Detecting Ultra-light Dark Matter with Precision Metrology · 2018-03-05 · Detecting Ultra-light Dark Matter with Precision Metrology Surjeet Rajendran, UC Berkeley 14년 10월

Detecting Ultra-light Dark Matter with Precision

Metrology

Surjeet Rajendran, UC Berkeley

14년 10월 18일 토요일

Dark Matter


Dark Matter

A New Particle

Non gravitational interactions?


Dark Matter

A New Particle

Non gravitational interactions?

How do we detect them?

Weak effects. Need high precision14년 10월 18일 토요일

Precision Instruments

Impressive developments in the past two decades

(SQUIDs, atomic magnetometers) (atom and optical interferometers)

Magnetic Field / 10�16 TpHz

Accelerometers / 10�13 gpHz


Precision Instruments

Impressive developments in the past two decades

(SQUIDs, atomic magnetometers) (atom and optical interferometers)

Rapid technological advancements

Use to detect new physics?

Magnetic Field / 10�16 TpHz

Accelerometers / 10�13 gpHz


Outline

1. Brief Theory Overview

2. Axion Detection with Nuclear Magnetic Resonance

3. Dark Photon Detection with Radios

4. B-L Gauge Boson with Accelerometers

5. Conclusions


The Dark Matter Landscape

10-43 GeV 1019 GeV



10-22 eV10-43 GeV 1019 GeV100 eV

bosonic

Fit in galaxy



10-22 eV10-43 GeV 1019 GeV100 eV 102 GeV

(SM)

bosonic

Fit in galaxy

Standard Model scale ~ 100 GeV



10-22 eV10-43 GeV 1019 GeV100 eV 102 GeV

(SM)

bosonic

Fit in galaxy


One Possibility: Same scale for Dark Matter?Weakly Interacting Massive Particles (WIMPs)

WIMPs



10-22 eV10-43 GeV 1019 GeV100 eV 102 GeV

(SM)

bosonic

Fit in galaxy



WIMPs

Other Generic Candidates: Axions, Massive Vector Bosons

(yr-1)


Axions From High Energy Physics

Easy to generate axions from high energy theories

have a global symmetry broken at a high scale fa

string theory or extra dimensions naturally create axions from non-trivial topology

naturally gives large fa ~ GUT (1016 GeV) or Planck (1019 GeV) scales

Can also similarly get light vector bosons



10-22 eV10-43 GeV 1019 GeV100 eV 102 GeV

(SM)

bosonic

Fit in galaxy



WIMPs




10-22 eV10-43 GeV 1019 GeV100 eV 102 GeV

(SM)

bosonic

Fit in galaxy



WIMPs


10-6 eV10-15 eV(GHz)(Hz)(yr-1)

How do we search for them?This Talk: Bosons between GHz - Hz

Range includes popular candidates such as the QCD axion


Bosonic Dark MatterPhotons

~

E = E0 cos (!t� !x)

Detect Photon by measuring time varying

field


Bosonic Dark Matter

a

V

a(t) � a0 cos (mat)

Photons

~

E = E0 cos (!t� !x)

Dark Bosons

Early Universe: Misalignment Mechanism

m2aa

20 ⇠ ⇢DM


field Spatially uniform, oscillating field


Bosonic Dark Matter

a

V


Photons

~

E = E0 cos (!t� !x)

Dark Bosons


m2aa

20 ⇠ ⇢DM


field

Today:Random Field

Correlation length ~ 1/(ma v)

Spatially uniform, oscillating field


Temporal Coherence


Temporal Coherence

a

x

Field Homogenous over ~ 1/(ma v)


Temporal Coherence

a

x

v


Coherence Time ~ 1/(ma v2) ~ 1 s (MHz/ma)

v ~ 10-3

Random over longer timescales


Temporal Coherence

a

x

v


Coherence Time ~ 1/(ma v2) ~ 1 s (MHz/ma)

v ~ 10-3

Random over longer timescales

Or: power in the field is spread by kinetic energy ~ mav2


Bosonic Dark Matter

a

V


Photons

~

E = E0 cos (!t� !x)

Dark Bosons


m2aa

20 ⇠ ⇢DM


field

Today:Random Field


Coherence Time~ 1/(ma v2)

~ 1 s (MHz/ma)



Bosonic Dark Matter

a

V


Photons

~

E = E0 cos (!t� !x)

Dark Bosons


m2aa

20 ⇠ ⇢DM


field

Today:Random Field


Coherence Time~ 1/(ma v2)

~ 1 s (MHz/ma)


Detect effects of oscillating dark matter field

Resonance possible. Q ~ 106 (set by v ~ 10-3)14년 10월 18일 토요일

What kind of Bosons?Naturalness. Structure set by symmetries.



