Exploring string axiverse in GW cosmology Yuko Urakawa (Nagoya - PowerPoint PPT Presentation

a la Misao :-) Exploring string axiverse in GW cosmology Yuko Urakawa (Nagoya university, IAR) J.Soda & Y.U.(1710.00305) N. Kitajima, J.Soda,& Y.U.(in progress) w/ Naoya Kitajima (Nagoya U.), Jiro Soda (Koba U.)

Axions (or ALPs) from string theory Superstring theory in compact 6D 4D low energy EFT + Axions + Moduli …. Wide mass ranges Probe of exDim Inflaton, DM candidate (Fuzzy DM) Wu et al.(00), … Conlon et al. (05) ex. Large Volume Scenario Predicts light mass axions

Scalar potential of axion continuous shift sym. φ → φ + 2 π n / f NP effects φ → φ + c n ∈ Z e.g. instanton effects V( φ ) ~ Λ 4 cos φ /f Are you sure with ? cos φ /f - Dilute instanton gas approximation for φ /f << 1 V ( φ ) ∝ φ 2 ? for φ /f ≧ 1 Witten(79, 80) cos φ /f f eff ∝ N SU(N) in large N on RxT 3 Plateau structure Dubovski et al. (11), Yamazaki & Yonekura(17), …

Scalar potential of axion continuous shift sym. φ → φ + 2 π n / f NP effects φ → φ + c n ∈ Z e.g. instanton effects V( φ ) ~ Λ 4 cos φ /f Potential can be more flatten than cos φ /f  � 1 i) Dilute instanton gas approximation V ( � ) = M 4 1 � (1 + ( � /F ) 2 ) p Yamazaki & Yonekura(17), Nomura, Watari, & Yamazaki (17) ii) Non-min. coupling w/gravity, Non-canonical kinetic term Kallosh & Linde + (13, 14,…) → α attractor model iii) Superposition of multiple cosine terms e.g., alignment mechanism Kim, Nilles, & Peloso (04)

Plateau phenomenology : φ = inflaton V ( φ ) φ 2 /2 φ i) Reconcile the tension w/ PLANCK observation V( φ ) ∝ φ 2 → plateau structure Recall Renata’s talk

plateau Nomura, Watari, & Yamazaki (17), Nomura & Yamazaki (17) Pure natural inflation  � 1 V ( � ) = M 4 1 � (1 + ( � /F ) 2 ) p r 0.20 Consistent w/ 0.15 Planck, BICEP/KECK 0.10 0.05 n s 0.95 0.96 0.97 0.98 0.99

Plateau phenomenology : φ inflaton V ( φ ) φ 2 /2 φ i) Reconcile the tension w/ PLANCK observation V( φ ) ∝ φ 2 → plateau structure Recall Renata’s talk ii) Drastic reheating process - GW emission Antusch +(17), Kawasaki+(17), … - Oscillon/I-ball formation Gleiser(94), Kasuya+(03),Amin + (10, 12, 17),….

Plateau phenomenology: Post inflation φ ( t ) δφ ( t, x ) Onset of oscillation inst. turbulence (b)GW H/m << 1 axion bio-marker

Soda & Y.U.(17) Outline of the story Kitajima, Soda & Y.U.(in prep.) 1. Axion slowly rolls down H / m >> 1 V ( φ ) φ 2 /2 φ

Soda & Y.U.(17) Outline of the story Kitajima, Soda & Y.U.(in prep.) 1. Axion slowly rolls in plateau V ( φ ) φ 2 /2 2. Onset of oscillation H osc / m < 1 Especially w/plateau (or w/fine tuned IC) cos φ /f φ H osc / m << 1

α -attractor (tanh φ f ) 2 V ( φ ) = ( m a f ) 2 Background evolution 2 1 + c (tanh φ f ) 2 n Soda & Y.U.(17) RD 5 4 3 2 1 0 - 1 - 2 50 100 200 500 x= m/ H Onset of oscillation is not m ~ H , but delayed!

Soda & Y.U.(17) Outline of the story Kitajima, Soda & Y.U.(in prep.) 1. Axion slowly rolls in plateau V ( φ ) φ 2 /2 2. Onset of oscillation H osc / m < 1 3. Exponential growth due to PR φ if H osc / m << 1 No disturbance due to cosmic exp.

Parametric resonance Repeat: Up & Down in a half of osc. period → Periodic ext. force → Enhancing the amplitude “Parametric resonance instability” Mathieu equation d 2 A ~ n 2 resonance band dx 2 ˜ ϕ + ( A � 2 q cos 2 x ) ˜ ϕ = 0 ex. First band ϕ / e γ x with ˜ by γ ' q/ 2 = xplains the c dependence of the growth Energy transfer φ ( t ) δφ ( t, x )

Linear perturbation Soda & Y.U.(17) PR in k r /( a osc m ) ~ O (1), k r /( a osc H ) >> 1 PR 10 14 10 10 tachyonic growth 10 6 100.00 0.01 10 - 6 ~ 50 100 200 500 k = k /( a i m )

Energy transfer Kitajima, Soda & Y.U.(in prep.) Lattice simulation N grid =(128) 3 10 1 10 0 saturation 10 -1 10 -2 10 -3 10 -4 ⟨ φ ⟩ 10 -5 ( ⟨ δφ 2 ⟩ ) 1/2 10 -6 ρ ( ⟨ φ ⟩ ) δρ ( φ ) 10 -7 5 10 15 20 25 30 m τ

