2 day mini-workshop:

Axion Cosmology
Yukawa Institute for Theoretical Physics, Kyoto University
May 14 - 15, 2019

Exploring the string axiverse and parity violation in gravity
with gravitational waves

International Journal of Modern Physics D Vol. 27, No. 9 (2018) 1850096

Speaker：Daiske Yoshida
Collaborator：Jiro Soda
Kobe University

2 day mini-workshop: Axion Cosmology @Yukawa Institute for Theoretical Physics, Kyoto University, May 14 - 15, 2019Menu
1. Traces of the string axiverse
2. Axion dark matter
3. Dynamical Chern-Simons gravity
4. Parametric Resonance
5. Estimations
6. Conclusion

2 day mini-workshop: Axion Cosmology @Yukawa Institute for Theoretical Physics, Kyoto University, May 14 - 15, 2019Menu
1. Traces of the string axiverse
2. Axion dark matter
3. Dynamical Chern-Simons gravity
4. Parametric Resonance
5. Estimations
6. Conclusion

2 day mini-workshop: Axion Cosmology @Yukawa Institute for Theoretical Physics, Kyoto University, May 14 - 15, 2019

Traces of String Axiverse

01/14• String theory gives a lot of massive pseudo-scalar ﬁelds (Axion).

A. Arvanitaki, et al (2010),
P. Svrcek and E. Witten (2006)• Their mass is 10 33 ⇠ 10 10 eV. Its range is the very wide.
10 18 eV
CMB
Polarization

10 33 eV

MatterPower
Spectrum10 28 eV

10 20 eV

Target!

BH Super-radiance
10 14 eV

10 10 eV

• It is indicated that the axion can behave as the cold dark matter.
W. Hu, R. Barkana, and A. Gruzinov (2000)• The string axiverse gives the parity-violated interactions as follows,F̃ F, R̃R . In this talk, we concentrate on the modiﬁed gravity.
<latexit sha1_base64="rT5kHtyMovzvFxJwHp6pp0m3ZuA=">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</latexit>2 day mini-workshop: Axion Cosmology @Yukawa Institute for Theoretical Physics, Kyoto University, May 14 - 15, 2019Menu
1. Traces of the string axiverse
2. Axion dark matter
3. Dynamical Chern-Simons gravity
4. Parametric Resonance
5. Estimations
6. Conclusion

2 day mini-workshop: Axion Cosmology @Yukawa Institute for Theoretical Physics, Kyoto University, May 14 - 15, 2019

Axion Dark Matter

02/14

•

The cold dark matter is the dust which is pressureless.

•

The occupation number of the state of the axion dark matter is estimated by

N
x3

•

n
⇢DM
43
⇠
=
⇠
10
p3
p3
m p3

✓

⇢DM
0.3 GeV/cm3◆✓

10

The oscillation of the axion as a classical ﬁeld is given by1 ˙2 1 2→ Energy density : T00 = ⇢DM =
+ m
2
2

10

m

eV

◆4

.

A. Khmelnitsky & V. Rubakov, 2014(t) '<latexit sha1_base64="lQp6zw2hvXelqX43n/INfxYgg70=">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</latexit>

1 2
2
⇠ m
2

0 cos (mt)1v ⇠ 10 3 , E ' m + mv 2 ⇠ m
2<latexit sha1_base64="oxv+iMOJB35ax6la2kooUoXFDec=">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</latexit>

2010−10 eV
Φ0 ≃ 2.1 × 10 eVm()
7

Pressure :

•

1 ˙2
pDM =
2

1 2
m
2

2

⇠

1 2
m
2

.

ρ
0.3 GeV/cm3

20 cos 2mt

The period of the oscillation of the axion can be estimated as 1/m. Then, by theaverage under the long time scale T ≫ 1/m , the pressure of the oscillating axion
can be regarded as zero. Then, the oscillating axion behaves as the CDM.

