Outline Introduction Inflation Supersymmetry D-term Inflation right-handed sneutrino correction results Right-Handed Sneutrino Modification of D-term Hybrid Inflation in Non-mininal Supergravity Chia-Min Lin (with John McDonald) Cosmology and Astroparticle Physics Group, University of Lancaster Chia-Min Lin (with John McDonald) Cosmology and Astroparticle Physics Group, University of Lancaster Right-Handed Sneutrino Modification of D-term Hybrid Inflation
Outline Introduction Inflation Supersymmetry D-term Inflation right-handed sneutrino correction results Introduction Inflation Supersymmetry D-term Inflation right-handed sneutrino correction results Chia-Min Lin (with John McDonald) Cosmology and Astroparticle Physics Group, University of Lancaster Right-Handed Sneutrino Modification of D-term Hybrid Inflation
Outline Introduction Inflation Supersymmetry D-term Inflation right-handed sneutrino correction results Topics ◮ Inflation Chia-Min Lin (with John McDonald) Cosmology and Astroparticle Physics Group, University of Lancaster Right-Handed Sneutrino Modification of D-term Hybrid Inflation
Outline Introduction Inflation Supersymmetry D-term Inflation right-handed sneutrino correction results Topics ◮ Inflation ◮ SUSY Inflation Chia-Min Lin (with John McDonald) Cosmology and Astroparticle Physics Group, University of Lancaster Right-Handed Sneutrino Modification of D-term Hybrid Inflation
Outline Introduction Inflation Supersymmetry D-term Inflation right-handed sneutrino correction results Topics ◮ Inflation ◮ SUSY Inflation ◮ What is D-term inflation? Chia-Min Lin (with John McDonald) Cosmology and Astroparticle Physics Group, University of Lancaster Right-Handed Sneutrino Modification of D-term Hybrid Inflation
Outline Introduction Inflation Supersymmetry D-term Inflation right-handed sneutrino correction results Topics ◮ Inflation ◮ SUSY Inflation ◮ What is D-term inflation? ◮ What are the problems with D-term Inflation? Chia-Min Lin (with John McDonald) Cosmology and Astroparticle Physics Group, University of Lancaster Right-Handed Sneutrino Modification of D-term Hybrid Inflation
Outline Introduction Inflation Supersymmetry D-term Inflation right-handed sneutrino correction results Topics ◮ Inflation ◮ SUSY Inflation ◮ What is D-term inflation? ◮ What are the problems with D-term Inflation? ◮ Provide a solution. Chia-Min Lin (with John McDonald) Cosmology and Astroparticle Physics Group, University of Lancaster Right-Handed Sneutrino Modification of D-term Hybrid Inflation
Outline Introduction Inflation Supersymmetry D-term Inflation right-handed sneutrino correction results Inflation Once upon a time, the Universe was dominated by some mysterious vacuum energy: V ( φ ) = 3 H 2 M 2 Pl ≈ ρ φ ≈ const . ρ ≈ 0 ⇒ H ≡ ˙ a ∴ ˙ a ≈ const . da a = Hdt ⇒ a ∝ e Ht People named this dramatic expansion “Inflation”. The problem is, what in the world is V ( φ ) after all?! Chia-Min Lin (with John McDonald) Cosmology and Astroparticle Physics Group, University of Lancaster Right-Handed Sneutrino Modification of D-term Hybrid Inflation
Outline Introduction Inflation Supersymmetry D-term Inflation right-handed sneutrino correction results Inflation So people start to play the game of Inflation by inventing all kinds of potentials... Chia-Min Lin (with John McDonald) Cosmology and Astroparticle Physics Group, University of Lancaster Right-Handed Sneutrino Modification of D-term Hybrid Inflation
Outline Introduction Inflation Supersymmetry D-term Inflation right-handed sneutrino correction results Inflation Chia-Min Lin (with John McDonald) Cosmology and Astroparticle Physics Group, University of Lancaster Right-Handed Sneutrino Modification of D-term Hybrid Inflation
Outline Introduction Inflation Supersymmetry D-term Inflation right-handed sneutrino correction results Inflation Slow-roll inflation: A scalar potential of the field(s) V ( φ, ... ) tells you almost everything! η = M 2 V ′′ / V and ǫ = ( M 2 / 2)( V ′ / V ) 2 Spectral index: n = 1 + 2 η − 6 ǫ Curvature perturbation: V 3 1 P ζ = 12 π 2 M 6 V ′ 2 etc. Chia-Min Lin (with John McDonald) Cosmology and Astroparticle Physics Group, University of Lancaster Right-Handed Sneutrino Modification of D-term Hybrid Inflation
