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Innovations in Supergravity Inflation Models: Addressing the η-Problem and Tribrid Inflation

This presentation by Stefan Antusch, shedding light on recent advancements in supergravity inflation models, addresses the longstanding η-problem in cosmology. By introducing the concept of Heisenberg symmetry and the new class of Tribrid Inflation models, it outlines potential connections to particle physics, specifically within the framework of supersymmetric Grand Unified Theories (SUSY GUTs). The collaborative efforts dive into the requirements for “slow roll” inflation and present innovative strategies to stabilize potentials, driving our understanding of the early universe’s inflationary phase forward.

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Innovations in Supergravity Inflation Models: Addressing the η-Problem and Tribrid Inflation

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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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