2 day mini-workshop: Axion Cosmology @Yukawa Institute for Theoretical Physics, Kyoto University, May 14 - 15, 2019

Size of Axion Dark Matter

03/14• In space, the matters are collected by the gravitational forces.

→ It appears the equilibrium between the characteristic pressure ofmatters and the gravitational force induced by matters themselves.

→ This equilibrium is expressed by the size of the halo of matters.
→ Jeans length of the axion dark matter is given by

rJ = 4.3 ⇥ 10<latexit sha1_base64="KNaJHkPmq0Jd9i+gg5xbwM5occ0=">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</latexit>

3

pc ⇥

✓

0.3 GeV/cm⇢

3◆1/4 ✓

10

10

m

eV

◆1/2

• Jeans length is the maximum size which the matters can exist stably inspace.

→ In this talk, we assume the axion dark matters have the enoughenergy density and behave as the classical oscillating ﬁeld.

→ In low energy scale, the potential of the axion can be approximated by

1 2 2V∼ m Φ .
2

2 day mini-workshop: Axion Cosmology @Yukawa Institute for Theoretical Physics, Kyoto University, May 14 - 15, 2019Menu
1. Traces of the string axiverse
2. Axion dark matter
3. Dynamical Chern-Simons gravity
4. Parametric Resonance
5. Estimations
6. Conclusion

2 day mini-workshop: Axion Cosmology @Yukawa Institute for Theoretical Physics, Kyoto University, May 14 - 15, 201904/14

Dynamical Chern-Simon Gravity•

The action is given byS=<latexit sha1_base64="xs4xxIf+ps2fu3G8cblAamp/6E4=">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</latexit>

Z

dx

4p

V

g

h

↵=

•

1
R + ↵ R̃R
4r

Dynamical or non-dynamical
→

 2
`
2

1
(rµ ) (rµ )2

1R̃R ⌘ ✏
|2

V( )

⇢

R↵ ⇢ R ↵
{z
}

⌘R̃↵

This is switched by the existence of the dynamical term of theaxion ﬁeld.

R/L

R/L

i✏ilm nl emj (n) = ±eij (n)•Because the axion ﬁeld is the pseudo scalar, this interaction term induces•

The upper bound of the coupling constant•ithe circular polarized gravitational waves.

ℓ ∼ 108km

is given as follows,ℓin non dynamical theory by Y. Ali-Haimoud & Y. Chen (2011).
in dynamical theory by Y. Nakamura et. al. (2018).

The ghost modes exist in this theory. We assume this theory as the eﬀective
theory of gravity.

2 day mini-workshop: Axion Cosmology @Yukawa Institute for Theoretical Physics, Kyoto University, May 14 - 15, 201905/14

Equations of Motion of dCS Gravity• The action of the dynamical Chern-Simons gravity is
S=

Z

dx
V

4p

Z

1
4p
gR+ ↵
dx
g R̃R
4 V
Z
1
4p
dx
g [g µ⌫ (rµ )(r⌫ ) + 2V ( )]2 V

• The equations of motion are derived by↵1Gµ⌫ + Cµ⌫ =Tµ⌫ for the gravitational ﬁeld and
2C µ⌫ ⌘ (r↵ )✏↵

rµ r

µ

dV ( )
=
d

↵
R̃R
4

(µ

r R

⌫)

+ (r↵ rfor the axion ﬁeld.

)R̃ (µ⌫)↵2 day mini-workshop: Axion Cosmology @Yukawa Institute for Theoretical Physics, Kyoto University, May 14 - 15, 2019Menu
1. Traces of the string axiverse
2. Axion dark matter
3. Dynamical Chern-Simons gravity
4. Parametric Resonance
5. Estimations
6. Conclusion

2 day mini-workshop: Axion Cosmology @Yukawa Institute for Theoretical Physics, Kyoto University, May 14 - 15, 2019

• The Swings

Parametric Resonance

06/14→ The parameters vary at roughly twice the natural frequency of thearms of the swing, the amplitude of it will grow.