Spin 0

Axions and other goldstone bosons

Easy to get in many UV theories



Spin 0



Electromagnetism Nuclear Force Nuclear Spin⇣

afaFF̃

⌘ ⇣afaGG̃

⌘ ⇣@µafa

N̄�µ�5N⌘

QCD Axion General Axions



Spin 0 Spin 1




afaFF̃

⌘ ⇣afaGG̃

⌘ ⇣@µafa

N̄�µ�5N⌘


Anomaly free Standard Model couplings



Spin 0 Spin 1




afaFF̃

⌘ ⇣afaGG̃

⌘ ⇣@µafa

N̄�µ�5N⌘



Nuclear Spin Electro-magnetism

NucleonCurrent✓

F0µ⌫

faN̄�µ⌫N

◆ ⇣✏F

0F⌘ ⇣

gA0

µJµB�L

⌘

Dipole moment KineticMixing

B-L



Spin 0 Spin 1




afaFF̃

⌘ ⇣afaGG̃

⌘ ⇣@µafa

N̄�µ�5N⌘




NucleonCurrent✓

F0µ⌫

faN̄�µ⌫N

◆ ⇣✏F

0F⌘ ⇣

gA0

µJµB�L

⌘

Dark Matter =) a = a0 cos (mat)

Hz / ma / GHz


B-L



Spin 0 Spin 1




afaFF̃

⌘ ⇣afaGG̃

⌘ ⇣@µafa

N̄�µ�5N⌘

Current Searches QCD Axion General Axions



NucleonCurrent✓

F0µ⌫

faN̄�µ⌫N

◆ ⇣✏F

0F⌘ ⇣

gA0

µJµB�L

⌘


Hz / ma / GHz


B-L(ma ~ GHz)



Spin 0 Spin 1




afaFF̃

⌘ ⇣afaGG̃

⌘ ⇣@µafa

N̄�µ�5N⌘

Current Searches QCD Axion General Axions



NucleonCurrent✓

F0µ⌫

faN̄�µ⌫N

◆ ⇣✏F

0F⌘ ⇣

gA0

µJµB�L

⌘


Hz / ma / GHz


B-L

This Talk

(ma ~ GHz)


Cosmic Axion Spin Precession Experiment (CASPEr)

PRX 4 (2014) arXiv: 1306.6089PRD 88 (2013) arXiv: 1306.6088 PRD 84 (2011) arXiv: 1101.2691

Dmitry BudkerPeter Graham

Micah LedbetterAlex Sushkov

with


Current Searches: ADMX

1014

1018

1016

fa (GeV)

1012

1010

108

13



1014

1018

1016

fa (GeV)

1012

1010

108

Axion dark matter

13



1014

1018

1016

fa (GeV)

1012

1010

108

Axion dark matter

axion emission affects SN1987A, White Dwarfs, other astrophysical objectscollider & laser experiments, ALPS, CAST

� 1f4

a

γ

Blaser experiments:

L � a

faF �F =

a

fa

�E · �Bin most models:

13



1014

1018

1016

fa (GeV)

1012

1010

108

Axion dark matter


� 1f4

a

γ

Blaser experiments:

L � a

faF �F =

a

fa


axion-photon conversion suppressed � 1f2

a

size of cavity increases with fa

signal �1f3

a

a

γ

Bmicrowave cavity (ADMX)

13



1014

1018

1016

fa (GeV)

1012

1010

108

Axion dark matter


� 1f4

a

γ

Blaser experiments:

L � a

faF �F =

a

fa


axion-photon conversion suppressed � 1f2

a

size of cavity increases with fa

signal �1f3

a

a

γ

Bmicrowave cavity (ADMX)

Other ways to search for light (high fa) axions?

