Post on 03-Feb-2020
Listening for Invisible Axions with Gravitational Waves
Ben A. Stefanek
Audible AxionsC. Machado, W. Ratzinger, P. Schwaller, BAS
JHEP 01 (2019) 053 arXiv:1811.01950
The Audible Axion Model (4 parameters)
• Weconsiderthefollowingeffec3vefieldtheoryconsis3ngofanaxion-likepar3cle(ALP)andamasslessdarkphoton
• Weassumesomeexplicitbreakingoftheglobalsymmetryatthescale,whichgeneratesamassfortheALP
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�i = ✓f , �0i ⇡ 0 , ✓ ⇠ O(1)
<latexit sha1_base64="qjZFLiw3lKPEGoNjyG7vIqFBZZc=">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</latexit><latexit sha1_base64="qjZFLiw3lKPEGoNjyG7vIqFBZZc=">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</latexit><latexit sha1_base64="qjZFLiw3lKPEGoNjyG7vIqFBZZc=">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</latexit><latexit sha1_base64="qjZFLiw3lKPEGoNjyG7vIqFBZZc=">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</latexit>
⇤ =p
mf
Vacuum Misalignment
• SincetheALPhasnoreasontobeneartheminimumofthepoten3alwhenit3lts,wegenericallyexpectini3alcondi3onsoftheform
�3
�i = ✓f , �0i ⇡ 0 , ✓ ⇠ O(1)
<latexit sha1_base64="qjZFLiw3lKPEGoNjyG7vIqFBZZc=">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</latexit><latexit sha1_base64="qjZFLiw3lKPEGoNjyG7vIqFBZZc=">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</latexit><latexit sha1_base64="qjZFLiw3lKPEGoNjyG7vIqFBZZc=">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</latexit><latexit sha1_base64="qjZFLiw3lKPEGoNjyG7vIqFBZZc=">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</latexit>
V (�)
��i = ✓f
ALP and Dark Photon Abundances
• TheALPbeginstooscillatewhentheHubbleratedropsbelowtheALPmass
• Forsimplicity,weassumethenoini3alabundanceforthedarkphoton.However,itcanbesourcedastheALProlls.
�4
V (�)
��i = ✓f
⌦osc
� =⇢osc�
⇢osctot
⇡ m2✓2f2/2
3M2
PH2
osc
⇡✓
✓f
MP
◆2
⇢osc� ⇠ 1
2m2�2
iHosc
⇠ m,
Dark Photon Production
• WeassumethattheALPbeginsoscilla3nginapost-infla3onaryradia3on-dominatedFRWuniverse(),inwhichtheALPobeys
andthedarkphotonobeysawaveequa3onsourcedby
�5
✓@2
@⌧2�r2
◆~X = ↵
�0
f~r⇥ ~X , ~r · ~X = 0 .