ω0
ωp

ωp

GW

,

ω0

Enhanced GW

axion• The parametric resonance is induced by Mathieu equation.

ẍ(t) + !02 (1f0 sin (!p t)) x(t) = 0• The properties of the Mathieu equation are noted.
→ The (ﬁrst) resonance frequency is given by!p ' 2!0<latexit sha1_base64="MQkCBsUDajQRYu1FHjx/OgLi+20=">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</latexit>→ The growth rate of the amplitude is given byh ∝ e Γη1
|f0 | !0max =4

2 day mini-workshop: Axion Cosmology @Yukawa Institute for Theoretical Physics, Kyoto University, May 14 - 15, 2019

07/14

Gravitational Wave in dCS Gravity••

We choose the ansatz of the spacetime below,

ds2 ' a(⌘)2 ( d⌘ 2 + ij dxi dxj + hij dxi dxj )For the interest in the circular polarization, we take the circular polarization basis which
are deﬁned by
1
1
+
⇥
R

hTT
ij =

X
A

hA e Aij

eij (n) = p

hR = p (h+ ih⇥ )21
hL = p (h+ + ih⇥ )2eij (n) + ieij (n)21eLij (n) = p e+ij (n)2ie⇥
ij (n)

Then, the equations of the gravitational wave is derived by

•

⇣

a2

✏A

⌘
⇣
↵
0
k h00A + 2aa0


✏A

⌘
⇣
↵
00
k h0A + a2


✏A

⌘
↵
0
k k 2 hA = 0


We can neglect the eﬀect of the expansion of space in the time scale when thegravitational waves pass Galaxy. Then, the scale factor can be estimated asa(⌘) ' 1 . Then, we can get the solution of the axion ﬁeld, Φ ≃ Φ0 cos(mη) .

•Finally, the equations of the gravitational wave is derived as

h00A +✏A cos(m⌘)
0
2
k
h
+
k
hA = 0Ak
1 + ✏A m sin(m⌘)

✏A ⌘

(

1
1

: A=R
: A=L

↵ 2
⌘ m


0

2 day mini-workshop: Axion Cosmology @Yukawa Institute for Theoretical Physics, Kyoto University, May 14 - 15, 2019

Growth of Amplitudes of GWs

08/14• These Plots shows the growth of the amplitude in the circular polarization basis.
We used the values below` = 108 km, m = 10 10 eV, ⇢ = 0.3 ⇥ 106 GeV/cm3' 0.02

10.0
8

7.5
6

5.0

4

hL

2

2.5

0

0

hR

→ There is the diﬀerence between the growth of the amplitude in R- and Lcircular polarization basis. In these conditions, the amplitude of hR becomes 104
times bigger than the amplitude of hL . So, the fully circular polarized wave
appears.
International Journal of Modern Physics D Vol. 27, No. 9 (2018) 1850096

2 day mini-workshop: Axion Cosmology @Yukawa Institute for Theoretical Physics, Kyoto University, May 14 - 15, 2019

09/14

Strength of Circular Polarization• This plot shows the time evolution of the strength of the circularpolarization.
We used the same values before slide.

8

6→ The horizontal axe shows the
time
.

4

η

2

→ The vertical axe shows thefrequencyof the GWs.

kparity(⌘) ⌘

0.5

0

0

→ The plotted function is deﬁnedby|h |2 |h |2
R

1.0

8

L

6

|hR |2 + |hL |2

-0.5

4

parity ∼ ± 1 : R or L

2
-1.0

• The color shows the strength of the circular polarization.

0→ At the resonance frequency, the GW is completely circular polarized.
International Journal of Modern Physics D Vol. 27, No. 9 (2018) 1850096

2 day mini-workshop: Axion Cosmology @Yukawa Institute for Theoretical Physics, Kyoto University, May 14 - 15, 2019

09/14

Strength of Circular Polarization• This plot shows the time evolution of the strength of the circularpolarization.
We used the same values before slide.
→ The horizontal axe shows thetime.

the time-average of the polarization

ηk→ The plotted function is deﬁnedby|h |2 |h |2

parity(⌘) ⌘RL

averaged violation→ The vertical axe shows thefrequencyof the GWs.