S. Thomas

13


CASPEr: Axion Effects on Spin



Neutron

General Axions



Neutron in Axion Wind

General Axions

~v

Spin rotates about dark matter velocity

⇣@µafa

N̄�µ�5N⌘

HN � afa

ma ~va.~SN




General Axions

~v


⇣@µafa

N̄�µ�5N⌘

HN � afa

ma ~va.~SN




General Axions

~v


Effective time varying magnetic field

⇣@µafa

N̄�µ�5N⌘

Beff / 10

�16cos (mat) T

HN � afa

ma ~va.~SN



Neutron inHidden Photon Field

Hidden Photons

Spin rotates about dark matter electric or

magnetic field


~E, ~B

HN � 1fa

~E0.~SN

✓F

0µ⌫

faN̄�µ⌫�5N

◆

Beff / 10

�13cos (mat) T




General Axions

~v



Other light dark matter (e.g. dark photons) also induce similar spin precession

⇣@µafa

N̄�µ�5N⌘

Beff / 10

�16cos (mat) T

HN � afa

ma ~va.~SN




General Axions

~v




⇣@µafa

N̄�µ�5N⌘

Neutron

QCD Axion

Beff / 10

�16cos (mat) T

HN � afa

ma ~va.~SN




General Axions

~v




⇣@µafa

N̄�µ�5N⌘ +

-

Neutron in QCD Axion Dark Matter

QCD axion induces electric dipole moment for neutron and proton

Dipole moment along nuclear spin

Oscillating dipole: d ⇠ 3⇥ 10

�34cos (mat) e cm

QCD Axion

⇣afaGG̃

⌘

Beff / 10

�16cos (mat) T

HN � afa

ma ~va.~SN




General Axions

~v




⇣@µafa

N̄�µ�5N⌘





�34cos (mat) e cm

Apply electric field, spin rotates

~E+

-

QCD Axion

⇣afaGG̃

⌘

Beff / 10

�16cos (mat) T

HN � afa

ma ~va.~SN




General Axions

~v




⇣@µafa

N̄�µ�5N⌘





�34cos (mat) e cm


~E+

-

QCD Axion

⇣afaGG̃

⌘

Beff / 10

�16cos (mat) T

HN � afa

ma ~va.~SN




General Axions

~v




Measure SpinRotation,

detect Axion⇣

@µafa

N̄�µ�5N⌘





�34cos (mat) e cm


~E+

-

QCD Axion

⇣afaGG̃

⌘

Beff / 10

�16cos (mat) T

HN � afa

ma ~va.~SN


�Bext

�µ

Larmor frequency = axion mass ➔ resonant enhancement

CASPEr

axion “wind” ~vaOR ~E⇤

Axion affects physics of nucleus, NMR is sensitive probe


SQUIDpickuploop

�Bext

�µ

Larmor frequency = axion mass ➔ resonant enhancement

CASPEr

axion “wind” ~vaOR ~E⇤

SQUID measures resulting transverse magnetizationNMR well established technology, noise understood, similar setup to previous experiments

Example materials: LXe, ferroelectric PbTiO3, many others

Axion affects physics of nucleus, NMR is sensitive probe


Magnetization Noise

a material sample has magnetization noise

noise arises from quantum spin projection

every spin necessarily has random quantum projection onto transverse direction

�Bext

�µ

18

Mn(!) ⇠ µN

r3

pnr3hS(!)i ⇠ µN

pnV hS(!)i

S (!) is Lorentzian, peaked at Larmor frequency, bandwidth ~ 1/T2

T. Sleator, E. L. Hahn, C. Hilbert, and J. Clarke, PRL 55, 171742 (1985)


CASPEr-General Axions

L � 10 cmtake sample size:

many options for increasing sensitivity

M(t) ⇡ npµ⇣gaNN

p2⇢DMv

⌘ sin ((2µBext

�ma) t)

2µBext

�masin (2µB

ext

t)

p ⇡ 1

for axion wind and other types of DM:

19

(or multiple loops over smaller sample)


gaNN (⇥µa) N̄�µ�5N

SN 1987A

New Force

QCD Axion

ALP DM ADMX

10!14 10!12 10!10 10!8 10!6 10!4 10!2 100

10!20

10!18

10!16

10!14

10!12

10!10

10!8

10!6

10!4

102 104 106 108 1010 1012 1014

mass !eV"

g aNN!GeV

!1 "frequency !Hz"

phase 1 phase 2

~ year to scan one decade of frequency


magnetization noise


gaNN (⇥µa) N̄�µ�5N

CASPEr NOWexisting experiments

e.g. He/Xe comag

SN 1987A

New Force

QCD Axion

ALP DM ADMX

10!14 10!12 10!10 10!8 10!6 10!4 10!2 100

10!20

10!18

10!16

10!14

10!12

10!10

10!8

10!6

10!4

102 104 106 108 1010 1012 1014

mass !eV"

g aNN!GeV

!1 "frequency !Hz"

phase 1 phase 2

~ year to scan one decade of frequency


magnetization noise


CASPEr-QCD Axion

but atomic magnetometers ~ 10�17 T�Hz

10�16 T�Hz

➜ we take SQUID magnetometer:L � 10 cmtake sample size:

example material: �s � 10�2µ = 0.6µN207Pb =�

many options for increasing sensitivity

M(t) � nµ�SdnE�psin ((2µBext �ma) t)

2µBext �masin (2µBextt)

21

(or multiple loops over smaller sample)

M.V. Romalis

5

n E⇤ p T2

Max. Bext

Phase 1 1022 1

cm

3

3⇥ 108 V

cm

10�3 1 ms 10 T

Phase 2 1022 1

cm

3

3⇥ 108 V

cm

1 1 s 20 T

TABLE I: Parameters for Phase 1 and 2 regions in Figure 2.

magnetization noise (calculated in the Supplemental Materials), which could be reached if the magnetometer isimproved. The sample magnetization noise limit for the phase 1 experiment is not shown, but was calculated and isnot a limiting factor for phase 1. Note the phase 2 noise is small enough that it would not hinder detection of theQCD axion over the entire relevant frequency range.

For both phases we assumed the nucleus is 207Pb so that ✏s ⇡ 10�2 and the nuclear magnetic moment is µ = 0.6µN ,where µN = 3.15 ⇥ 10�14 MeV

T . Other parameters are shown in Table I. With these parameters, the limit on thesensitivity of both phase 1 and phase 2 experiments is set by the magnetometer sensitivity. The upper limit on theALP mass for the solid curves in Fig. 2 comes from requiring that the Larmor frequency be less than the maximumachievable frequency using a 10 T (phase 1) or 20 T (phase 2) applied B-field. The change in slope in the solid phase2 sensitivity curve comes when ⌧a = T2.

Phase 1 can cover a large piece of unexplored ALP parameter space. Phase 2 reaches the QCD axion for couplingconstants fa & 1016 GeV. If the magnetometer is improved and the magnetization noise limit reached, the QCD axioncould possibly be detected over the entire region fa & 3 ⇥ 1013 GeV. Significant technological challenges have to beovercome before this experiment reaches the ultimate sensitivity goals of Phase 2. The technological challenges ofPhase 1 are relatively easier to overcome and it can immediately begin cutting into ALP dark matter in the allowedregion of parameter space in Fig. 2 [17]. In fact, modifications of current EDM techniques that are optimized tosearch for a time varying signal can also begin constraining this parameter space.

IV. NOISE SOURCES

Transverse, time-varying magnetic fields that vary at frequencies in the measurement bandwidth are a source ofnoise. The fundamental source of noise is due to the quantum projection of each spin along the transverse directionscausing a transverse magnetization of the sample [42, 55]. This noise can be decreased by using larger sample volumes.Note that the sensitivity limit set by this fundamental magnetization noise (red dashed line) in Fig. 2 would allowdetection of the QCD axion over the entire frequency range accessible in this experiment.