Outline Introduction Inflation Supersymmetry D-term Inflation right-handed sneutrino correction results Supersymmetry (Boson ↔ Fermion) Every particle corresponds to its superpartner, which must be HEAVY due to SUSY breaking. Chia-Min Lin (with John McDonald) Cosmology and Astroparticle Physics Group, University of Lancaster Right-Handed Sneutrino Modification of D-term Hybrid Inflation
Outline Introduction Inflation Supersymmetry D-term Inflation right-handed sneutrino correction results Supersymmetry Reasons for implanting SUSY into Inflation: ◮ Have scalar fields Chia-Min Lin (with John McDonald) Cosmology and Astroparticle Physics Group, University of Lancaster Right-Handed Sneutrino Modification of D-term Hybrid Inflation
Outline Introduction Inflation Supersymmetry D-term Inflation right-handed sneutrino correction results Supersymmetry Reasons for implanting SUSY into Inflation: ◮ Have scalar fields ◮ Quantum corrections could be suppressed. Chia-Min Lin (with John McDonald) Cosmology and Astroparticle Physics Group, University of Lancaster Right-Handed Sneutrino Modification of D-term Hybrid Inflation
Outline Introduction Inflation Supersymmetry D-term Inflation right-handed sneutrino correction results Supersymmetry Reasons for implanting SUSY into Inflation: ◮ Have scalar fields ◮ Quantum corrections could be suppressed. ◮ no SUSY, no good GUT. Chia-Min Lin (with John McDonald) Cosmology and Astroparticle Physics Group, University of Lancaster Right-Handed Sneutrino Modification of D-term Hybrid Inflation
Outline Introduction Inflation Supersymmetry D-term Inflation right-handed sneutrino correction results Supersymmetry Reasons for implanting SUSY into Inflation: ◮ Have scalar fields ◮ Quantum corrections could be suppressed. ◮ no SUSY, no good GUT. ◮ etc. Chia-Min Lin (with John McDonald) Cosmology and Astroparticle Physics Group, University of Lancaster Right-Handed Sneutrino Modification of D-term Hybrid Inflation
Outline Introduction Inflation Supersymmetry D-term Inflation right-handed sneutrino correction results Supersymmetry Scalar potential V = V F + V D SUSY: V F = | F | 2 ≡ | W m | 2 V D = 1 2( g q n | φ n | 2 + ξ ) 2 � 2 n SUGRA: M 2 ) − 3 | W | 2 V F = e K / M 2 � ( W m + WK m M 2 ) K m † n ( W n + WK n � M 2 V D = 1 2(Re f ) − 1 g 2 ( q n K n φ n + ξ ) 2 Chia-Min Lin (with John McDonald) Cosmology and Astroparticle Physics Group, University of Lancaster Right-Handed Sneutrino Modification of D-term Hybrid Inflation
Outline Introduction Inflation Supersymmetry D-term Inflation right-handed sneutrino correction results Conventional D-term Inflation The superpotential of D-term hybrid inflation is given by W D = λ S Φ + Φ − One-loop potential: V ( S ) = V 0 + g 4 ξ 2 16 π 2 ln( | S | 2 Λ 2 ) Chia-Min Lin (with John McDonald) Cosmology and Astroparticle Physics Group, University of Lancaster Right-Handed Sneutrino Modification of D-term Hybrid Inflation
Outline Introduction Inflation Supersymmetry D-term Inflation right-handed sneutrino correction results Problems of conventional D-term Inflation From WMAP n = 0 . 958 ± 0 . 016 However, n = 0 . 983 From cosmic string study (for example astro-ph:0702223): ξ 1 / 2 < 3 . 9 × 10 15 GeV (assume an upper limit of 10%) However, ξ 1 / 2 = 7 . 9 × 10 15 GeV Chia-Min Lin (with John McDonald) Cosmology and Astroparticle Physics Group, University of Lancaster Right-Handed Sneutrino Modification of D-term Hybrid Inflation
Outline Introduction Inflation Supersymmetry D-term Inflation right-handed sneutrino correction results Non-minimal Supergravity We consider the K¨ ahler potential of the form: K = | S | 2 + | Φ + | 2 + | Φ − | 2 + f + ( | S | 2 ) | Φ + | 2 + f − ( | S | 2 ) | Φ − | 2 + b | S | 4 M 2 M 2 M 2 P P P where f ± ( | S | 2 | S | 2 = c ± s 2 ) = c ± . M 2 M 2 2 P P Chia-Min Lin (with John McDonald) Cosmology and Astroparticle Physics Group, University of Lancaster Right-Handed Sneutrino Modification of D-term Hybrid Inflation
Outline Introduction Inflation Supersymmetry D-term Inflation right-handed sneutrino correction results D-term Inflation The effective scalar potential for the D-term inflationary model reads V eff ( | S | ) = g 2 ξ 2 g 2 2 ln( z g 2 ξ � � �� 1 + Λ 2 ) + f V ( z ) . 2 16 π 2 where f V ( z ) = ( z + 1) 2 ln(1 + 1 z ) + ( z − 1) 2 ln(1 − 1 z ) and z ≡ λ 2 s 2 2 g 2 ξ exp ( s 2 2 + bs 4 1 4 ) (1 + f + )(1 + f − ) Chia-Min Lin (with John McDonald) Cosmology and Astroparticle Physics Group, University of Lancaster Right-Handed Sneutrino Modification of D-term Hybrid Inflation
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