Finnish-Japanese Workshop on Particle Physics 2007 Moduli Problem, Thermal Inflation and Baryogenesis Masahiro Kawasaki Institute for Cosmic Ray Research University of Tokyo
Cosmological Moduli Problem Superstring Theory Light Moduli Field Φ m φ m 3/2 Long Lifetime gravitationally suppressed interactions Cosmological Difficulty BBN Cosmic Density...
V 1 2 m2 φφ 2 + 1 2 H2 (φ φ 0 ) 2 V H m φ Hubble induced mass V H < m φ Moduli starts oscillation with large amplitude φ 0 M G 10 18 GeV
Cosmic Density Coughlan, Fischler, Kolb, Raby, Ross (1983) Banks et al (1994), de Carlos et al (1993) ( Ω φ 5 10 16 m ) φ GeV for stable moduli Moduli Decay τ φ M pl m 2 φ 10 14 sec ( mφ GeV ) 3 m φ < 0.1 GeV Background Radiations(X-rays, γ-rays) BBN (Destroy Light elements) CBR (spectral distortion) Constraints on Density
Cosmological Constraint h 2 10 2 10 1 10 0 10!1 10!2 10!3 10!4 10!5 10!6 10!7 10!8 10!9 10!10 Ω φ = (ρ φ /s)/(ρ cr,0 /s 0 ) X and rays Cosmic Density 10!8 10!7 10!6 10!5 10!4 10!3 10!2 10!1 10 0 10 1 10 2 10 3 10 4 m [GeV] BBN(rad) CBR BBN (hadron) Asaka,MK (1999) + MK, Kohri, Moroi (2005) for BBN
Cosmological Constraint h 2 10 2 10 1 10 0 10!1 10!2 10!3 10!4 10!5 10!6 10!7 10!8 10!9 10!10 Ω φ = (ρ φ /s)/(ρ cr,0 /s 0 ) ( Ω φ 5 10 16 m ) φ X and rays GeV BBN(rad) Cosmic Density CBR 10!8 10!7 10!6 10!5 10!4 10!3 10!2 10!1 10 0 10 1 10 2 10 3 10 4 m [GeV] BBN (hadron) Serious Problem Asaka,MK (1999) + MK, Kohri, Moroi (2005) for BBN
Solution to Moduli Problem Large Entropy Production dilute moduli Thermal Inflation Domain Wall Decay Others Lyth, Stewart (1995) MK, F.Takahashi (2005) Heavy Moduli Large Hubble induced mass....... V CH 2 φ 2 C 1 Linde (1996)
Thermal Inflation Lyth, Stewart (1995) Yamamoto (1986) Flaton (χ) potential V V 0 + (T 2 m 2 0) χ 2 + χ 6 finite temp 2 M V( ) T > m 0 V 0 T=0 m 0 < T < V 1/4 0 Vacuum energy dominates Inflation with e-fold ~10
Thermal Inflation dilute big bang moduli
Thermal Inflation dilute big bang moduli However, V 1 2 m2 φφ 2 + 1 2 H2 (φ φ 0 ) 2 1 2 m2 φ ( φ + H2 m 2 φ φ 0 ) 2 + During TI the minimum of the potential deviates from 0 new oscillations of moduli Moduli Density = Big Bang Moduli+TI Moduli
Minimum Moduli Density Predicted by TI h 2 10 2 10 1 10 0 10!1 10!2 10!3 10!4 10!5 10!6 10!7 10!8 10!9 10!10 Moduli Density X and rays T > 10MeV R Cosmic Density 10!8 10!7 10!6 10!5 10!4 10!3 10!2 10!1 10 0 10 1 10 2 10 3 10 4 m [GeV] BBN(rad) CBR BBN (hadron) Hashiba, MK, Yanagida (1997) Asaka,MK (1999)
Baryon Number of the Universe? Large entropy production with Low T R dilute pre-existing baryons Most of conventional baryogenesis mechanisms may not work Affleck-Dine baryogenesis work for m φ < O(10)MeV n b /s 2 10 9 Ω φ (m φ /GeV) 1
Baryon Number of the Universe? Large entropy production with Low T R dilute pre-existing baryons Most of conventional baryogenesis mechanisms may not work Affleck-Dine baryogenesis However, Q-ball Formation work for Obstacle to AD m φ < O(10)MeV n b /s 2 10 9 Ω φ (m φ /GeV) 1
Late-time Affleck-Dine Leptogenesis by LH Flat Direction u Superpotential Stewart, MK, Yanagida (1996) Joeng et al (2004) MSSM W = y u QH u u + y d QH d d + y e LH d e + λ χ 4M χ4 + λ ν 2M (LH u)(lh u ) + λ µ M χ2 H u H d χ Flaton neutrino mass µ term for χ 0 LH has a large vev after thermal inflation u Leptogenesis
Scalar Potential of Flat Directions V = V F + V D + V SB L = ( 0 l F-term D-term V D = g2 2 ( hu 2 l 2 h d 2) 2 Soft SUSY breaking terms CP phase ), H u = ( ) hu, H 0 d = ( h d 0 ) V F = 1 M 2 { λ χ χ 3 + 2λ µ χh u h d 2 + λ ν lh 2 u 2 + λ µ χ 2 h d + λ ν l 2 h u 2 + λ µ χ 2 h u 2 } V SB = V 0 m 2 χ χ 2 + m 2 L l 2 m 2 H u h u 2 + m 2 H d h d 2 { } Aχ λ + χ 4M χ4 + A µλ µ M χ2 h u h d + A νλ ν 2M l2 h 2 u + c.c. L arg(λ µ λ ν) arg(λ χ λ µ)
Dynamics of Flat Directions (1) At the end of thermal inflation χ = 0 m 2 LH u m 2 L m 2 H u < 0 LH u flat direction rolls away from the origin (2) Flaton rolls down χ = χ 0 µ term 0.003 (1) (2) m 2 LH u m 2 L m 2 H u + µ 2 > 0 LH u direction starts to rotate Lepton number generation l 0.002 0.001 0-0.001-0.01 0 0.01 0.02 0.03 l
Lattice Calculation Nakayama, MK (2006) We studied the full dynamics by using lattice simulation including all relevant scalar fields Initial angular dependence of baryon asymmetry 6 10 10 T R = 1 GeV 4 2 arg(λ µ λ ν) = π/16 n B s 0 2 4 6 net baryon asym 8 0 0.5 1 1.5 2 2.5 3 l λ µ = 35 λ ν = 10 4 m χ = 180 GeV, m Hu = 700 GeV, m Hd = 800 GeV, m L = 640 GeV, λ χ = 4, A µ = 450 GeV, A ν = 200 GeV, A χ = 20 GeV, arg(λ χ λ µ) = π/4
Resultant baryon asymmetry vs CP violation 10 8 10 11 6 4 n B s 2 0-2 - 4-6 - 8 10 0 1 2 3 4 5 6 * λ µ λ ν arg(λ µ λ ν) = π/4, 5π/4 no CP violation Net baryon asymmetry can be created due to CP
n B s 1 T R 12 10 8 6 4 2 10 11 µ µ µ µ = λ µ φ 2 0 M m ν = λ ν h u 2 M 0 0.0001 0.001 0.01 0.1 m ν µ 800 840 GeV m ν 10 3 10 1 ev This scenario works However, we only investigated restricted parameter space
Conclusion Moduli Problem is solved by thermal inflation However, baryon number is also diluted by thermal inflation Baryon number can be re-generated through late-time AD mechanism