Gravitational waves from axions Fumi Takahashi (Tohoku) Sep. 26th - - PowerPoint PPT Presentation

Gravitational waves from axions

Fumi Takahashi (Tohoku)

• Sep. 26th 2016 @Fermilab

Joint KEK Theory Fermilab Theory Meeting Higaki, Jeong, Kitajima, FT, 1512.05295, 1603.02090, Higaki, Jeong, Kitajima, Sekiguchi, FT, 1606.05552, Takeshi Kobayashi, FT, 1607.04294

The Strong CP Problem

Lθ = θ g2

s

32π2 Gaµν ˜ Ga

µν

Experimental bound from neutron electric dipole moment reads

|θ| < 10−10

Why is so small is the strong CP problem.

θ

¯ θ ≡ θ − arg det (MuMd)

• cf. More precisely, the physical strong CP phase is

which makes the problem even more puzzling.

In the Peccei-Quinn solution, the strong CP phase is promoted to a dynamical variable:

Peccei, Quinn `77, Weinberg `78, Wilczek `78

a

T ΛQCD T ΛQCD

a

Lθ = ✓ θ + a fa ◆ g2

s

32π2 Gaµν ˜ Ga

µν

ma ' 6 ⇥ 10−6 eV ✓ fa 1012 GeV ◆−1

Axion-like particles (ALPS) do not satisfy the above relation.

In the PQ mechanism, the axion DM is produced as coherent oscillations [misalignment mechanism].

a

T ΛQCD T ΛQCD

a

Ωah2 = 0.18 θ2

i

✓ fa 1012 GeV ◆1.19 ✓ ΛQCD 400 MeV ◆

+ thermal production for small fa + non-thermal production from saxion decay

CDM HDM DR

Production

Terrestrial Celestial Cosmological

Detection

Direct Indirect

ALPS,OSQAR, PVLAS,

CAST, IAXO Solar axion

LSTW, Photon pol.

Axion DM

ADMX, CAPP,ORPHEUS

LC-circuits, CASPEr,

XMASS, EDELWISE,XENON100.

Spectral irreg. Transparency

Fermi, IACT.

Excessive cooling

• f WD, RGB, HB, NS

Isocurvature, DR, spectral distortion, caustics, GW, etc.

Planck, COrE+, PIXIE

Fifth force

ARIADNE

Production

Terrestrial Celestial Cosmological

Detection

Direct Indirect

ALPS,OSQAR, PVLAS,

CAST, IAXO Solar axion

LSTW, Photon pol.

Axion DM

ADMX, CAPP,ORPHEUS

LC-circuits, CASPEr,

XMASS, EDELWISE,XENON100.

Spectral irreg. Transparency

Fermi, IACT.

Excessive cooling

• f WD, RGB, HB, NS

Tension with high-scale inflation?

Isocurvature, DR, spectral distortion, caustics, GW, etc.

Planck, COrE+, PIXIE

Fifth force

ARIADNE

Axion isocurvature perturbations

x ρ photon DM/baryon Adiabatic perturbation x ρ photon DM/baryon Isocurvature perturbation

Planck 2015 (Planck TT, TE, EE + lowP)

βiso = PS PR + PS < 0.038 (95% CL)

S = Ωa ΩCDM δΩa Ωa = Ωa ΩCDM 2δθi θi = Ωa ΩCDM Hinf πθifa

Adiabatic Isocurvature

CMB angular power spectrum

Planck

Adiabatic Isocurvature

CMB angular power spectrum

Planck

(Taken from Kawasaki’s slide)

Adiabatic Isocurvature

CMB angular power spectrum

S = 2 Ωa ΩCDM δθi θi = Ωa ΩCDM Hinf πθifa

∼ cos(kcst)

∼ sin(kcst)

10-3 10-2 10-1 100 101 102 103 104 105 106 107 108 109

r = 0.1

fa GeV / H

GeV

/

inf

r = 1 r = 0.01

109 1010 1011 1012 1013 1014

r = Ωa/ΩDM

Isocurvature constraint on Hinf

Kobayashi, Kurematsu, FT, 1304.0922

Axion DM is in severe tension w/ many inflation models!

10-3 10-2 10-1 100 101 102 103 104 105 106 107 108 109

r = 0.1

fa GeV / H

GeV

/

inf

r = 1 r = 0.01

109 1010 1011 1012 1013 1014

r = Ωa/ΩDM

Isocurvature constraint on Hinf

Kobayashi, Kurematsu, FT, 1304.0922

Hinf 107−8 GeV

Axion DM is in severe tension w/ many inflation models!

