Inflation and Thermal Right-Handed Sneutrino Dark Matter Apostolos - PowerPoint PPT Presentation

Inflation and Thermal Right-Handed Sneutrino Dark Matter Apostolos Pilaftsis School of Physics and Astronomy, University of Manchester, Manchester M13 9PL, United Kingdom GGI, Florence, 25–29 June 2012

Plan of the Talk • F D -Term Hybrid Inflation • Natural Solution to the Gravitino Overabundance Problem • Right-Handed Sneutrino as Thermal Dark Matter • Further Cosmological and Particle-Physics Implications • Conclusions and Future Directions ∗ Talk based on B. Garbrecht and A.P., PL B636 (2006) 154; B. Garbrecht, C. Pallis and A. P., JHEP 0612 (2006) 038; F. Deppisch and A. P., JHEP 10 (2008) 080 GGI, 25–29 June 2012 Inflation & Thermal Right-Handed Sneutrino Dark Matter A. Pilaftsis

• Standard Big-Bang Cosmology and WMAP Density perturbations as observed by WMAP δT ∼ δρ ∼ 10 − 5 T ρ GGI, 25–29 June 2012 Inflation & Thermal Right-Handed Sneutrino Dark Matter A. Pilaftsis

– Inflation Dynamics Number of e -folds: � t end � φ N 1 dφ V N e = dt H ( t ) ≈ ≈ 50 – 60 m 2 V φ t N φ end Pl Power spectrum of curvature perturbations: V 3 / 2 1 P 1 / 2 ≈ 4 . 86 × 10 − 5 ( k 0 = 0 . 002 Mpc − 1 ) √ = R 3 πm 3 | V φ | 2 Pl Spectral index: n s − 1 = d ln P 1 / 2 R = 2 η − 6 ε ≈ − 0 . 037 +0 . 015 (WMAP 5 years data) − 0 . 014 d ln k Slow-roll parameters: � V φ � 2 ε = 1 V φφ 2 m 2 η = m 2 ≪ 1 , ≪ 1 Pl Pl V V GGI, 25–29 June 2012 Inflation & Thermal Right-Handed Sneutrino Dark Matter A. Pilaftsis

• F D -Term Hybrid Inflation – Hybrid Inflation [A.D. Linde, PLB259 (1991) 38] φ c 30 4 20 V 10 3 0 2 -4 -4 φ -2 -2 1 0 0 χ 2 2 4 4 0 = λ 4( | χ | 2 − M 2 ) 2 + 1 2 g | χ | 2 | φ | 2 + 1 2 m 2 | φ | 2 V 4 M 4 + 1 V ≃ λ 2 m 2 | φ | 2 Inflation starts, when φ ≫ φ c ∼ M , χ = 0 → Inflation ends with the so-called waterfall mechanism GGI, 25–29 June 2012 Inflation & Thermal Right-Handed Sneutrino Dark Matter A. Pilaftsis

– F -Term Hybrid Inflation [ E. Copeland, A. Liddle, D. Lyth, E. Stewart, D. Wands, PRD49 (1994) 6410; G. Dvali, Q. Shafi, R. Schaefer, PRL73 (1994) 1886 ] Superpotential: W = κ � S ( � X 1 � X 2 − M 2 ) Real Potential determined from F terms: | ∂W/∂S | 2 + | ∂W/∂X 1 | 2 + | ∂W/∂X 2 | 2 V = κ 2 | X 1 X 2 − M 2 | 2 + κ 2 | S | 2 ( | X 1 | 2 + | X 2 | 2 ) = Start of inflation: S in > M , X in = κ 2 M 4 . 1 , 2 = 0 , with V X 1 , 2 -Mass Matrix: � | κ | 2 | S | 2 � − κ 2 M 2 M 2 X 1 , 2 = − κ ∗ 2 M 2 | κ | 2 | S | 2 det M 2 End of inflation: S < M → X 1 , 2 < 0 → waterfall mechanism. GGI, 25–29 June 2012 Inflation & Thermal Right-Handed Sneutrino Dark Matter A. Pilaftsis

– Slope of the Potential Potential is too flat! ∂V/∂S = 0 . Radiative lifting of the S -flat direction: � | S | 2 � V 1 − loop = κ 4 M 4 16 π 2 ln M 2 H H 2 | S | 2 + κ 2 M 4 | S | 4 SUGRA corrections: V SUGRA = − c 2 Pl + . . . 2 m 4 Number of e -folds: N e = 4 π 2 ( S in ) 2 ≈ 55 m 2 κ 2 Pl ∼ 10 − 2 − ∼ 10 − 1 m Pl → predictive scenario For 10 − 3 < → S in < ∼ κ < � � � 2 = 5 × 10 − 5 → M ∼ 10 16 GeV. Power spectrum: P 1 / 2 4 N e M = R 3 m Pl M close to the GUT or gauge-coupling unification scale M X . Spectral index: n s − 1 = − 1 N e ≈ − 0 . 02 (mSUGRA). GGI, 25–29 June 2012 Inflation & Thermal Right-Handed Sneutrino Dark Matter A. Pilaftsis

