The ALP miracle collaboration with F. Takahashi & W. Yin Ryuji - PowerPoint PPT Presentation

The ALP miracle collaboration with F. Takahashi & W. Yin Ryuji Daido Tohoku Univ. @PPP2017 1702.03284 JCAP05(2017)044

� ��� There are two unknown degree of freedom in the CDM. (except for the origin of .) 1. Introduction •Inflaton •Dark matter Both are neutral and occupied a significant fraction of the energy density of the Universe. Very flat potential for slow-roll inflation. Cold, neutral, and long-lived . Λ Λ V

� ��� Thermal history Inflaton decays and produce radiation, while DM must be produced somehow. inflaton radiation DM Scale factor ? V ρ

Inflaton = DM ? cf. Kofman, Linde, Starobinsky `94, Mukaida, Nakayama 1404.1880, Bastero-Gil, Cerezo, Rosa,1501.05539 see also Lerner, McDonald 0909.0520, Okada, Shafi 1007.1672, Khoze 1308.6338 for inflaton WIMP. If the reheating is incomplete, some of inflaton condensate may remain. DM=inflaton radiation Incomplete reheating! inflaton Scale factor The remnant inflaton condensate due to incomplete reheating can be dark matter. ρ

What we did •Inflaton = DM = Axion-like particle (ALP) •The observed CMB and LSS data fix the relation between the ALP mass and decay constant. •Successful reheating and DM abundance point to specific values within the reach of IAXO. g φγγ = O (10 − 11 ) GeV − 1 m φ = O (0 . 01) eV ,

2. Axion and Inflation Axion is a pseudo NG boson, and enjoys a discrete shift symmetry. Since dangerous radiative corrections are naturally suppressed, axion is compatible with inflation. and can be expressed as Fourier series, The axion potential is periodic, i.e. φ → φ + 2 π nf n ∈ Z V ( φ ) = V ( φ + 2 π f ) ∆ φ = 2 π f c n e in φ X V ( φ ) = f n ∈ Z

・Super-Planckian decay constant Freese, Frieman, Olinto `90 •Natural inflation by recent observations. ・Predicted are not favored ・Large field inflation is required. Axion and Inflation The simplest model is the natural inflation. V ( ϕ )/ Λ 4 2.0 1.5 1.0 0.5 ϕ / f - 1 1 2 3 4 ( n s , r )

•Axion hilltop inflation Odd n (Minimal extension) Planckian. • The decay constant can be sub- Czerny, Higaki, Takahashi 1403.0410, 1403.5883 Czerny, Takahashi 1401.5212, symmetric upside down • Inflaton is light both during inflation Axion and Inflation and in the true min. Flatness=longevity Hilltop inflation can be realized with two cosine terms. ✓ ✓ φ ◆ ✓ ◆◆ − κ n φ V inf ( φ ) = Λ 4 cos f + θ n 2 cos + C f f + ( κ − 1) Λ 4 = V 0 − λφ 4 − Λ 4 θφ 2 f 2 φ 2 + . . . V ( φ ) / Λ 4 1.5 f ⌧ M P 1.0 0.5 m 2 φ = V 00 ( φ min ) = − V 00 ( φ max ) -1 0 1 2 3 4 5

•Axion hilltop inflation Planck normalization symmetric upside down Odd n Czerny, Higaki, Takahashi 1403.0410, 1403.5883 Czerny, Takahashi 1401.5212, (Minimal extension) Hilltop inflation can be realized with two cosine terms. Spectral index Axion and Inflation ✓ ✓ φ ◆ ✓ ◆◆ − κ n φ V inf ( φ ) = Λ 4 cos f + θ n 2 cos + C f f + ( κ − 1) Λ 4 = V 0 − λφ 4 − Λ 4 θφ 2 f 2 φ 2 + . . . V ( φ ) / Λ 4 ◆ − 3 ✓ N ∗ 1.5 λ ' 7 . 5 ⇥ 10 − 14 . 50 ✓ H ∗ 1.0 ◆ 1 ◆ 1 ✓ H inf 2 2 N ∗ ' 61 + ln + ln 10 14 GeV H inf 0.5 n s ' 1 + 2 η ( φ ∗ ) ' 1 � 3 -1 0 1 2 3 4 5 N ∗