A more detailed discussion of this projection noise, as well as other, technical, sources of experimental noise, suchas vibrations, is included in the Appendix. Choosing an optimal experimental strategy requires engineering studiesthat are left for future work. The static EDM searches require control over the dc components of these magneticfields, while our experiment requires control over the ac component at relatively high frequencies & kHz. Such controlshould be easier to achieve and it thus seems plausible that these sources of noise can be adequately suppressed. Forexample, control over ac magnetic-field noise at comparable levels in the background of a large external field has beendemonstrated in current cavity searches for the axion [34].

V. CONCLUSIONS

The proposed experiment appears to have su�cient sensitivity to detect axion dark matter, especially when fa is inthe theoretically favored range between the grand unified and Planck scales. It is also sensitive to ALPs that couple tothe nucleon EDM, probing sources of symmetry breaking in the ALP sector. The signal in this solid-state NMR-basedexperiment benefits from the large number (& 1022) of spins in a solid state system. In conjunction with precisionmagnetometers, this approach enables sensitivity to this region of parameter space using current technology. In fact,with some improvements in magnetometer sensitivity, this technique could be used to detect the QCD axion withfa essentially all the way down to the region that can be probed by microwave cavity experiments such as ADMX.Together then, these techniques may cover almost the entire QCD axion dark matter range.

We do not know of any other approach that can be sensitive to this region of parameter space using presenttechnology. Previous proposals that were aimed at searching for the time varying EDM induced by ALP dark matterwere focussed on detecting them through interferometry in ultra-cold molecular systems. These proposals requiresignificant technology development to reach the sensitivity necessary to detect QCD axion dark matter, primarily

10221

cm3 3⇥ 108V

cm


ADMX

QCD Axion

SN 1987A

Static EDM

ALP DM

10!14 10!12 10!10 10!8 10!6 10!4 10!2 100

10!20

10!15

10!10

10!5

102 104 106 108 1010 1012 1014

mass !eV"

gd!GeV

!2"frequency !Hz"

dN = � i

2gd a N̄⇥µ��5NFµ�

phase 2phase 1

magnetization noise

Verify signal with spatial coherence of axion field

CASPEr-QCD Axion


Dark Photon Detection witha Radio

Peter GrahamKent Irwin

Saptarshi ChaudhuriJeremy Mardon

Yue Zhao

with

(to appear)


Dark Photon Dark Matter

Many theories/vacua have additional, decoupled sectors, new U(1)’s

Natural coupling (dim. 4 operator): L � "FF 0

mass basis:

photon with small mass and suppressed couplings to all charged particles

L = �1

4

�Fµ⌫F

µ⌫ + F 0µ⌫F

0µ⌫�+ 1

2m2

�0A0µA

0µ � eJµEM

�Aµ + "A0

µ

�





mass basis:


L = �1

4

�Fµ⌫F

µ⌫ + F 0µ⌫F

0µ⌫�+ 1

2m2

�0A0µA

0µ � eJµEM

�Aµ + "A0

µ

�

oscillating E’ field(dark matter)





mass basis:


L = �1

4

�Fµ⌫F

µ⌫ + F 0µ⌫F

0µ⌫�+ 1

2m2

�0A0µA

0µ � eJµEM

�Aµ + "A0

µ

�


can drive currentbehind EM shield


Annoying Fact

L = �1

4

�Fµ⌫F

µ⌫ + F 0µ⌫F

0µ⌫�+ 1

2m2

�0A0µA

0µ � eJµEM

�Aµ + "A0

µ

�


Annoying Fact

L = �1

4

�Fµ⌫F

µ⌫ + F 0µ⌫F

0µ⌫�+ 1

2m2

�0A0µA

0µ � eJµEM

�Aµ + "A0

µ

�

Send m0

� ! 0

L = �1

4

�Fµ⌫F

µ⌫ + F 0µ⌫F

0µ⌫�� eJµEM

�Aµ + "A0

µ

�


Annoying Fact

L = �1

4

�Fµ⌫F

µ⌫ + F 0µ⌫F

0µ⌫�+ 1

2m2

�0A0µA

0µ � eJµEM

�Aµ + "A0

µ

�

Only one linear combination couples to charged particles

Orthogonal component is completely sterile

Send m0

� ! 0

L = �1

4

�Fµ⌫F

µ⌫ + F 0µ⌫F

0µ⌫�� eJµEM

�Aµ + "A0

µ

�


Annoying Fact

L = �1

4

�Fµ⌫F

µ⌫ + F 0µ⌫F

0µ⌫�+ 1

2m2

�0A0µA

0µ � eJµEM

�Aµ + "A0

µ

�

Only one linear combination couples to charged particles

Orthogonal component is completely sterile

Send m0

� ! 0

L = �1

4

�Fµ⌫F

µ⌫ + F 0µ⌫F

0µ⌫�� eJµEM

�Aµ + "A0

µ

�

Physical e↵ects decouple m0

� ! 0


shieldoscillating E’ field

(dark matter)

L

CTunable resonant LC circuit

(a radio)

Dark Matter Radio Station


Metal box to shield

backgrounds

oscillating E’ field

conduction electrons in wall

respond to E’ field,generating E and B

fields


oscillating E’ field

conduction electrons in wall

respond to E’ field,generating E and B

fields

net effect is a B field inside the

box

B ~ ε (mγ’ R) × 10-5 T

oscillates at ω = mγ’

Metal box to shield

backgrounds


Projected Sensitivity (Preliminary)

-16 -15 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0-18

-16

-14

-12

-10

-8

-6

-4

-2

0 Hz kHz MHz GHz THz

log10 mg'@eVD

log 10∂

f = mg'ê2pJupiter Earth

CMB

Coulomb

HB

Sun

CROWSNo Hidden-Photon DM

Axion DMsearchResonant

LC circuit

Stage 1

Stage 1

Stage 2

LC oscillator search: size ~ 1m!! Q~106 ~1 month scan per decade

Stage 1: room temp Stage 2: T~0.1K


B-L Dark Matter with Accelerometers

(under development)

Peter GrahamJeremy Mardon

Yue Zhao

with


B-L Dark Matter

Other than electromagnetism, only other anomaly free standard model current

Protons, Neutrons, Electrons and Neutrinos are all charged

L = �1

4

�F 0µ⌫F

0µ⌫�+ 1

2m2

�0A0µA

0µ � gJµB�LA

0µ

Electrically neutral atoms are charged under B-L

Force experiments constrain g < 10-21


B-L Dark Matter

Other than electromagnetism, only other anomaly free standard model current


can accelerate atoms

Protons, Neutrons, Electrons and Neutrinos are all charged

L = �1

4

�F 0µ⌫F

0µ⌫�+ 1

2m2

�0A0µA

0µ � gJµB�LA

0µ

Electrically neutral atoms are charged under B-L

Force experiments constrain g < 10-21


B-L Dark Matter


B-L Dark Matter

Seems promising!

Dark Matter force depends upon net neutron numberTime dependent equivalence principle violation!

Atomic EP Test

Improvements possible with resonant schemes


Conclusions


WIMPsScalable

Goodman & Witten (1985): � � 10�38 cm2

Z

h

W


WIMPsScalable

Goodman & Witten (1985): � � 10�38 cm2

Z

h

WSimilar approach seems possible in searching for oscillating fields



10-22 eV10-43 GeV 1019 GeV100 eV 102 GeV

(SM)

bosonic WIMPs

10-6 eV10-15 eV(GHz)(Hz)(yr-1)



10-22 eV10-43 GeV 1019 GeV100 eV 102 GeV

(SM)

bosonic WIMPs

10-6 eV10-15 eV(GHz)(Hz)(yr-1)

Search for single, hard particle scattering

� �

N N



10-22 eV10-43 GeV 1019 GeV100 eV 102 GeV

(SM)

bosonic WIMPs

10-6 eV10-15 eV(GHz)(Hz)(yr-1)


� �

N N

Time dependent momentsof coherent classical field

Interactions restricted by symmetry

Frequencies can naturally be lab accessible (Hz - GHz)

Lab-scale experiments



10-22 eV10-43 GeV 1019 GeV100 eV 102 GeV

(SM)

bosonic WIMPs

10-6 eV10-15 eV(GHz)(Hz)(yr-1)


� �

N N

Time dependent momentsof coherent classical field

Interactions restricted by symmetry

Frequencies can naturally be lab accessible (Hz - GHz)

How do we cover full range?

