Listening for Invisible Axions with Gravitational...
Transcript of Listening for Invisible Axions with Gravitational...
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=">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</latexit><latexit sha1_base64="XXbNyufBdwBhFg65J0tkOqfdE4I=">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</latexit><latexit sha1_base64="XXbNyufBdwBhFg65J0tkOqfdE4I=">AAAC/XicbVHLbtQwFHXCqw2PzgA7NhYVokhllHRThIRUKAuWRWLakcbD6MZxJlYdO7KdQaPI4mvYoW5YsOt/sOBfcDJTYNpeKdHxOefa18dpJbixcfwrCG/cvHX7zsZmdPfe/Qdbvf7DY6NqTdmQKqH0KAXDBJdsaLkVbFRpBmUq2El6etjqJ3OmDVfyk11UbFLCTPKcU7CemvbOIiJYbncwyTXQhlSgLQfxudlz7u8KEwt1R+GXmEhIBbQrovmssC/InNFm5PAbTEBUBVzsVPDnrsldJy+bHLG8ZOaigezuYlKYCihrkrgsXbTmpZmy+N/msfcPpr3teBB3ha+CZAW2D97GP373z+XRtB/sk0zRumTSUgHGjJO4spOmvRgVzB9ZG+YnOIUZG3sowQ84abpgHX7mmQznSvtPWtyx/3c0UBqzKFPvLMEW5rLWktdp49rmryYNl1VtmaTLg/JaYKtw+0o445pRKxYeANXcz4ppAT5X698yiohkX6gqS5BZQ1hlXPfnQkm3rs2X4hz09Xq6MqRKZO1FlFj1uMhHnVwO9io43hsk8SD56DN/h5a1gZ6gp2gHJWgfHaAP6AgNEQ0eB6+Dw+B9+DX8Fn4Pz5bWMFj1PEJrFf78Axq6+QQ=</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)