeds
5the DM abundance by O(10 ).

The axion abundance can be suppressed if
3✓=O(10)
1. Fine-tuning of the initial angle, i

2. Late-time entropy production.
Dine, Fischler ̀83, Steinhardt and Turner ̀83, Lazarides et al ̀90,Kawasaki, Moroi, Yanagida ̀96, Kawasaki, FT, ̀04

Eﬀects on the axion dynamics“Axion window”

10 GeV . fa . 10812GeVPreskill, Wise, Wilczek ̀83, Abbott, Sikivie ̀83, Dine, Fischler ̀83
Mayle et al ̀88, Raﬀelt and Seckel ̀88, Turner 88.

If fa = O(1016 ) GeV , the axion abundance exceeds5the DM abundance by O(10 ).

The axion abundance can be suppressed if
3✓=O(10)
1. Fine-tuning of the initial angle, i

2. Late-time entropy production.
Dine, Fischler ̀83, Steinhardt and Turner ̀83, Lazarides et al ̀90,Kawasaki, Moroi, Yanagida ̀96, Kawasaki, FT, ̀04

3. Dissipation into hidden photon (?)

Eﬀects on the axion dynamics
However, it may not be that simple.
If the coupling is too large, it may acts as an extra
frictional force, which may delay the beginning ofthe oscillation and enhance the abundance ?
0⌦a?

Eﬀects on the axion dynamics•The abundance of the axion zero mode isreduced (dissipation), or enhanced (friction)?

Eﬀects on the axion dynamics•The abundance of the axion zero mode is
reduced (dissipation), or enhanced (friction)?
•The axion non-zero modes are also created by
the produced hidden photons.
¨ + 2H ˙

r2+a2 @V@ÄH + r ⇥ (r ⇥ AH ) =H

fa=hHȦH · (r ⇥ AH )2fa a

˙ (r ⇥ AH )(r ) ⇥ ȦHi

Eﬀects on the axion dynamics•The abundance of the axion zero mode isreduced (dissipation), or enhanced (friction)?
•The axion non-zero modes are also created by
the produced hidden photons.
¨ + 2H ˙

r2+a2 @V@ÄH + r ⇥ (r ⇥ AH ) =H

fa=hHȦH · (r ⇥ AH )2
fa a

˙ (r ⇥ AH )(r ) ⇥ ȦHi

•The axion non-zero modes not only contributeto the ﬁnal axion density, but also stop thetachyonic preheating.

Eﬀects on the axion dynamics•The abundance of the axion zero mode is
reduced (dissipation), or enhanced (friction)?
•The axion non-zero modes are also created by
the produced hidden photons.
¨ + 2H ˙

r2+a2 @V@ÄH + r ⇥ (r ⇥ AH ) =H

fa=hHȦH · (r ⇥ AH )2
fa a

˙ (r ⇥ AH )(r ) ⇥ ȦHi

•The axion non-zero modes not only contributeto the ﬁnal axion density, but also stop thetachyonic preheating.
The back reaction on the axion dynamics canbe studied by lattice simulations.

A comment on related work• Agrawal et al studied the eﬀects on the axion abundancein the same set-up, and found a large suppression.

~104
Suppressedby 10-10 !

~10-6
Agrawal et al, 1708.05008
H• The upper bound on the decay constant would be relaxed
17f'
10GeV, if this is true.
to a• They presumed that production of the axion nonzero
modes is negligible in their analysis.

Numerical results
We performed a simulation of the axion electrodynamics using
extended Yeeʼs algorithm, and adopted a periodic comoving box witha grid number Ngrid= 2563.

comoving energy density [ma2fa2]100
βH=0 —

10βH=20 —βH=300 —-1

10-210-3axion
gauge field
510152025
scale factor

303540

Kitajima, Sekiguchi, FT, 1711.06590

101100H

axion number ratio n/nβ =0

Numerical results

10-1

10-2

Suppressed byat most O(102).

10-31101001000

βH
Kitajima, Sekiguchi, FT, 1711.06590

101100H

axion number ratio n/nβ =0

Numerical results

10-1

10-2

Suppressed byat most O(102).

10-31101001000

βH
Kitajima, Sekiguchi, FT, 1711.06590

101100H

axion number ratio n/nβ =0

Numerical results

10-1

10-2

Suppressed byat most O(102).

10Strongly
dampedregime-31101001000

βH
Kitajima, Sekiguchi, FT, 1711.06590

101100H

axion number ratio n/nβ =0

Numerical results

10-1

Agrawal et al

10-2

Suppressed byat most O(102).