Lab-scale experiments


Backup


A Different Operator For Axion Detection

Strong CP problem: creates a nucleon EDM d ⇥ 3� 10�16 � e cmL � � G �G

So how can we detect high fa axions?

37

the axion: creates a nucleon EDM d ⇥ 3� 10�16 a

fae cmL � a

faG eG


A Different Operator For Axion Detection

Strong CP problem: creates a nucleon EDM d ⇥ 3� 10�16 � e cmL � � G �G

witha(t) � a0 cos (mat) ma �(200 MeV)2

fa� MHz

�1016 GeV

fa

⇥

axion gives all nucleons an oscillating EDM (kHz-GHz) independent of fa,a non-derivative operator

axion dark matter �DM � m2aa2 � (200MeV)4

�a

fa

⇥2

� 0.3GeVcm3

so today:�

a

fa

⇥⇥ 3� 10�19 independent of fa

So how can we detect high fa axions?

37

the axion: creates a nucleon EDM d ⇥ 3� 10�16 a

fae cmL � a

faG eG


Axions and the CMB

if symmetry broken before inflation → inflation can induce isocurvature perturbations of axion,weak constraint on ALPs probed by CASPEr.

Assuming BICEP detected gravitational waves in the CMB (some tension with Planck):

if symmetry broken after inflation → topological defects (strings + domain walls), constrained by observations

38

Hinf ⇠ 1014 GeV


Axions and the CMB




38

Hinf ⇠ 1014 GeV


Axions and the CMB




38

Requires knowing physics all the way up to GUT scale ⇠ 1016 GeV

for QCD axion, constrains one cosmological history.

many others possible.

Hinf ⇠ 1014 GeV


QCD Axion and BICEP

39

Need a high temperature, transient mass, sometime before QCD phase transition.

Need not be on during inflation.

Axion oscillates earlier, damps to high temperature

minimum.

Misalignment of minima gives axion dark matter.

Dark matter from choice of parameters instead of initial conditions.

a

V


QCD Axion and BICEP

40


a

V

e.g. thermal monopole density,high temperature mass,and many others

Fischler & Preskill (1983)

e.g. Kaplan & Zurek (2005), Jeong & Takahashi (2013), G. Dvali (1995)

QCD axion offers unique probe of high energy cosmology,an era difficult even for gravitational wave detectors

Bound depends upon high energy physics, while strong CP, axion dark matter rely upon low energy physics.


QCD Axion and BICEP

40


a

V







QCD Axion and BICEP

40


a

V







Two Tenets of Axion Cosmology

1. ma << H: Field is constant as universe expands. Retains energy

density.

2. ma >> H: Field oscillates, amplitude damps, energy

density decreases like matter.



a

V


density.





a

V


density.



ma can be strongly temperature dependent (e.g. QCD axion)

If ma is on earlier, there is more damping, fewer overproduction issues


QCD Axion Over-Production

inflationary cosmology does not prefer flat prior in ϴi over flat in fa

ai

ma rapidly turns on

⇤QCDaround ~

fa ⇤QCDRate set by and



a

V


ai

ma rapidly turns on

⇤QCDaround ~




a

V

requires late time entropy production eases this

�ai

fa

⇥ ⇤fa

MPl� 10�3.5

ai

fa� 1

fa

MPl� 10�7 ai

fa� 10�2fa

MPl� 10�3e.g. or


ai

ma rapidly turns on

⇤QCDaround ~




a

V

requires late time entropy production eases this

�ai

fa

⇥ ⇤fa

MPl� 10�3.5

ai

fa� 1

fa

MPl� 10�7 ai

fa� 10�2fa

MPl� 10�3e.g. or


ai

all fa in DM range (all axion masses ≲ meV) equally reasonable


ma rapidly turns on

⇤QCDaround ~


Bounds on axion-like-particles are highly model dependent14년 10월 18일 토요일

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Detecting Ultra-light Dark Matter with Precision Metrology · 2018-03-05 · Detecting Ultra-light Dark Matter with Precision Metrology Surjeet Rajendran, UC Berkeley 14년 10월