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Particle Physics Models of Inflation in Supergravity: New Developments

Particle Physics Models of Inflation in Supergravity: New Developments. Stefan Antusch based on collaborations with: K. Dutta, M. Bastero-Gil, J.P. Baumann, V. Domcke, S.F. King, and P.M. Kostka. Max-Planck- Institut für Physik (Werner-Heisenberg-Institut ).

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Particle Physics Models of Inflation in Supergravity: New Developments

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  1. Particle Physics Models of Inflation in Supergravity: New Developments Stefan Antuschbased on collaborations with: K. Dutta, M. Bastero-Gil, J.P. Baumann, V. Domcke, S.F. King, and P.M. Kostka Max-Planck-Institutfür Physik(Werner-Heisenberg-Institut) Talk at COSMO/CosPA 2010, September 30th, Tokyo, Japan

  2. Inflation = Era of accelerated expansion in the very early universe picture from WMAP website

  3. Outline • New possible solution to the η-problem in SUGRA inflation:Heisenberg symmetry with stabilised modulus • New class of models, very suitable for applying symmetry solutions to the η-problem: Tribrid Inflation • New possibile connection to particle physics (application of‘Tribrid Inflation’): Unified Matter Inflation in SUSY GUTs

  4. Inflationary epoch in the early universe • Requirements for “slow roll“ inflation • “Slow roll parameters” small: ε, |η|, ξ << 1, V ~ V0 dominates“slope of V” “inflaton mass”

  5. The η-problem • Challenge for realising inflation: Flat enough potential, • Generic (effective field theory) • In supergravity (with K = ϕ*ϕ and V0 from F-term) V ⊂ with E.J Copeland, A.R. Liddle, D.H. Lyth, E.D. Stewart, D. Wands ('94)

  6. Approaches to solve the η-problem: 3 strategies requires tuning of parameters!(at 1%-level) • Expansion of K in fields/MP: • 'Shift' symmetry: • Heisenberg symmetry: protects Im[ϕ] from obtaininga SUGRA mass by symmetry! (used in many works ...) solves the η-problem for |ϕ| by symmetry! Gaillard, Murayama, Olive ('95),S.A., Bastero-Gil, Dutta, King, Kostka (’08,’09) T: 'modulus field’ → has to be stabilised

  7. Remark:Symmetries have to be broken to allow for slope of V(ϕ)!→ approximate symmetries Approaches to solve the η-problem: 3 strategies • Expansion of K in fields/MP: • 'Shift' symmetry: • Heisenberg symmetry:

  8. Heisenberg symmetry solution to the η-problem • Example for K: • Field X: Provides the vacuum energy V0 by |FX|2 during inflation • Consider suitable W with (i) Winf = 0, Wϕ = 0 during inflation and (ii) which yields a tree-level ϕ-flat potential in global SUSY limit • Parameter κρ: Couples ρ to V0 } K invariant under Heisenberg symmetry Example: No-scale form; More general: f(ρ) S.A., M. Bastero-Gil, K. Dutta, S. F. King, P. M. Kostka ('08)

  9. Heisenberg symmetry solution to the η-problem • Calculate Lkin and VF: • In the the (ϕ,ρ)-basis: no kinetic mixing between ϕ and ρ • The F-term scalar potential depends only on ρ (and not on ϕ) → η-problem solved! → ρ can be stabilsed by large V0

  10. Modulus field ρ gets stabilized quickly andallows for >> 60 e-foldsof inflation! With V = Vtree + Vloop ρ,ϕ ϕ S.A., M. Bastero-Gil, K. Dutta, S. F. King, P. M. Kostka ('08)

  11. A new class of inflation models:Tribrid Inflation • Simple example (singlet fields, global SUSY to start with): • Three fields, X, H and Φ relevant for the model → “Tribrid Inflation“ Driving superfield Waterfall superfield Inflaton superfield First model of this class in: S.A., Bastero-Gil, King, Shafi (’04)“Tribrid Inflation” in SUGRA: S.A., Dutta, Kostka (’09);S.A., M. Bastero-Gil, K. Dutta, S. F. King, P. M. Kostka ('08)