– F D -Term Hybrid Inflation [B. Garbrecht and A.P., PL B636 (2006) 154] H d + ρ κ � S ( � X 1 � X 2 − M 2 ) + λ � S � H u � S � � N i � W = N i 2 N j + W ( µ =0) ij � L i � H u � + h ν MSSM + Subdominant FI D -term of U(1) X : − g X 2 m 2 FI D X Remarks: • Mass scales: m Pl , M , m FI and M SUSY . • � S � ∼ 1 κ M SUSY sets the Electroweak and the Singlet Majorana scale: µ = λ � S � , m N = ρ � S � • Lepton Number Violation mediated by right-handed neutrinos N i occurs at the EW scale µ ∼ m N . → BAU may be explained by thermal EW-scale resonant leptogenesis. GGI, 25–29 June 2012 Inflation & Thermal Right-Handed Sneutrino Dark Matter A. Pilaftsis

[B. Garbrecht, C. Pallis, A.P., JHEP 0612 (2006) 038] 2.0 1-Loop (a) , mSUGRA , ρ = λ = 4 κ 16 GeV) 1.5 ρ = λ = κ a S = 1 TeV M (10 1.0 0.5 -5 -4 -3 -2 10 10 10 10 κ 1.020 1-Loop (b) , 1.015 mSUGRA , ρ = λ = 4 κ 1.010 ρ = λ = κ 1.005 a S = 1 TeV n s 1.000 0.995 0.990 0.985 0.980 -5 -4 -3 -2 10 10 10 10 κ GGI, 25–29 June 2012 Inflation & Thermal Right-Handed Sneutrino Dark Matter A. Pilaftsis

Next-to-mSUGRA with − c 2 H H 2 S 2 [B. Garbrecht, C. Pallis, A.P., JHEP 0612 (2006) 038] 2.5 c H = 0.07 (a) , c H = 0.14 , 2.0 ρ = λ = 4 κ 16 GeV ) ρ = λ = κ a S = 1 TeV 1.5 M ( 10 1.0 0.5 -3 -2 10 10 κ 1.08 c H = 0.07 (b) , 1.06 c H = 0.14 , ρ = λ = 4 κ 1.04 ρ = λ = κ a S = 1 TeV 1.02 n s 1.00 n s − 1 ≈ − 1 N e − c 2 H 0.98 0.96 0.94 -3 -2 10 10 κ GGI, 25–29 June 2012 Inflation & Thermal Right-Handed Sneutrino Dark Matter A. Pilaftsis

– Post-inflationary Dynamics 1 1 2 ( X 1 ± X 2 ) = � X ± � + X ± = 2 ( R ± + iI ± ) , √ √ √ m 2 v with � X + � = 2 M and � X − � = 2 = FI √ √ 2 2 M Sector Boson Fermion Mass D -parity „ ψ X + « √ Inflaton S , R + , I + ψ κ = 2 κM + ψ † S ( κ -sector) „ ψ X − « − U(1) X Gauge V µ [ I − ] , R − ψ g = gM − i λ † ( g -sector) m 4 g 2 32 π (4 λ 2 + 3 ρ 2 ) m κ , 1 Γ κ = Γ g = M 4 m g . FI 128 π GGI, 25–29 June 2012 Inflation & Thermal Right-Handed Sneutrino Dark Matter A. Pilaftsis

– Reheat Temperature and Gravitino Constraint ∼ H ( T reh Inflaton decays reheat the Universe, when Γ κ > κ ) : � 90 � 1 / 4 � T reh = Γ κ m Pl κ π 2 g ∗ ∼ 10 9 GeV) implies Generic Gravitino constraint ( T reh < κ � � � � 2 � 10 16 GeV � T reh λ 2 + 3 ∼ 3 · 10 − 15 × κ 4 ρ 2 < κ 10 9 GeV M ∼ 10 − 5 < For κ ≈ λ ≈ ρ → κ, λ, ρ Minimal F D -Term Hybrid Inflation ruled out by n s − 1 < 0 , unless . . . there is an extra source of entropy release GGI, 25–29 June 2012 Inflation & Thermal Right-Handed Sneutrino Dark Matter A. Pilaftsis

