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

Gravitational waves from axions Fumi Takahashi (Tohoku) Sep. 26th 2016 @Fermilab Higaki, Jeong, Kitajima, FT, 1512.05295, 1603.02090, Higaki, Jeong, Kitajima, Sekiguchi, FT, 1606.05552, Takeshi Kobayashi, FT, 1607.04294 Joint KEK Theory Fermilab Theory Meeting

Experimental bound from neutron electric dipole The Strong CP Problem moment reads Why is so small is the strong CP problem. cf. More precisely, the physical strong CP phase is which makes the problem even more puzzling. L θ = θ g 2 32 π 2 G aµ ν ˜ s G a µ ν | θ | < 10 − 10 θ ¯ θ ≡ θ − arg det ( M u M d )

In the Peccei-Quinn solution, the strong CP phase is promoted to a dynamical variable: Axion-like particles (ALPS) do not satisfy the above relation. Peccei, Quinn `77, Weinberg `78, Wilczek `78 g 2 ✓ ◆ θ + a 32 π 2 G aµ ν ˜ s G a L θ = µ ν f a T � Λ QCD T � Λ QCD a a ◆ − 1 ✓ f a m a ' 6 ⇥ 10 − 6 eV 10 12 GeV

In the PQ mechanism, the axion DM is produced as coherent oscillations [misalignment mechanism]. HDM CDM DR ◆ 1 . 19 ✓ ✓ ◆ f a Λ QCD Ω a h 2 = 0 . 18 θ 2 10 12 GeV i 400 MeV + thermal production for small f a + non-thermal production from saxion decay T � Λ QCD T � Λ QCD a a

Production Solar axion Spectral irreg. of WD, RGB, HB, NS Isocurvature, DR, Terrestrial Axion DM Photon pol. LSTW, spectral distortion, Excessive cooling caustics, GW, etc. Fifth force Indirect Direct Detection Cosmological Celestial Transparency ADMX, CAPP,ORPHEUS LC-circuits, CASPEr, CAST, IAXO ALPS,OSQAR, XMASS, EDELWISE,XENON100. PVLAS, ARIADNE Planck, COrE+, PIXIE Fermi, IACT.

Production Tension with Excessive cooling high-scale inflation? Transparency Spectral irreg. Isocurvature, DR, Terrestrial Axion DM Photon pol. LSTW, Solar axion spectral distortion, caustics, GW, etc. Fifth force Indirect Direct Detection Cosmological Celestial of WD, RGB, HB, NS ADMX, CAPP,ORPHEUS LC-circuits, CASPEr, CAST, IAXO ALPS,OSQAR, XMASS, EDELWISE,XENON100. PVLAS, ARIADNE Planck, COrE+, PIXIE Fermi, IACT.

(Planck TT, TE, EE + lowP) Axion isocurvature perturbations Planck 2015 Adiabatic perturbation Isocurvature perturbation ρ ρ photon photon DM/baryon DM/baryon x x δ Ω a 2 δθ i Ω a Ω a Ω a H inf S = = = Ω CDM Ω a Ω CDM θ i Ω CDM πθ i f a P S β iso = < 0 . 038 (95% CL) P R + P S

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 ∼ cos( kc s t ) ∼ sin( kc s t ) Ω a δθ i Ω a H inf S = 2 = Ω CDM θ i Ω CDM πθ i f a

Axion DM is in severe tension w/ many inflation models! Isocurvature constraint on H inf r = 0.01 10 9 r = 0.1 10 8 r = Ω a / Ω DM r = 1 10 7 10 6 GeV 10 5 10 4 / 10 3 inf 10 2 H 10 1 10 0 10 - 1 10 - 2 10 - 3 10 9 10 10 10 11 10 12 10 13 10 14 f a GeV Kobayashi, Kurematsu, FT, 1304.0922 /

Axion DM is in severe tension w/ many inflation models! Isocurvature constraint on H inf r = 0.01 10 9 r = 0.1 10 8 r = Ω a / Ω DM r = 1 10 7 10 6 H inf � 10 7 − 8 GeV GeV 10 5 10 4 / 10 3 inf 10 2 H 10 1 10 0 10 - 1 10 - 2 10 - 3 10 9 10 10 10 11 10 12 10 13 10 14 f a GeV Kobayashi, Kurematsu, FT, 1304.0922 /

Axion DM is in severe tension w/ many inflation models! Isocurvature constraint on H inf r = 0.01 10 9 r = 0.1 10 8 r = Ω a / Ω DM r = 1 10 7 10 6 H inf � 10 7 − 8 GeV GeV 10 5 10 4 / 10 3 inf Anharmonic 10 2 H effects 10 1 10 0 10 - 1 10 - 2 10 - 3 10 9 10 10 10 11 10 12 10 13 10 14 f a GeV Kobayashi, Kurematsu, FT, 1304.0922 /

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. axion DM is possible for f a = 10 10 GeV. Hiramatsu, Kawasaki, Saikawa and Sekiguchi, 1202.5851,1207.3166 Linde and Lyth `90 Lyth and Stewart `92 Solutions to isocuvature problem • Axions are produced from domain walls and