<latexit sha1_base64="k5LcM/+B/HgUV2skEHsI59kFVug=">AAAC/XicbVHLbtQwFHXCq4TXFNixsagQRSqjpJsiJKRCWbAsEm1HGg+jG8eZWPUjsp1Bo8jia9ihbljwLez4FJzMFJi2V0p0fM659vVxXgtuXZr+iuJr12/cvLVxO7lz9979B4PNh8dWN4ayI6qFNqMcLBNcsSPHnWCj2jCQuWAn+elBp5/MmbFcq09uUbOJhJniJafgAjUdnCVEsNJtY1IaoC2pwTgO4nO76/3fFSYOmp7CLzFRkAvoVsTwWeVekDmj7cjjN5iAqCs436niz31b+l5eNnniuGT2vIHs7GBS2Rooa7NUSp+seWmhHf63eRr8w+lgKx2mfeHLIFuBrf236Y/fCKHD6Wa0RwpNG8mUowKsHWdp7SZtdzEqWDiysSxMcAozNg5QQRhw0vbBevwsMAUutQmfcrhn/+9oQVq7kHlwSnCVvah15FXauHHlq0nLVd04pujyoLIR2GncvRIuuGHUiUUAQA0Ps2JaQcjVhbdMEqLYF6qlBFW0hNXW938utPLr2nwpzsFcrecrQ65F0V1Ei1WPT0LU2cVgL4Pj3WGWDrOPIfN3aFkb6Al6irZRhvbQPvqADtERotHj6HV0EL2Pv8bf4u/x2dIaR6ueR2it4p9/APpY98o=</latexit><latexit sha1_base64="XXbNyufBdwBhFg65J0tkOqfdE4I=">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</latexit><latexit sha1_base64="XXbNyufBdwBhFg65J0tkOqfdE4I=">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</latexit><latexit sha1_base64="qXcdG47eW2/hM3r/dhbH/7Xky9w=">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</latexit>
�00 + 2aH�0 + a2@V
@�=
↵
fa2 ~E · ~B ,
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�0<latexit sha1_base64="(null)">(null)</latexit><latexit sha1_base64="(null)">(null)</latexit><latexit sha1_base64="(null)">(null)</latexit><latexit sha1_base64="(null)">(null)</latexit>
⌦� < ⌦rad
Source for dark photons(while ALP rolls)
Dark E and B, sink for ALP
Dark Photon Production: Quantum Picture
Wequan3zethedarkphotonfieldas
whichleadstothefollowingequa3onforthemodefunc3ons
AstheALProlls,thereexistmomentaforwhichisnega3ve.Thecorrespondingmodesaretachyonicandgrowexponen3ally:
�6
Xi(x, ⌧) =X
�=±
Zd3k
(2⇡)3v�(k, ⌧) "
i�(k) a�(k) e
ik·x+ h.c.<latexit sha1_base64="(null)">(null)</latexit><latexit sha1_base64="(null)">(null)</latexit><latexit sha1_base64="(null)">(null)</latexit><latexit sha1_base64="(null)">(null)</latexit>
v±(k, ⌧) ⇠ e|!±|⌧<latexit sha1_base64="(null)">(null)</latexit><latexit sha1_base64="(null)">(null)</latexit><latexit sha1_base64="(null)">(null)</latexit><latexit sha1_base64="(null)">(null)</latexit>
!2±
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Circular pols. ( )
v00± + !2±(⌧)v± = 0 , !2
±(⌧) = k2 ⌥ k↵
f�0
k⇥ "± = ⌥ik"±
Dark Photon Spectrum and Parity Violation
Becausetheini3alsignofdetermineswhichhelicitybecomestachyonicfirst,thesystemviolatesparityandonehelicityexperiencesexponen3allymoreproduc3onthantheother.
Tachyonicmodes:
Mosttachyonicmode:
�7
2 5 10 20 50
10-25
10-20
10-15
10-10
10-5
1
� / (� ����)
��/�����
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!2+(⌧) = k2 � k
↵
f�0
k(⌧)
0 < k <↵�0
f,
k
m. ↵✓
k =↵�0
2f. ↵✓
2m
Gravitational Waves
Darkphotonmodesintherangewhichwereini3allyinvacuumgrowexponen3allywhentheaxionbeginstooscillate
Theserapidlygrowingmodesamplifyquantumfluctua3onsofthedarkphotonintoa3me-varying,anisotropicclassicalenergydistribu3onwhichsourcesgravita3onalwaves
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⇧ij(k, ⌧) =⇤klij
a2
Zd3q
(2⇡)3
hEk(q, ⌧)El(k� q, ⌧) + Bk(q, ⌧)Bl(k� q, ⌧)
i.