Spectral index The typical inflaton mass: n s = 0 . 968 ± 0 . 006 0.04 0.03 θ ×( f / M pl ) - 3 0.02 0.01 0.00 - 0.01 - 0.06 - 0.04 - 0.020.00 0.02 0.04 0.06 0.08 ( κ - 1 )×( f / M pl ) - 2 cf . n s ' 1 + 2 η ( φ ∗ ) 3 Λ 2 1 f = O (0 . 1) H inf m φ ∼ θ

Relation between and The Planck normalization of density perturbation and the spectral index fix the relation between and , : Planck normalization : Friedman eq. : Scalar spectral index f m φ f m φ ◆ 4 ✓ Λ ∼ 10 − 13 λ ∼ f Λ 4 ∼ H 2 inf M 2 pl m φ ∼ 0 . 1 H inf cf . n s ' 1 + 2 η ( φ ∗ ) ⌘ 1 / 2 ⇣ m φ ⌘ 0 . 51 ⇣ n f ∼ 5 × 10 7 GeV 3 1 eV

Mass and coupling to photons Limits taken from Essig et al 1311.0029 RD, Takahashi, and Yin 1702.03284 L = g φγγ g φγγ = c γ α φ F µ ν ˜ F µ ν X π f q i Q 2 4 c γ = i 10 -9 i ψ i → e i β q i γ 5 / 2 ψ i Telescopes HB CAST φ → φ + β f 10 -10 10 -11 ALPS-II IAXO CMB τ 10 -12 EBL Z V S QCD axion K Successful 10 -13 X-ray inflation 10 -14 10 -4 10 -3 10 -2 10 -1 10 0 10 1 10 2 10 3 m [eV] φ

The inflaton oscillates about in a quartic potential. The effective mass, Incomplete reheating later times. with time, and so, decay and dissipation become inefficient at 3. Reheating and ALP DM φ min = π f = 12 λφ 2 m 2 e ff ( t ) = V 00 ( φ amp ) amp decreases 1.5 1.0 0.5 -1 0 1 2 3 4 5

SM particles Photons, 3. Reheating and ALP DM ALP Dark Matter Remnant dissipation Decay & Inflaton (ALP) condensate 1.5 1.0 0.5 -1 0 1 2 3 4 5 � ρ φ � ξ ≡ � ρ φ + ρ R � after reheating

・Reheating ✓The decay rate into two photons: cf. Moroi, Mukaida, Nakayama and Takimoto,1407.7465 ✓The dissipation rate is roughly estimated as 1.5 v ! 2 2 m ( th ) u Γ dec ( φ → γγ ) = c 2 γ α 2 m 3 u e ff γ t 1 − 1.0 64 π 3 f 2 m e ff γ 0.5 φ m ( th ) ∼ eT -1 0 1 2 3 4 5 γ γ e ff ( t ) = V 00 ( φ amp ) = 12 λφ 2 m 2 amp φ e − Γ dis , γ = C c 2 γ α 2 T 3 m 2 e ff 8 π 2 f 2 e 4 T 2 e + γ

for successful reheating . Inflation Radiation DM Scale factor The remnant inflaton condensate is expressed by Solving following equations, we found ・Reheating ρ � ρ φ � ξ ≡ � ξρ tot ρ φ + ρ R � after reheating H ' Γ dec + Γ dis g φγγ & 10 − 11 GeV − 1 ξ . O (0 . 01)

reheating Successful 10 -9 Telescopes HB CAST 10 -10 10 -11 ALPS-II IAXO CMB τ 10 -12 EBL KSVZ QCD axion Successful 10 -13 X-ray inflation 10 -14 10 -4 10 -3 10 -2 10 -1 10 0 10 1 10 2 10 3 m [eV] φ