10-3 10-2 10-1 100 101 102 103 104 105 106 107 108 109

r = 0.1

fa GeV / H

GeV

/

inf

r = 1 r = 0.01

109 1010 1011 1012 1013 1014

r = Ωa/ΩDM

Isocurvature constraint on Hinf

Kobayashi, Kurematsu, FT, 1304.0922

Hinf 107−8 GeV

Anharmonic effects

Axion DM is in severe tension w/ many inflation models!

Solutions to isocuvature problem

1)Restoration of Peccei-Quinn symmetry during inflation.

Figure taken from

• M. Kawasaki’s slide

Linde and Lyth `90 Lyth and Stewart `92

1)Restoration of Peccei-Quinn symmetry during inflation.

• Axions are produced from domain walls and

axion DM is possible for fa = 1010GeV.

Hiramatsu, Kawasaki, Saikawa and Sekiguchi, 1202.5851,1207.3166

Linde and Lyth `90 Lyth and Stewart `92

Solutions to isocuvature problem

1)Restoration of Peccei-Quinn symmetry during inflation.

• Axions are produced from domain walls and

axion DM is possible for fa = 1010GeV. 2)Dynamical axion decay constant

Hiramatsu, Kawasaki, Saikawa and Sekiguchi, 1202.5851,1207.3166

Axion: phase component Saxion: radial component

Linde and Lyth `90 Linde, `91 Linde and Lyth `90 Lyth and Stewart `92

Solutions to isocuvature problem

δθ = const.

δa = δainf ✓ f0 finf ◆ finf f0

At small scales, however, axion fluctuations can be enhanced significantly!

Takeshi Kobayashi, FT, 1607.04294

Φ = f + s √ 2 eia/f

The enhancement of axion fluctuations at small scales can be understood by noting that “angular momentum” is conserved when the decay constant changes. δ ˙ θ 6= 0

δ ˙ θf > δ ˙ θi

finf finf

f0 f0

3)MSW-like resonance btw. axion and ALP.

Solutions to isocuvature problem

Hill, Ross `88, Kitajima, FT 1411.2011

Level crossing!

mat

1 10 100 1 0.1 0.01

m1/ma m2/ma

' ma(T) ' mH ' mH ' ma(T = 0)

m2

H < m2 a(T = 0)

The level crossing necessarily occurs if .

3)MSW-like resonance btw. axion and ALP.

Solutions to isocuvature problem

Hill, Ross `88, Kitajima, FT 1411.2011

Level crossing!

mat

1 10 100 1 0.1 0.01

m1/ma m2/ma

' ma(T) ' mH ' mH ' ma(T = 0)

m2

H < m2 a(T = 0)

The level crossing necessarily occurs if .

3)MSW-like resonance btw. axion and ALP.

Solutions to isocuvature problem

Hill, Ross `88, Kitajima, FT 1411.2011

Level crossing!

mat

1 10 100 1 0.1 0.01

m1/ma m2/ma

' ma(T) ' mH ' mH ' ma(T = 0)

m2

H < m2 a(T = 0)

The level crossing necessarily occurs if .

3)MSW-like resonance btw. axion and ALP.

Solutions to isocuvature problem

Hill, Ross `88, Kitajima, FT 1411.2011

4)Heavy axions during inflation

• Stronger QCD during inflation
• Extra explicit PQ breaking

Jeong, FT 1304.8131 Choi et al, 1505.00306 Higaki, Jeong, FT, 1403.4186, Barr and J.E.Kim, 1407.4311 FT and Yamada 1507.06387 Kawasaki, FT, Yamada 1511.05030 Nomura, Rajendran, Sanches, 1511.06347 Dine, Anisimov hep-ph/0405256

• cf. Dvali, `95,

m2

a & H2 inf

a

The extra PQ breaking term must be sufficiently suppressed at present.

e.g. Witten effect

Aligned QCD axion

Higaki, Jeong, Kitajima, FT, 1512.05295, 1603.02090, Higaki, Jeong, Kitajima, Sekiguchi, FT, 1606.05552

No axion isocurvature perturbations if the PQ symmetry is restored during or after inflation.

Is high TR or Hinf necessary?

Classical axion window:

TR, Hinf & Fa

109 GeV . Fa . 1012 GeV

Decay constant = PQ breaking scale?