1.0

0.5

0.0

-0.5

|hR |2 + |hL |2parity ∼ ± 1 : R or L

-1.0
4.9 × 10-11

4.95× 10-11

5.× 10-11

5.05× 10-11

5.1 × 10-11

k [eV]

Proceedings, 4th Workshop on Cosmology and the Quantum Vacuum: Segovia, Spain, September 4-8, 2017

• The color shows the strength of the circular polarization.

→ At the resonance frequency, the GW is completely circular polarized.

2 day mini-workshop: Axion Cosmology @Yukawa Institute for Theoretical Physics, Kyoto University, May 14 - 15, 2019Menu
1. Traces of the string axiverse
2. Axion dark matter
3. Dynamical Chern-Simons gravity
4. Parametric Resonance
5. Estimations
6. Conclusion

2 day mini-workshop: Axion Cosmology @Yukawa Institute for Theoretical Physics, Kyoto University, May 14 - 15, 2019

Tools for Estimations

10/14• From the general theory of the parametric resonance, we can give theformulae for the estimations of the resonance frequency and the rate of theampliﬁcation in the length.

• Resonance

⇣
⌘
m
kr
m
→ Resonance frequency : kr =) fr =' 1.2 ⇥ 104 Hz22⇡
10 10 eV
r
m m
m m
↵ 2
 2
→ Width of the resonance :. kr .
+⌘ m 0 ↵=
`

2
8
2
8
2

• Ampliﬁcation of the amplitude of GW

We can convert Γ into the length R×10 in which the amplitude of the GWs
becomes 10 times bigger.
→ Typical length :R⇥10 ' 5.2 ⇥ 10 8 pc
s
✓
◆
✓
◆
2
2
10 10 eV
108 km
0.3 GeV/cm3⇥m`⇢<latexit sha1_base64="lXa04mvJvuaE+WTq94Sga7/3flQ=">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</latexit>2 day mini-workshop: Axion Cosmology @Yukawa Institute for Theoretical Physics, Kyoto University, May 14 - 15, 2019•

Simple Estimation

11/14

The length in which the GWs becomes 10 times bigger is estimated as

R⇥10 ' 5.0 ⇥ 10 8 pc
s
✓
◆
✓
◆
2
2
10
8
10
eV
10 km
0.3 GeV/cm3⇥m`⇢<latexit sha1_base64="SP+bbe6K+NtW17DplHZDGzB2ews=">AAADO3ichZHLbhMxFIbPDLcSLg2wQWJjETUqEgSnpSIgIVWwgGWbkrRSp4lmjJNYsWemHidSseYFeAEWrEBCCPEObNjwAgh1z4bLriA2LDgzGUA0gno09u/f5zs+toNYisRQuuu4hw4fOXps5njpxMlTp2fLZ862k2ikGW+xSEZ6I/ATLkXIW0YYyTdizX0VSL4eDO9k6+tjrhMRhffNTsy3lN8PRU8w36DVLb9vdq1nhOIJqdOUVL0E9TZZqlHy2+7YK42UeJetpxWJGUqPlKreIIl9xu2SUmkR6kneM/PE62mf2ZzDnAXH22lqFbJa9AfmUscupFPxDdyE5NFDhdEel3IfkGxrYwuA1hZ/FXWXt68y1VnMID2IUpJ2yxVao3kj06JeiAoUbSUqvwAPHkAEDEaggEMIBrUEHxL8NqEOFGL0tsCip1GJfJ1DCiVkRxjFMcJHd4h9H2ebhRviPMuZ5DTDXST+GkkCc/QdfUn36Fv6in6kP/6Zy+Y5slp2cAwmLI+7s4/Or30/kFI4Ghj8of5bs4EeNPJaBdYe5052Cjbhxw8f763dbM7ZKn1GP2P9T+kufYMnCMdf2fNV3nwCJXyA+v7rnhathdqNGl29Vlm+XbzEDFyAizCP130dluEerEALmHPLYY50lPva/eB+cr9MQl2nYM7BX8399hNzQtde</latexit>•

If the GWs which have the resonance frequency through in Galaxy for1012 times bigger.
10 kpc, the amplitude of the GWs become

10•This eﬀect will be detected in the diﬀerence between the waveform fromthe interferometers and from the numerical template of the GWs in pure GR.