Outline of the story 1. Axion slowly rolls in plateau V ( φ ) φ 2 /2 2. Onset of oscillation H osc / m < 1 3. Exponential growth due to PR φ if H osc / m < 1 Energy transfer φ ( t ) δφ ( t, x ) 4. Rescattering → PR becomes inefficient eg. Kofman, Linde, Starobinsky δφ δρ ~ O(1) , φ ρ

Outline of the story 1. Axion slowly rolls in plateau V ( φ ) φ 2 /2 2. Onset of oscillation H osc / m < 1 plateau 3. Exponential growth due to PR φ if H osc / m < 1 No disturbance due to cosmic exp. 4. Rescattering → PR becomes inefficient eg. Kofman, Linde, Starobinsky 5. Turbulence turbulence → GW emission Micha & Tkachev (02,04) see also Caprini & Durrer(06)

Kolmogorov turbulence stationary turbulence: source k r (IR) → sink k r (UV) in k-space kinetic theory dn k /dt = I k [ n ] Collision integral take λφ 4 theory, now w/ φ ( t ) k r k s λ λ 4-body 3-body assump: const. flux in k for massless φ Micha & Tkachev (02,04) s=5/3 for 4-body dn/dlnk=k 3 n ( k ) ∝ k 3 - s s=3/2 for 3-body

Lattice simulation Kitajima, Soda, Y.U. (in preparation) Momentum trans due to turbulence 3-body 10 -2 ∝ k 3/2 scattering 10 -4 dn φ / d ln k [ m  f  ] φ ( t ) ≠ 0 10 -6 10 -8 10 -10 10 -12 10 -14 PR 10 -16 1 10 100 N grid =(256) 3 k / m

GW spectrum Kitajima, Soda, Y.U. (in preparation) momentum transfer converges earlier for GW 10 -5 f~0.01M pl 10 -6 10 -7 Ω GW 10 -8 em x Ω r at present 10 -9 10 -10 10 -11 1 10 100 k / m

New window of string axiverse Kitajima, Soda, Y.U. (in preparation) 10 -6 DECIGO SKA 10 -8 ET LISA 10 -10 Ω GW h 2 10 -12 u-DECIGO 10 -14 10 -16 10 -18 10 -20 10 -10 10 -8 10 -6 10 -4 10 -2 10 0 10 2 10 4 f [Hz] Axions from string theory f ~ 10 15 -10 16 GeV e.g.,Svrcek & Witten (06)

Plateau phenomenology: φ = DM φ ( t ) δφ ( t, x ) Onset of oscillation inst. turbulence Equal time ~ DM (b)GW H/m << 1 axion if Ω c ~ Ω axion bio-marker (N implications to small scales issues?

preliminary GWs from axion DM Kitajima, Soda, Y.U. (in preparation) Lattice sim. Ω GW ~ 10 -10 x (f/0.01M p ) 4 Abundance of axion freq. of GW f 0 mass m + abundance of axion decay const. f Crude Order estimation β φ = Ω φ / Ω c ≦ 1 using φ ( t, x ) ~ f ( a osc / a ) 3/2 2 � κ � nHz � 4 � Ω GW ≃ 3 . 41 × 10 − 16 ∆ 2 β 2 φ f 0 10 Δ : Sym. suppression (< 1) κ = k peak / m e.g., α - attractor Δ ２ ~0.2, κ = 12

Outline of the story 1. Axion slowly rolls in plateau V ( φ ) φ 2 /2 2. Onset of oscillation H osc / m < 1 3. Exponential growth due to PR φ if H osc / m < 1 No disturbance due to cosmic exp. 4. Rescattering → PR becomes inefficient eg. Kofman, Linde, Starobinsky 5. Momentum transfer due to turbulence → GW emission Micha & Tkachev (02,04) 6. GW& φ decoupled, Oscillon/I-ball formation Gleiser(94), Kasuya+(03),Amin + (10, 12, 17),….

Preliminary Oscillon formation Kitajima, Soda, Y.U. (in preparation) a ~ a 0 a ~ 20 a 0 rescattering a ~ 90 a 0 a ~ 35a 0 turbulence oscillon N grid =(128) 3

Plateau phenomenology: φ = DM φ ( t ) δφ ( t, x ) Onset of oscillation inst. turbulence Equal time ~ DM (b)GW H/m << 1 axion if Ω c ~ Ω axion bio-marker (N implications to small scales issues?

Outline of the story 1. Axion slowly rolls in plateau V ( φ ) φ 2 /2 2. Onset of oscillation H osc / m < 1 3. Exponential growth due to PR φ if not H osc / m << 1 4. PR finished due to red-shift Yet, for DM= axion, imprints on structure formation Resonance peak in spectrum

Future issues: More on φ =DM Alternative solution to small scale issues of Λ CDM?? ULA w/ m ~ 10 -22 eV → Emergent pressure smooths at k > k J k J : Jeans scale → Tension with small scale observations? Recall Takeshi’s talk Irsic et al. (17), Kim et al. (17), … for λ = 0 Non-negligible impact of self-interaction Zhang&Chiueh(17) ,Schieve&Chiueh(17),Desjacques + (17) Resonance scale k r > k J ∝ a 1/4 Evade tension?

Summary φ ( t ) δφ ( t, x ) Onset of oscillation inst. turbulence Equal time ~ DM (b)GW H/m << 1 axion if Ω c ~ Ω axion bio-marker (N implications to small scales issues?