10Strongly
dampedregime-31101001000

βH
Kitajima, Sekiguchi, FT, 1711.06590

3. Axion coupled to hidden photons
and monopoles

Kawasaki, FT, Yamada,1511.05030,1708.06047

Witten eﬀectWitten ̀79

Let us ﬁrst consider the θ-term of hidden U(1):This θ is not the2✓eµ⌫L✓ =FF̃=µ⌫232⇡

2strong CP phase.

✓eE·B
28⇡

which usually has no eﬀect as it is a total derivative.
The term, however, has an interesting eﬀect in themonopole background.

B

B+θ-term

Monopole

QM = 4⇡/eEDyon

QM = 4⇡/e

QE 6= 0

Witten eﬀect

Witten ̀79

B

A monopole acquires an electric charge,and becomes a dyon if ✓ 6= 0 .

e✓
QE = ne +2⇡DyonEn = 0, ±1, ±2, · · ·QM = 4⇡/eA monopole magnetic charge QM = 4⇡/e is used.

QE 6= 0The mass of dyons is heavier than the monopole mass:

1 m2W

MD = MM +2 MMq' v Q2M + Q2E

✓n✓
2⇡

◆2

The non-zero value of θ costs more energy as it induces
an electric ﬁeld around the monopole.

Axion coupled to hidden monopoles
Kawasaki, FT, Yamada, 1511.05030

Consider the axion coupling to U(1)H:e2 aµ⌫L✓ =Fµ⌫ F̃ =232⇡ fa

e2 aE·B
28⇡ faThen, the QCD axion acquires an extra mass about a = 0
by the Witten eﬀect in the presence of hidden monopoles:
2ma,M '↵ nM
16⇡ 2 rc fa2

nM :(anti-)monopole number density
11rc '=evmW

cf. Fischler and Preskill, ̀83

e2
↵=
4⇡

: monopole radius• The extra axion mass naturally decreases as the monopole
density is diluted by the cosmic expansion.

Consistent w/ theneutron EDM constraint.

Evolution of axion
22• The axion starts to oscillate when ma,M ' H .

Tosc,1 ' 65 GeV↵2✓2

⌦M h0.12◆✓

fa1012 GeV◆ 2.

Witten eﬀecta• No extra axion coherent oscillations are induced during
the QCD phase transition if ma,M /H & O(10) .

fa . 10

12GeV↵

1.1

✓

2

⌦M h
0.12

◆0.55

.

“Adiabatic suppression mechanism”
Linde ̀96.

+QCD instanton
Witten eﬀectaKawasaki, FT, Yamada,1511.05030,1708.06047

Axion abundance
Kawasaki, FT, Yamada, 1511.05030

The ﬁnal axion abundance is given by2⌦a h ' 3 ⇥ 104↵

2 2✓i✓0.12⌦M h2◆✓

fa1012 GeV◆3The axion abundance is suppressed, and it is inversely
proportional to the monopole abundance!

The Witten eﬀect also solves the axion domain wall
problem when the PQ symmetry spontaneously broken afterinﬂation.
See talk by Kawasaki

QCD axion and monopole DM
0.12
f a =4×10 12 GeV

0.10

0.06

2 =120.

ΩM hh
ΩM

22 +h
Ωa0.08

0.04
0.02
0.00
0.00

f a =2×10 12 GeV
fa =1012 GeV

0.02

0.04

ictabaindoai
No press
sup0.06

Ωa h

0.08

0.100.12

2Kawasaki, FT, Yamada,1511.05030,1708.06047

Hidden monopole DM
The monopoles with mass MM = (1the observed DM.

10) PeV account for
Murayama, Shu 0905.1720

In the minimal case of the ʼt Hooft-Polyakov monopole w/oother charged particles, the massive gauge bosons give alarger contribution.
Baek, Ko, Park 1311.1035, Khoze, Ro 1406.2291
2e.g. The observed DM is realized with v ' 10 TeV, ↵ = O(0.1)
for which the monopole fraction is O(10)%.
N.B. The massive gauge boson abundance can be reduced
by adding matter ﬁelds.

Summary✓We have studied the cosmological evolution of theaxion coupled to hidden photons.
✓The axion density can be suppressed by O(102) bytachyonic resonance.
•The ﬁne-tuning of the misalignment angle can be
16-3
f=
10GeV .
relaxed from O(10 ) to O(0.1) for a• The axion abundance enhanced for suﬃciently
large coupling.
✓In the presence of hidden monoples, the Witten
eﬀect suppresses the QCD axion abundance.
•Hidden monopoles become self-interacting DM.

BE