•

If we found no diﬀerence in the waveform, we can give the constraint to thecoupling constants or the energy density of the axion dark matter.
→ If you believe ℓ ∼ 108km , thenρ will be constraint by ρ ≤ 10−26 GeV/cm3 .

→ If you believe ρ ∼ 0.3 GeV/cm3 , then ℓ will be constraint by ℓ ≤ 10 km .

2 day mini-workshop: Axion Cosmology @Yukawa Institute for Theoretical Physics, Kyoto University, May 14 - 15, 2019

Maps of Constraints

m = 10-10 [eV], 10 [Mpc]

107

107

10-3

10-3
ρ [GeV/cm3 ]ρ [GeV/cm3 ]m = 10-10 [eV], 10 [kpc]

10-13

10-23

0.01

12/14

10-13

10-23

1

100

104

106

108

0.01

1

l [km]

100

104

106

108

l [km]The green region is excluded by the observation.
The blue line shows the local dark matter density 0.3 GeV/cm3.
The red line represents the 10 times enhancement of GWs.
The red dashed line represents the 0.1 times enhancement.
The red dotted line represents the 0.01 times enhancement.
International Journal of Modern Physics D Vol. 27, No. 9 (2018) 1850096

2 day mini-workshop: Axion Cosmology @Yukawa Institute for Theoretical Physics, Kyoto University, May 14 - 15, 2019

13/14

Sensitivity Curves and Axion Dark Matter
Target!!!!
fr ' 1.2 ⇥ 104 Hz

These Sources are from “http://rhcole.com/apps/GWplotter/".

⇣m
10 10 eV⌘

2 day mini-workshop: Axion Cosmology @Yukawa Institute for Theoretical Physics, Kyoto University, May 14 - 15, 2019Menu
1. Traces of the string axiverse
2. Axion dark matter
3. Dynamical Chern-Simons gravity
4. Parametric Resonance
5. Estimations
6. Conclusion

2 day mini-workshop: Axion Cosmology @Yukawa Institute for Theoretical Physics, Kyoto University, May 14 - 15, 2019Conclusion

14/14• String axiverse generates the axions which have the lightmass and the dCS coupling between the axion ﬁeld and thegravitational ﬁeld.

• The coherently oscillating axion can behave as the cold dark
matter well, so, through the above coupling, themonochromatic and parity violated gravitational waves are
generally induced.

• This eﬀect may use to detect the counterpart of the GR.
→

They might give the new constraint to the abundance of

the axion dark matter or the CS-coupling.

• This analysis can connect the problems about the CDM andthe modiﬁed gravity.

2 day mini-workshop: Axion Cosmology @Yukawa Institute for Theoretical Physics, Kyoto University, May 14 - 15, 2019

Related Researches• Articles“Electromagnetic memory eﬀect induced by axion dark matter”
DY and Jiro Soda, Phys. Rev. D 96, 064005 (2017)“Exploring the string axiverse and parity violation in gravity withgravitational waves”,
DY and Jiro Soda, International Journal of Modern Physics D Vol. 27, No.
9 (2018) 1850096“Electromagnetic waves propagating in the string axiverse”,
DY and Jiro Soda, Progress of Theoretical and Experimental Physics, Volume
2018, Issue 4, 1 April 2018, 041E01• Proceedings“Exploring String Axions with Gravitational Waves”,
Jiro Soda and DY, Galaxies 5 (2017) no.4, 96