Quadratic Quartic After the reheating, decreases like radiation until the potential becomes quadratic. •ALP condensate as CDM cf. ρ φ w ≡ P ρ = n − 2 for φ n n + 2 ∝ ( φ − φ min ) 4 ∝ ( φ − φ min ) 2

•ALP condensate as CDM DM should be formed before SM radiation quartic quadratic Scale factor Matter-radiation equality DM Sarkar, Das, Sethi, 1410.7129 ρ φ z c z eq ∼ 3000 z c & O (10 5 ) by SDSS and Ly-alpha 3 ✓ 3 . 909 ◆ 1 ◆ 1 3 ✓ Ω φ h 2 ◆ ✓ 5 × 10 5 ✓ g ∗ s ( T R ) ◆ ξ . 0 . 02 . 106 . 75 g ∗ s ( T c ) 0 . 12 1 + z c

•ALP condensate as CDM SM radiation DM equality Matter-radiation Scale factor quadratic quartic Sarkar, Das, Sethi, 1410.7129 ρ φ z c z eq ∼ 3000 ρ φ 4 m φ T R s ' 3 3 4 ξ p ✓ ξ ◆ − 3 2 λ fx 4 ✓ Ω φ h 2 ◆ m φ ' 0 . 07 x − 1 eV , 0 . 01 0 . 12 ✓ 106 . 75 4 ✓ 1 + z c ◆ 1 ◆ 1 ◆ 1 ◆ 3 4 ✓ Ω φ h 2 4 ✓ g ∗ s ( T c ) 4 & 0 . 04 x − 1 eV , g ∗ s ( T R ) 3 . 909 0 . 12 5 ⇥ 10 5

DM abundance reheating Successful 10 -9 Telescopes HB CAST 10 -10 10 -11 ALPS-II IAXO CMB τ 10 -12 EBL KSVZ QCD axion Successful 10 -13 X-ray inflation 10 -14 10 -4 10 -3 10 -2 10 -1 10 0 10 1 10 2 10 3 m [eV] φ

DM abundance HDM constraint reheating Successful 10 -9 Telescopes HB CAST 10 -10 10 -11 ALPS-II IAXO CMB τ 10 -12 EBL KSVZ QCD axion Successful 10 -13 X-ray inflation 10 -14 10 -4 10 -3 10 -2 10 -1 10 0 10 1 10 2 10 3 m [eV] φ

HDM constraint DM abundance reheating Successful 10 -9 Telescopes HB CAST 10 -10 10 -11 ALPS-II IAXO CMB τ 10 -12 EBL KSVZ QCD axion Successful 10 -13 X-ray inflation 10 -14 10 -4 10 -3 10 -2 10 -1 10 0 10 1 10 2 10 3 m [eV] φ

HDM constraint DM abundance The ALP miracle! reheating Successful 10 -9 Telescopes HB CAST 10 -10 10 -11 ALPS-II IAXO CMB τ 10 -12 EBL KSVZ QCD axion Successful 10 -13 X-ray inflation 10 -14 10 -4 10 -3 10 -2 10 -1 10 0 10 1 10 2 10 3 m [eV] φ

Summary •Inflaton = DM = Axion-like particle (ALP) •The observed CMB and LSS data fix the relation between the ALP mass and decay const. •Successful inflation, reheating and DM abundance point to within the reach of IAXO. 10 -9 Telescopes HB CAST 10 -10 10 -11 ALPS-II IAXO CMB τ 10 -12 EBL KSVZ QCD axion 10 -13 X-ray 10 -14 g φγγ = O (10 − 11 ) GeV − 1 10 -4 10 -3 10 -2 10 -1 10 0 10 1 10 2 10 3 m φ = O (0 . 01) eV , m [eV] φ