– Thermal History of the Universe ρ κ = κ 2 M 4 log ρ ρ g ρ κ = 2 . 1 · 10 − 2 × κg ρ κ ∼ a −3 κ Reheating: particles decay ρ g ∼ a −3 Preheating (instantaneous) g particles ∼ a −4 decay ∼ a −4 a coh. matter rad. Infla− osc. rad. tion GGI, 25–29 June 2012 Inflation & Thermal Right-Handed Sneutrino Dark Matter A. Pilaftsis

[B. Garbrecht, C. Pallis, A.P., JHEP 0612 (2006) 038] 6 -12 10 Y G < 10 ~ -13 Y G < 10 ~ -14 Y G < 10 ~ -5 5 1x10 10 -15 T g (GeV) m FI / M Y G < 10 ~ 4 10 3 -6 10 10 -4 -3 -2 10 10 10 κ GGI, 25–29 June 2012 Inflation & Thermal Right-Handed Sneutrino Dark Matter A. Pilaftsis

• Right-Handed Sneutrino as Thermal Dark Matter Related considerations: • D. Hooper, J. March-Russell and S. M. West, PLB605 (2005) 228. • C. Arina and N. Fornengo, JHEP0711 (2007) 029. • C. Arina, F. Bazzocchi, N. Fornengo, J. C. Romao and J. W. F. Valle, PRL101 (2008) 161802. . . . But all with significant Left-Handed Sneutrino component! GGI, 25–29 June 2012 Inflation & Thermal Right-Handed Sneutrino Dark Matter A. Pilaftsis

– Right-Handed Sneutrinos in the F D -Term Hybrid Model ∆( B − L ) = 0 or 2 − → R -Parity Conservation. Right-handed sneutrino mass matrix: � � ρ 2 v 2 S + M 2 ρA ρ v S + ρλv u v d M 2 e N N = ρA ∗ ρ 2 v 2 S + M 2 e ρ v S + ρλv u v d e N → m 2 N LSP = ρ 2 v 2 S + M 2 − N − ( ρA ρ v S + ρλv u v d ) . e e New LSP interaction: [B. Garbrecht, C. Pallis and A. P., JHEP 0612 (2006) 038] = 1 2 λρ � N ∗ i � N ∗ L LSP i H u H d + H . c . int SUSY version of the Higgs-Portal scenario. [V. Silveira and A. Zee, PLB161 (1985) 136; J. McDonald, PRD50 (1994) 3637.] GGI, 25–29 June 2012 Inflation & Thermal Right-Handed Sneutrino Dark Matter A. Pilaftsis

N LSP → � H u � H d → W + W − ( m e Process: � N LSP � N LSP > M W ) � 10 − 4 � � tan β M H � 2 Ω DM h 2 ∼ > − → λ , ρ ∼ 0 . 1 ρ 2 λ 2 g w M W N LSP → � H u � H d → b ¯ Process: � N LSP � ( M H d ≈ 2 m e b N LSP < 2 M W ) � � 2 M H Ω DM h 2 ∼ 10 − 4 × B − 1 ( H d → � N LSP � ∼ 10 − 2 λ , ρ > N LSP ) × − → 100 GeV Limits from Cosmological Inflation: 2 . 3 × 10 − 4 < λ ( M SUSY ) ρ ( M SUSY ) ( mSUGRA ) ∼ 5 . 8 × 10 − 4 < ( nmSUGRA ) ∼ GGI, 25–29 June 2012 Inflation & Thermal Right-Handed Sneutrino Dark Matter A. Pilaftsis

[F. Deppisch, A.P., JHEP 10 (2008) 080] Numerical estimate assisted by CPsuperH2.0 [J. S. Lee, M. Carena, J. Ellis, A. P., C. E. M. Wagner, arXiv:0712.2360 [ hep-ph ] . ] GGI, 25–29 June 2012 Inflation & Thermal Right-Handed Sneutrino Dark Matter A. Pilaftsis

[F. Deppisch, A.P., JHEP 10 (2008) 080] Dama � Na Dama � I 10 0 CoGeNT 10 � 1 Xenon100 ΛΡ 10 � 2 Xenon1T 10 � 3 � � 0 LSP mSUGRA N Χ 1 1 10 � 4 10 1 10 2 m N � 1 � GeV � m 0 = 70 GeV , m 1 / 2 = 243 GeV , A 0 = 300 GeV , tan β = 10 , µ = 303 GeV . GGI, 25–29 June 2012 Inflation & Thermal Right-Handed Sneutrino Dark Matter A. Pilaftsis