  12. A new class of inflation models:Tribrid inflation • Simple example (singlet fields, global SUSY to start with): Driving superfield(its F-term generates the potential for H and provides the vacuum energy V0; During and after inflation: <X> = 0.) V(H,Φ=0) } V0 |FX |2 ⇒

  13. A new class of inflation models:Tribrid inflation • Simple example (singlet fields, global SUSY to start with): Waterfall superfield(contains the “waterfall field” (e.g. GUT- or Flavour-Higgs field) that ends inflation by a 2nd order phase transition and gives mass to ϕ after inflation) Driving superfield(its F-term generates the potential for H and provides the vacuum energy V0; During and after inflation: <X> = 0.) V(H,Φ=0) } V0

  14. A new class of inflation models:Tribrid inflation • Simple example (singlet fields, global SUSY to start with): Inflaton superfield(contains the inflaton fieldas scalar component;For <ϕ> > ϕcrit it stabilises H at <H> = 0) V(H,Φ=0) } V0

  15. A new class of inflation models:Tribrid inflation • Simple example (singlet fields, global SUSY to start with): → Inflaton candidates are e.g.: Inflaton superfield(contains the inflaton fieldas scalar component;For <ϕ> > ϕcrit it stabilises H at <H> = 0) i) Right-handed Sneutrino(in ‘Tribrid Inflation’-type scenario): S.A., Bastero-Gil, King, Shafi (‘04)ii) Unified Matter Sparticle (16 of SO(10) SUSY GUT)S.A., Bastero-Gil, Baumann,Dutta, King, Kostka (‘10) V(H,Φ=0) } V0

  16. A new class of inflation models:Tribrid inflation • Simple example (singlet fields, global SUSY to start with): During inflation: Inflaton superfield(contains the inflaton fieldas scalar component;For <ϕ> > ϕcrit it stabilises H at <H> = 0)

  17. A new class of inflation models:Tribrid inflation • Simple example (singlet fields, global SUSY to start with): End of inflation: Inflaton superfield(contains the inflaton fieldas scalar component;For <ϕ> > ϕcrit it stabilises H at <H> = 0)

  18. A new class of inflation models:Tribrid inflation • Simple example (singlet fields, global SUSY to start with): After inflation: Inflaton superfield(contains the inflaton fieldas scalar component;For <ϕ> > ϕcrit it stabilises H at <H> = 0)

  19. Non-thermal leptogenesis after sneutrino inflation:very efficient way of generating the observed baryon asymmetry! A new class of inflation models:Tribrid inflation • Simple example (singlet fields, global SUSY to start with): After inflation: Recent study within ‘hybrid-like’ models:‘Sneutrino Hybrid Inflation and Leptogenesis’S.A., Baumann, Domcke, Kostka (‘10)

  20. Tribrid inflation in Supergravity • Example model in SUGRA: • η-problem solved: • Flat potential for ϕ at tree-level • Slope from V1-loop breaks the Heisenberg symmetry K invariant under Heisenberg symmetry S.A., M. Bastero-Gil, K. Dutta, S. F. King, P. M. Kostka (‘08)

  21. S.A., K. Dutta, P. M. Kostka ('09) running of the spectral index (αS) spectral index ns r = AT /AS M: scale of the phase transition very small(as typical for Hybrid-type models) Example: Predictions in a toy model ...

  22. Example: SO(10) GUTs Can the inflaton be a Gauge Non-Singlet? • Example model of GNS inflation in SUGRA: • Many additional challenges for GNS inflation ... all resolved! i = (1,...,4) S.A., Bastero-Gil, Baumann, Dutta, King, Kostka (‘10)

  23. More in Posters ... • ‘Unified Matter Inflation in SUSY GUTs‘Poster by Jochen Baumann • ‘Matter Inflation and Heisenberg Symmetry in Heterotic String Theory‘Poster by Sebastian Halter

  24. Summary and Conclusions • We discussed three recent developments ... • Heisenberg symmetry with stabilised modulus: Interesting solution to the η-problem in SUGRA inflation • Tribrid Inflation: New class of models, very suitable for applying symmetry solutions to the η-problem • Unified Matter Inflation in SUSY/SUGRA GUTs: Inflaton field can be in a GUT matter representation, e.g. in 16 of SO(10)

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