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v±(k, ⌧ ⌧ ⌧osc
) =1p2k
e�ik⌧
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h00ij(k, ⌧) + k2hij(k, ⌧) =
2
M2P
⇧ij(k, ⌧) ,Anisotropic
stressGravity Waves
!2± < 0
0 < k < ✓↵m
The Big Picture
�9
Cold Dark Matter
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H . m, Particle Production
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H > m<latexit sha1_base64="(null)">(null)</latexit><latexit sha1_base64="(null)">(null)</latexit><latexit sha1_base64="(null)">(null)</latexit><latexit sha1_base64="(null)">(null)</latexit>
P. Agrawal, G. Marques-Tavares, W. Xue: arXiv:1708.05008
• Theoscilla3ngALPproducesdarkphotonswhichsourceGW.ASerpar3cleproduc3on,theremainingALPabundancecanbeCDM.
Gravitational Wave Spectrum
�10
10-2 0.1 1 10 10010-13
10-12
10-11
10-10
10-9
10-8
10-7
� / (� ����)
����
kpeak ⇡ (↵✓)2/3 m, ⌦GW(kpeak) ⇡✓
f
MP
◆4 ✓✓2
↵
◆ 43
.
Properties of the GW Spectrum: Chirality
TheproducedGWspectrumishighlypolarizedbecausetheGWinherittheparityviola3oninthedarkphotonpopula3on
�11
2 5 10 20 50
10-25
10-20
10-15
10-10
10-5
1
� / (� ����)
��/�����
10-2 0.1 1 10 10010-13
10-12
10-11
10-10
10-9
10-8
10-7
� / (� ����)
����
+ =+ =
�12
10-9 10-7 10-5 10-3 10-1 101 103
10-16
10-14
10-12
10-10
10-8
10-16
10-14
10-12
10-10
10-8
f0 HHzL
h2WGW
0
LISA
BBO
DECIGO
LIGO ETIPTA
SKA
QCD
Axion
1QCD
Axion
2
ALP1
ALP2
ALP3
ALP4
ALP5
ALP6
Listening for Invisible Axions
⌦0GW ⇡ ⌦0
�
✓f
MP
◆4 ✓✓2
↵
◆ 43
f0 ⇡ m
✓T0
T⇤
◆(↵✓)2/3 =
rm
MPT0 (↵✓)
2/3 ,
�13
10-9 10-7 10-5 10-3 10-1 101 103
10-16
10-14
10-12
10-10
10-8
10-16
10-14
10-12
10-10
10-8
f0 HHzL
h2WGW
0
LISA
BBO
DECIGO
LIGO ETIPTA
SKA
QCD
Axion
1QCD
Axion
2
ALP1
ALP2
ALP3
ALP4
ALP5
ALP6
ALPs Detectable by Pulsar Timing Arrays:
f & 1017 GeV
m ⇠ 10�13 - 10�10 eV
�14
10-9 10-7 10-5 10-3 10-1 101 103
10-16
10-14
10-12
10-10
10-8
10-16
10-14
10-12
10-10
10-8
f0 HHzL
h2WGW
0
LISA
BBO
DECIGO
LIGO ETIPTA
SKA
QCD
Axion
1QCD
Axion
2
ALP1
ALP2
ALP3
ALP4
ALP5
ALP6
ALPs Detectable by LISA:
m ⇠ 0.01� 1 eV
f & 1017 GeV
�15
10-9 10-7 10-5 10-3 10-1 101 103
10-16
10-14
10-12
10-10
10-8
10-16
10-14
10-12
10-10
10-8
f0 HHzL
h2WGW
0
LISA
BBO
DECIGO
LIGO ETIPTA
SKA
QCD
Axion
1QCD
Axion
2
ALP1
ALP2
ALP3
ALP4
ALP5
ALP6
Future High Frequency Detectors:
f & 1017 GeV
m ⇠ 102-106 eV
Listening for Invisible Axions• BecauselargedecayconstantscorrespondtolargerGWamplitude,gravita3onal
wavedetectorscanprobeAudibleAxionmodelsfromthe“boVomup”!