1)Restoration of Peccei-Quinn symmetry during Linde, `91 Takeshi Kobayashi, FT, 1607.04294 inflation. Solutions to isocuvature problem Lyth and Stewart `92 Linde and Lyth `90 Linde and Lyth `90 At small scales, however, axion fluctuations can be Saxion: radial component Axion: phase component Hiramatsu, Kawasaki, Saikawa and Sekiguchi, 1202.5851,1207.3166 2)Dynamical axion decay constant axion DM is possible for f a = 10 10 GeV. enhanced significantly! • Axions are produced from domain walls and Φ = f + s 2 e ia/f √ ✓ f 0 ◆ δ a = δ a inf δθ = const . f inf f 0 f inf

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 ˙ θ f > δ ˙ θ i f 0 f inf f 0 f inf

3)MSW-like resonance btw. axion and ALP. crossing! Solutions to isocuvature problem The level crossing necessarily occurs if . Level Hill, Ross `88, Kitajima, FT 1411.2011 m 2 H < m 2 a ( T = 0) ' m a ( T = 0) 1 ' m H ' m H 0.1 m 2 /m a m 1 /m a ' m a ( T ) 0.01 1 10 100 m a t

3)MSW-like resonance btw. axion and ALP. crossing! Solutions to isocuvature problem The level crossing necessarily occurs if . Level Hill, Ross `88, Kitajima, FT 1411.2011 m 2 H < m 2 a ( T = 0) ' m a ( T = 0) 1 ' m H ' m H 0.1 m 2 /m a m 1 /m a ' m a ( T ) 0.01 1 10 100 m a t

3)MSW-like resonance btw. axion and ALP. crossing! Solutions to isocuvature problem The level crossing necessarily occurs if . Level Hill, Ross `88, Kitajima, FT 1411.2011 m 2 H < m 2 a ( T = 0) ' m a ( T = 0) 1 ' m H ' m H 0.1 m 2 /m a m 1 /m a ' m a ( T ) 0.01 1 10 100 m a t

3)MSW-like resonance btw. axion and ALP. FT and Yamada 1507.06387 suppressed at present. The extra PQ breaking term must be sufficiently cf. Dvali, `95, Dine, Anisimov hep-ph/0405256 Nomura, Rajendran, Sanches, 1511.06347 Solutions to isocuvature problem Kawasaki, FT, Yamada 1511.05030 Barr and J.E.Kim, 1407.4311 Higaki, Jeong, FT, 1403.4186, Choi et al, 1505.00306 Jeong, FT 1304.8131 4)Heavy axions during inflation Hill, Ross `88, Kitajima, FT 1411.2011 e.g. Witten effect m 2 a & H 2 inf • Stronger QCD during inflation • Extra explicit PQ breaking a

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. Classical axion window: Is high T R or H inf necessary? T R , H inf & F a 10 9 GeV . F a . 10 12 GeV

Decay constant = PQ breaking scale? However, this is not necessarily the case. If there are multiple PQ scalars, In a simple set-up, is possible. V ( Φ ) h Φ i ⇠ F a Φ : PQ scalar h Φ i ⌧ F a

Alignment mechanism See also Sikivie `86 The decay constant can be enhanced by the largest hierarchy Choi, Kim, Yun, 1404.6209, Higaki, FT, 1404.6923 Harigaya and Ibe, 1407.4893, Choi and Im, 1511.00132, Kaplan and Rattzzi, 1511.01827. Kim, Nilles, Peloso, hep-ph/0409138 among the PQ charges in the alignment mechanism, Clockwork axion model with N=2: Φ 2 2 Φ 1 i | Φ i | 2 + � i | Φ i | 4 ) X ( − m 2 V = i =1 Φ 1 Φ 3 � � + ✏ 2 + h . c . Φ i = f i + s i e ia i /f i √ 2 a = 3 f 1 a 1 − f 2 a 2 q 3 2 f 2 1 + f 2 f a = 2 , f a

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 Harigaya and Ibe, 1407.4893, Choi and Im, 1511.00132, Kaplan and Rattzzi, 1511.01827. Choi, Kim, Yun, 1404.6209, Higaki, FT, 1404.6923 N X i | Φ i | 2 + λ i | Φ i | 4 � − m 2 � V = i =1 N − 1 X Φ i Φ 3 � � + i +1 + h . c . ✏ i =1 f a ∼ 3 N f

Aligned QCD axion with Higaki, Kitajima, FT, 1408.3936 , Higaki, Jeong, Kitajima, FT, 1512.05295. In general, if we have N-1 of the N axions becomes massive, leaving one massless Adding a coupling to the PQ quarks much lower than the conventional axion window! Choi, Kim, Yun, 1404.6209, for N − 1 ✓ a i ◆ a i +1 X Λ 4 V ( a i ) = − i cos + n i , f i f i +1 i =1 mode, a . 0 1 0 1 N N N N a = 1 X Y X Y A f 2 ( − 1) i − 1 A f i a i , f 2 n 2 n j i , a = @ @ j f a i =1 j = i i =1 j = i ∆ L = y q Φ N ¯ QQ. a becomes the QCD axion with f i = f F a = f a ∼ 3 N f There are many axions and saxions at f (e.g. at TeV scale)

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 for e.g. Φ n +4 h Φ i ⇠ F a ⇠ 10 12 GeV n > 10 M n p h Φ i i ⌧ F a