However, this is not necessarily the case. If there are multiple PQ scalars,

Φ : PQ scalar

V (Φ)

In a simple set-up, is possible.

hΦi ⇠ Fa

hΦi ⌧ Fa

Alignment mechanism

The decay constant can be enhanced by the largest hierarchy among the PQ charges in the alignment mechanism,

Φ2

Φ1

Clockwork axion model with N=2:

Φi = fi + si √ 2 eiai/fi

fa = q 32f 2

1 + f 2 2 ,

a = 3f1a1 − f2a2 fa

Kim, Nilles, Peloso, hep-ph/0409138 See also Sikivie `86

Choi, Kim, Yun, 1404.6209, Higaki, FT, 1404.6923 Harigaya and Ibe, 1407.4893, Choi and Im, 1511.00132, Kaplan and Rattzzi, 1511.01827.

V =

2

X

i=1

(−m2

i |Φi|2 + i|Φi|4)

+ ✏

• Φ1Φ3

2 + h.c.

Alignment with multiple axions

Choi, Kim, Yun, 1404.6209, Higaki, FT, 1404.6923 Harigaya and Ibe, 1407.4893, Choi and Im, 1511.00132, Kaplan and Rattzzi, 1511.01827.

Alignment with multiple axions

Choi, Kim, Yun, 1404.6209, Higaki, FT, 1404.6923 Harigaya and Ibe, 1407.4893, Choi and Im, 1511.00132, Kaplan and Rattzzi, 1511.01827.

fa ∼ 3Nf

V =

N

X

i=1

• −m2

i |Φi|2 + λi|Φi|4

+

N−1

X

i=1

✏

• ΦiΦ3

i+1 + h.c.

Aligned QCD axion

Higaki, Kitajima, FT, 1408.3936 , Higaki, Jeong, Kitajima, FT, 1512.05295.

∆L = yqΦN ¯ QQ.

fi = f

for

a becomes the QCD axion with

f 2

a = N

X

i=1

@

N

Y

j=i

n2

j

1 A f 2

i ,

with

Adding a coupling to the PQ quarks N-1 of the N axions becomes massive, leaving one massless mode, a. In general, if we have

Fa = fa ∼ 3Nf

There are many axions and saxions at f (e.g. at TeV scale) much lower than the conventional axion window!

V (ai) = −

N−1

X

i=1

Λ4

i cos

✓ai fi + ni ai+1 fi+1 ◆ , a = 1 fa

N

X

i=1

(−1)i−1 @

N

Y

j=i

nj 1 A fiai,

Choi, Kim, Yun, 1404.6209,

Quality of U(1)PQ

Higaki, Jeong, Kitajima, FT, 1512.05295, 1603.02090,

In the conventional scenario, one needs to suppress PQ breaking terms up to high order In the aligned QCD axion models, the PQ symmetry breaking scale is much smaller, which relaxes the required high quality of the PQ symmetry.

Carpenter, Dine, Festuccia, `09

hΦii ⌧ Fa

n > 10

for

e.g.

Φn+4 M n

p

hΦi ⇠ Fa ⇠ 1012 GeV

Cosmic strings appear when the PQ symmetry is broken, and their tension is dominated by the gradient energy

• utside the core.

In the aligned QCD axion, the tension of each string is of

• rder f 2, much smaller than Fa2. Any correspondence

between the two?

Topological defects

µ ∼ µcore + Z R

δ

• 1

r ∂Φ ∂θ

• 2

2πrdr ≈ πf 2 ln ✓R δ ◆ ,

R

δ

: distance b/w strings : core radius

(credit: M. Hindmarsh)

Higaki, Jeong, Kitajima, Sekiguchi, FT, 1606.05552

Φ = f √ 2eiθ

in cylindrical coordinate

Topological defects

There is an isolated string-wall solution, “string bundle”, i.e., many strings glued by domain walls:

Higaki, Jeong, Kitajima, Sekiguchi, FT, 1606.05552

N = 2

N = 3

The aligned structure in the field space exhibits itself in the real space!

string wall

Topological defects

Higaki, Jeong, Kitajima, Sekiguchi, FT, 1606.05552

N = 2

The aligned structure in the field space exhibits itself in the real space!

There is an isolated string-wall solution, “string bundle”, where many strings are glued by domain walls:

Topological defects

Higaki, Jeong, Kitajima, Sekiguchi, FT, 1606.05552

The tension of the isolated string-wall system is equal to that of a single PQ field.

'

µeff ' π(32(N−1)f 2

1 + · · · + 32f 2 N−1 + f 2 N) ln

✓R δ ◆ = πF 2

a ln

✓R δ ◆

Topological defects

Higaki, Jeong, Kitajima, Sekiguchi, FT, 1606.05552

For large N, however, such isolated string bundles are probably not produced in the Universe, as they require exponentially large hierarchy in the cosmic string distribution.