�1610-14 10-9 10-4 10 106
10-18
10-16
10-14
10-12
10-10
10-8
10-6
m [eV]
1/f
a[G
eV-
1]
SKA
LISA
BBO
DECIGO ET
Astrophysics
IAXO
ADMX
QCD
Axion
Neff
Cosmological
BH
Superr
adia
nce
Listening for Invisible Axions• BecauselargedecayconstantscorrespondtolargerGWamplitude,gravita3onal
wavedetectorscanprobeAudibleAxionmodelsfromthe“boVomup”!
�1710-14 10-9 10-4 10 106
10-18
10-16
10-14
10-12
10-10
10-8
10-6
m [eV]
1/f
a[G
eV-
1]
SKA
LISA
BBO
DECIGO ET
Astrophysics
IAXO
ADMX
QCD
Axion
Neff
Cosmological
BH
Superr
adia
nce
Thank You!
Backup Slides
Properties of the GW Spectrum: Param Scaling
TheenergyinGWislimitedbytheenergyintheaxionfield
Roughes3mateforthepeakoftheGWspectrum
Es3ma3ngatthe3meofemissionleadsto
�19
⌦osc
� =⇢osc�
⇢osctot
⇡ m2✓2f2/2
3M2
PH2
osc
⇡✓
✓f
MP
◆2
.
kpeak ⇡ k(⌧⇤) , ⌦GW(kpeak) = ⌦2�
✓a⇤H⇤kpeak
◆2
.
⌦GW(kpeak) ⇡✓
f
MP
◆4 ✓✓2
↵
◆ 43
.kpeak ⇡ (↵✓)2/3 m,
Large decay constant requiredALP mass sets peak frequency
1 2 5 10 20 5010-8
10-4
1
104
108
1012
� / ����
ρ ���
(�+��)/ρ ����
ΔNeff = 0.3
ΔNeff = 0.03
ρϕa3
ρXa4
Quick Recap
�20
Cold Dark Matter
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H . m, Particle Production
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H > m<latexit sha1_base64="(null)">(null)</latexit><latexit sha1_base64="(null)">(null)</latexit><latexit sha1_base64="(null)">(null)</latexit><latexit sha1_base64="(null)">(null)</latexit>
0.1 1 10 10010-12
10-11
10-10
10-9
10-8
10-7
� / (� ����)
����
a /aosc = 6.7a /aosc = 10.3a /aosc = 66
P. Agrawal, G. Marques-Tavares, W. Xue: arXiv:1708.05008
Energy Density and Gauge Power Spectrum
1 2 5 10 20 5010-8
10-4
1
104
108
1012
� / ����
ρ ���
(�+��)/ρ ����
ΔNeff = 0.3
ΔNeff = 0.03
ρϕa3
ρXa4
1 2 5 10 20 50
10-43
10-33
10-23
10-13
10-3
� � / (� ����)�Ω
�/�����
a /aosc = 6.7a /aosc = 10.3a /aosc = 23a /aosc = 66
More on GW Spectrum
hij(k, ⌧) =2
aM2P
Z ⌧
⌧osc
d⌧ 0a(⌧ 0)G(k, ⌧, ⌧ 0)⇧ij(k, ⌧0)
d⇢GW
d log k=
M2P k
3
8⇡2a2Ph0
(k, ⌧) h0|h0ij(k, ⌧)h
0⇤ij (k
0, ⌧)|0i = (2⇡)3Ph0(k, ⌧)�(k� k0)
d⇢GW
d log k=
k3
4⇡2a4M2P
Z ⌧
⌧osc
d⌧ 0d⌧ 00a(⌧ 0)a(⌧ 00) cos [k(⌧ 0 � ⌧ 00)]⇧2(k, ⌧ 0, ⌧ 00)
h0|⇧ij(k, ⌧)⇧⇤ij(k
0, ⌧ 0)|0i = (2⇡)3⇧2(k, ⌧, ⌧ 0)�(k� k0)