Inflation from a SUSY Axion Model

Transcription

1 Inflation from a SUSY Axion Model Masahiro Kawasaki (ICRR, Univ of Tokyo) with Naoya Kitajima (ICRR, Univ of Tokyo) Kazunori Nakayama (Univ of Tokyo) Based on papers MK, Kitajima, Nakayama, PRD 82, (2010) MK, Kitajima, Nakayama, PRD 83, (2011) 1

2 1. Introduction Problems in the standard model of particle physics Strong CP problem : Why QCD preserves CP? Hierarchy problem : The EW scale is unstable against radiative correction Well-known solutions Peccei-Quinn mechanism Axion Supersymmetry This leads us to consider a SUSY Axion Model In this model Hybrid Inflation is naturally realized Copeland, Liddle, Lyth, Stewart, Wands (1994) Axion is dominant dark matter of the universe We have a consistent cosmological scenario.

3 2. SUSY Axion Model Superpotential W = κs(ψ Ψ f 2 a)+λψx X S X, X : gauge singlet : PQ fields Ψ, Ψ : Heavy quraks (Higgs) for KSVZ (DFSZ) axion model Scalar potential S X X Uð1Þ PQ 0 þ1 1 1=2 1=2 Uð1Þ R þ2 0 0 þ1 þ1 V F = κ 2 Ψ Ψ f 2 a 2 + κ 2 S 2 ( Ψ 2 + Ψ 2 ) global minimum Ψ Ψ =f 2 a, S =0 flat direction The flat direction is lifted up by soft SYSY-breaking potential V soft = c 1 m 2 3/2 Ψ 2 + c 2 m 2 3/2 Ψ 2 PQ scalars are stabilized at Ψ Ψ f a

4 Axion a and saxion σ ( scalar partner of axion) are related to PQ scalars as Ψ f a exp Saxion decay σ + ia 2fa KSVZ axion model In general, decay into two axions ( σ a + a) is dominant but it is suppressed when c 1 c 2 we assume Then the saxion decays into two gluons with decay rate DFSZ axion model Γ(σ 2g) Ψ f a exp α s 32π 3 m 3 σ f 2 a σ + ia 2fa The saxion decays into Higgses with decay rate Γ(σ 2h) 1 8π µ m σ 4 m 3 σ f 2 a µ = λψ

5 3. Inflation in SUSY Axion Model Superpotential in SUSY axion model includes W inf = κs(ψ Ψ f 2 a) This is the same form as that realizes SUSY hybrid inflation Copeland, Liddle, Lyth, Stewart, Wands (1994) Dvali, Shafi, Schaefer (1994)..... PQ scalars and S play roles of waterfall fields and inflaton, respectively Scalar potential V = κ 2 Ψ Ψ f 2 a 2 + κ 2 S 2 ( Ψ 2 + Ψ 2 ) For local minimum at where the potential is flat S f a Ψ= Ψ =0 "#$ ($ (% (& (' "# "$ "% "& "' ("$ ("# "# " V κ 2 f 4 a +(one loop corr.)+(sugra corr.) "#$ ($ (% (& "$ (' "# "& "% ("# "# "$

6 With appropriate Kähler potential we have successful inflation which is consistent with WMAP result However, PQ scale should be high f a GeV Axion overcloses the universe? Post-inflationary dynamics can solve this problem Successful inflation κ f a [GeV] Nakayama, F.Takahashi, Yanagida (2010)

7 4. Post-inflationary Dynamics For successful inflation we need f a GeV too large axion density This problem cannot be solved by tuning misalignment angle θ because PQ symmetry is broken after inflation and θ takes random values in different places of the universe However, after inflation saxion can oscillate with large amplitude and decay to produce huge entropy entropy production sufficiently dilutes axion together with other harmful relics

8 4.1 Inflaton Oscillation After inflation the inflaton starts oscillation PQ scalars roll down toward the flat direction PQ scalars have masses PQ scalars are stabilized at m 2 Ψ, Ψ κ2 S 2 Ψ= Ψ =f a Ψ /f a 10-2 S /f a

9 4.2 Reheating and Thermal Effect Inflaton can decay through Reheating temperature T R GeV κ /2 W = ksy Ȳ (Y = H or Q ) k 10 3 Finite-temperature effect due to heavy quarks which couple MSSM particles in thermal bath fa GeV 1/2 V th α s T 4 ln Ψ 2 T 2 This lifts up the flat direction and Ψ( Ψ) rolls down to smaller (larger ) value Ψ α s M p / f a / f a H / f a m th / f a Ψ/f a m th /f a Ψ/f a H/f a σ i α s M p σ Ψ f a f a time

10 4.3 Saxion Oscillation and Entropy Production When H m 3/2, the soft SUSY breaking masses dominate over thermal mass and PQ scalars ( ~ saxion ) start oscillation around Ψ Ψ f a Saxion decay temperature KSVZ axion T σ 5MeV DFSZ axion T σ 5MeV Entropy production mσ 10TeV mσ 1TeV 3/ GeV f a / GeV µ s before s after f a m th /f a / f a / f a H / f a m th / f a Ψ/f a Ψ/f a m 3/2 /f a m σ 2 f a time H/f a

11 4.4 Axion Density Axion density under the large entropy production Ω a h Tσ 1MeV Axion can be appropriately diluted and account for dark matter of the universe Other harmful relics are also diluted by entropy production thermally and non-thermally produced gravitinos thermally and non-thermally produced axinos fa GeV 2 Lazarides, Schaefer, Seckel, Shaf (1990), MK, Moroi, Yanagida (1996)

12 5. Baryogenesis All contents of the universe are diluted by late-time entropy production We need sufficiently large baryon asymmetry that survives the dilution Affleck-Dine mechanism can work A MSSM flat direction ( = squark, slepton, Higgs) has a large field value in the early universe V V = m 2 Φ Φ 2 + Φ 10 M 6 + Φ am 6 3/2 M 3 + h.c Φ n B s 3 Tσ m3/ δ CP 1MeV 1MeV + V th U(1) B 1/ GeV T R M 1000M p 3

13 6. Conclusions Inflation naturally takes place in a SUSY axion model Successful inflation requires high PQ scale f a GeV After inflation, thanks to finite temperature effect, saxion starts oscillation with large initial amplitude Saxion decays and produces huge entropy, by which axion is appropriately dilutes and its density becomes consistent with the present dark matter density Other harmful relics like gravitino and axino are also diluted Baryon asymmetry is obtained through Affleck-Dine mechanism