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

Γ ∼ 1 4π m3

φ

M 2

P

TR ∼ 1.2g−1/4

∗

p MP Γφ ∼ 1.2 × 10−7GeV × ⇣ mφ 1000GeV ⌘3/2

mφ > 10TeV TR > 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?

GeV TeV GUT

axion? wimp? wimpzilla? gut baryogenesis? leptogenesis? electroweak baryogenesis?

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

we consider:

Inflating curvaton

EX: when curvaton with a quadratic potential start to oscillate:

ρr ∼ 3m2M 2

P

ρσ ∼ 1 2m2σ2 ρr > ρσ σ < √ 6MP

If

σ > √ 6MP

Curvaton will drive a second stage of inflation! 1110.2951 dimopoulos, kohri, lyth, and matsuda

inflating curvaton

N2 . 45 − 1 2 ln ✓10−5MP H2 ◆

in the inflating curvaton scenario, cosmological scales are demanded to be outside the horizon at the time when the second inflating starts: curvature perturbation is given by

P 1/2

ζ

∼ 1 3 V 0

σ

˙ σ2(t2) H1 2π

inflaton moduli inflating curvaton affleck dine field

H1 mI ΓI mAD Γσ H mI mσ mAD

large small

σ φ δσ δθ

if hubble induced a-term is suppressed baryon number produced

bbn

H2 ∼ mσ

PNGB inflating curvaton

Vσ(σ) = m2

σf 2

 1 − cos ✓σ f ◆ V σ

πf

πf 2

Actually quadratic potential cannot work as inflating curvaton because the spectrum cannot dominate. for moduli field we expect:

mσ ∼ m3/2 f ∼ MP

fast-roll inflation

σe

curvature perturbation

F ≡ 3 2 s 1 + 4m2

σ

9H2

2

− 1 ! N2 ∼ 1 F ln

πf 2

πf − σ2 ! P 1/2

ζ

∼ 1 3 ✓ mσ FH2 ◆2 H1 2π(πf − σ2) ∼ 5 × 10−5

cmb normalization

AD baryogenesis

soft mass A-term F-term

∼ |Wφ|2 ∼ AmW W ∼ λφp M p−3 VAD(φ) = (−cH + m2

AD)|φ|2 + AHH + Am3/2

M p−3 λφp + |λ|2 |φ|2p−2 M 2p−6 φ V (φ)

|φ| ∼ ✓ c |λ|2 ◆

1 2(p−2)

M ✓ H √p − 1M ◆

1 p−2

AD baryogenesis

nB s ∼ 6 × 10−11 × ⇣ mσ 150TeV ⌘3/2 ✓75TeV mAD ◆5/7 ✓ m3/2 mAD ◆ p = 9

The reason for large p is we need large vev

nB = iq(φ ˙ φ∗ − ˙ φφ∗) = q|φ|2 ˙ θ φ = |φ|eiθ

baryon isocurvature perturbation

If Hubble induced a-term is suppressed:

δθ = H1 2π|φ1| SB ≡ δρB ρB − 3 4 δργ ργ = δ log ⇣nB s ⌘ H1 . 8 × 10−6MP f . 5MP mAD mσ < 5 √ 6

This condition is satisfied in our model since we consider

AH ⌧ 1 φ1 ≡ φmin(H1) mσ > mAD

how about oscillating curvaton + ad baryogenesis?

Ikegami and moroi hep-ph/0404253

residual baryon isocurvature perturbation

ζ = (1 − f)ζr + fζσ f = 3ρσ 4ρr + 3ρσ SB = 3(ζB − ζr)

if baryon number is produced before curvaton domination

f ⌧ 1 ζB = 0 SB = −3ζ

eventually we will have baryon isocurvature perturbation will be too large

ζi = −ψ − H ✓δρi ˙ ρi ◆

• scillating (moduli) curvaton with

AD baryogenesis?

moduli will start to dominate when:

Heq = √ 2mσ ✓ σ0 √ 6MP ◆4

to avoid large correlated baryon isocurvature perturbation we need

mAD < Heq σ0 > √ 6MP ✓ mAD √ 2mσ ◆1/4

but this implies curvaton will inflate!

non-thermal wimp

moroi and randall hep-ph/9906527 Acharya, Kane, Watson, and Kumar 0908.2430

nc

χ ⌘

H hσvi ⇠ Γσ hσvi ⇠ m3

σ

M 2

P hσvi

Ωχ = 0.1h−2 ⇣ mχ 100GeV ⌘ ✓3 ⇥ 10−7GeV−2 hσvi ◆ ✓150TeV mσ ◆3/2

wino lsp

Ω(thermal)

χ

h2 = 5 × 10−4 × ⇣ mχ 100 GeV ⌘2

Conclusion

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