Moduli Inflating Curvaton Chia-Min Lin Kobe University The - PowerPoint PPT Presentation

Moduli Inflating Curvaton Chia-Min Lin 林 家民 Kobe University The 3rd UTQuest workshop ExDiP 2012 Superstring Cosmophysics Obihiro, 6-12, August 2012

This talk is based on the following paper: Affleck-Dine baryogenesis in inflating curvaton scenario with O(10-10^2TeV) mass moduli curvaton Kazuyuki Furuuchi and Chia-Min Lin arXiv:1111.6411 JCAP 1203 (2012) 024 CML and Kazuyuki Furuuchi

Moduli (Polonyi) Problem m 3 Γ ∼ 1 φ M 2 4 π P ⌘ 3 / 2 m φ ⇣ T R ∼ 1 . 2 g − 1 / 4 p M P Γ φ ∼ 1 . 2 × 10 − 7 GeV × ∗ 1000GeV m φ > 10TeV T R > 1MeV We do not really know the thermal history of the universe before BBN.

it is possible that before bbn the universe is cold and dominated by moduli matter if so, the question is how can we have dark matter and baryogenesis then? GUT wimpzilla? gut baryogenesis? leptogenesis? electroweak baryogenesis? TeV wimp? axion? GeV

we consider: baryogenesis: Affleck dine baryogenesis dark matter: non-thermal (wino-like) lsp from the decay of moduli field we also assume moduli field is inflating curvaton and responsible for primordial density perturbation

Inflating curvaton 1110.2951 dimopoulos, kohri, lyth, and matsuda EX: when curvaton with a quadratic potential start to oscillate: ρ r ∼ 3 m 2 M 2 P ρ σ ∼ 1 2 m 2 σ 2 √ σ < 6 M P ρ r > ρ σ √ σ > 6 M P If Curvaton will drive a second stage of inflation!

inflating curvaton in the inflating curvaton scenario, cosmological scales are demanded to be outside the horizon at the time when the second inflating starts: ✓ 10 − 5 M P ◆ N 2 . 45 − 1 2 ln H 2 curvature perturbation is given by ∼ 1 V 0 H 1 P 1 / 2 σ ζ 3 σ 2 ( t 2 ) ˙ 2 π

inflaton m I moduli inflating curvaton m σ σ affleck dine field φ m AD baryon number produced H 1 Γ I m AD Γ σ H 2 ∼ m σ m I bbn H large small δθ if hubble induced a-term is suppressed δσ

PNGB inflating curvaton Actually quadratic potential cannot work as inflating curvaton because the spectrum cannot dominate.  ✓ σ ◆� V σ ( σ ) = m 2 σ f 2 1 − cos f V for moduli field we expect: m σ ∼ m 3 / 2 f ∼ M P π f π f σ fast-roll inflation 2 σ e

curvature perturbation ! π f N 2 ∼ 1 2 F ln π f − σ 2 ✓ m σ ◆ 2 ∼ 1 H 1 P 1 / 2 2 π ( π f − σ 2 ) ∼ 5 × 10 − 5 ζ 3 FH 2 cmb normalization s ! 1 + 4 m 2 F ≡ 3 σ − 1 9 H 2 2 2

AD baryogenesis λφ p + | λ | 2 | φ | 2 p − 2 AD ) | φ | 2 + A H H + Am 3 / 2 V AD ( φ ) = ( − cH + m 2 M p − 3 M 2 p − 6 soft mass A-term F-term λφ p ∼ | W φ | 2 ∼ AmW W ∼ M p − 3 V ( φ ) φ ✓ c 1 1 ◆ ✓ ◆ H 2( p − 2) p − 2 | φ | ∼ M √ p − 1 M | λ | 2

AD baryogenesis φφ ∗ ) = q | φ | 2 ˙ n B = iq ( φ ˙ φ ∗ − ˙ φ = | φ | e i θ θ p = 9 The reason for large p is we need large vev ◆ 5 / 7 ✓ m 3 / 2 ⌘ 3 / 2 ✓ 75TeV ◆ ⇣ n B m σ ∼ 6 × 10 − 11 × 150TeV s m AD m AD

baryon isocurvature perturbation A H ⌧ 1 If Hubble induced a-term is suppressed: H 1 δθ = 2 π | φ 1 | S B ≡ δρ B δρ γ ⇣ n B − 3 ⌘ = δ log φ 1 ≡ φ min ( H 1 ) ρ B ρ γ s 4 5 m AD H 1 . 8 × 10 − 6 M P f . 5 M P < √ 6 m σ This condition is satisfied in our model since we consider m σ > m AD

how about oscillating curvaton + ad baryogenesis? Ikegami and moroi hep-ph/0404253

residual baryon isocurvature perturbation 3 ρ σ ζ = (1 − f ) ζ r + f ζ σ f = 4 ρ r + 3 ρ σ ✓ δρ i ◆ S B = 3( ζ B − ζ r ) ζ i = − ψ − H ρ i ˙ if baryon number is produced ζ B = 0 f ⌧ 1 before curvaton domination S B = − 3 ζ eventually we will have baryon isocurvature perturbation will be too large

oscillating (moduli) curvaton with AD baryogenesis? ◆ 4 ✓ σ 0 √ H eq = 2 m σ moduli will start to dominate when: √ 6 M P to avoid large correlated baryon isocurvature perturbation we need ✓ m AD ◆ 1 / 4 √ m AD < H eq σ 0 > 6 M P √ 2 m σ but this implies curvaton will inflate!

non-thermal wimp moroi and randall hep-ph/9906527 Acharya, Kane, Watson, and Kumar 0908.2430 m 3 h σ v i ⇠ Γ σ H n c χ ⌘ h σ v i ⇠ σ M 2 P h σ v i ◆ 3 / 2 ⌘ ✓ 3 ⇥ 10 − 7 GeV − 2 ◆ ✓ 150TeV m χ Ω χ = 0 . 1 h − 2 ⇣ h σ v i 100GeV m σ wino lsp ⌘ 2 m χ ⇣ Ω ( thermal ) h 2 = 5 × 10 − 4 × χ 100 GeV

Conclusion AD baryogenesis can work for p=9 flat direction no isocurvature perturbation wino dark matter primordial density perturbation (no large non-gaussianity)