• #(Si) − #( ¯

Si)

• = O(1).
• #(Si) − #( ¯

Si)

• = 3N−i

Initial condition,

• r scaling law:

The string-wall network will be infinitely large.

Numerical simulation

Higaki, Jeong, Kitajima, Sekiguchi, FT, 1606.05552

N = 2

Strings glued by walls remain, and domain walls disappear in the case of N=2.

Numerical simulation

Higaki, Jeong, Kitajima, Sekiguchi, FT, 1606.05552

N = 2

Strings glued by walls remain, and domain walls disappear in the case of N=2.

Numerical simulation

Higaki, Jeong, Kitajima, Sekiguchi, FT, 1606.05552

N = 2

Strings glued by walls remain, and domain walls disappear in the case of N=2.

Numerical simulation

Higaki, Jeong, Kitajima, Sekiguchi, FT, 1606.05552

N = 3

Domain walls remain, stretching between strings, in the case of N = 2. They follow the scaling law.

Numerical simulation

Higaki, Jeong, Kitajima, Sekiguchi, FT, 1606.05552

N = 3

Domain walls remain, stretching between strings, in the case of N > 2. They follow the scaling law.

Numerical simulation

Higaki, Jeong, Kitajima, Sekiguchi, FT, 1606.05552

N = 3

Domain walls remain, stretching between strings, in the case of N > 2. They follow the scaling law.

Gravitational waves from domain walls

The domain walls annihilate at the QCD phase transition, producing a significant amount of gravitational waves.

Higaki, Jeong, Kitajima, Sekiguchi, FT, 1606.05552 Hiramatsu, Kawasaki, Saikawa, Sekiguchi, 1202.5851

Gravitational waves

Gravitational waves from domain walls

Higaki, Jeong, Kitajima, Sekiguchi, FT, 1606.05552

The peak frequency is determined by the Hubble horizon at the QCD phase transition. The energy density of walls: ρdw ∼ σH The tension of walls: σ = 8maHf 2

maH ∼ √✏f

Amount of GWs:

EGW ∼ GM 2 R ∼ G(σH−2)2 H−1

Gravitational waves from domain walls

Higaki, Jeong, Kitajima, Sekiguchi, FT, 1606.05552

The peak frequency is determined by the Hubble horizon at the QCD phase transition.

ΩGW (⌫peak)h2 ' 2 ⇥ 10−11✏ ⇣ g∗ 80 ⌘− 4

3 ✓ Tann

1 GeV ◆−4 ✓ f 100 TeV ◆6

GW density parameter: with a frequency dependence, ΩGW (ν) ∝ ν3 , for . ν < νpeak

Hiramatsu, Kawasaki, Saikawa, 1309.5001

Gravitational waves from domain walls

Higaki, Jeong, Kitajima, Sekiguchi, FT, 1606.05552

Gravitational waves from domain walls

Higaki, Jeong, Kitajima, Sekiguchi, FT, 1606.05552

Frequency corresponding to the Hubble radius at the QCD phase transition.

Gravitational waves from domain walls

Higaki, Jeong, Kitajima, Sekiguchi, FT, 1606.05552

ΩGW (⌫peak)h2 ' 2 ⇥ 10−11✏ ⇣ g∗ 80 ⌘− 4

3 ✓ Tann

1 GeV ◆−4 ✓ f 100 TeV ◆6

GW density parameter: with a frequency dependence, ΩGW (ν) ∝ ν3 , for . ν < νpeak

Hiramatsu, Kawasaki, Saikawa, 1309.5001

Pulsar timing constraint:

ΩGW h2 < 2.3 × 10−10

at

ν1yr ' 3 ⇥ 10−8 Hz

• P. D. Lasky et al. 1511.05994

credit: D. J. Champion

Constraint on the PQ breaking scale:

f . 200 TeV × ✏−1/6

Will be improved by a factor of 2 by future SKA.

Summary

The axion isocurvature problem point to either (1)low-scale inflation,

• r

(2)various interesting (exotic) possibilities, such as PQ symmetry restoration, axion string-wall system, hidden monopoles, many (s)axions, GWs.

Hinf . 107−8 GeV

Summary

✓In the aligned QCD axion, the PQ symmetry is likely restored, avoiding the isocurvature bound. ✓Robust against Planck suppressed PQ symmetry breaking terms. ✓Domain walls remain until the QCD phase transition, and their annihilation produces nano-Hz GW, which can be searched for by the pulsar timing array.

Φ2

Φ1