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					        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

Talk at COSMO/CosPA 2010,             Max-Planck-Institut für Physik
September 30th, Tokyo, Japan     1    (Werner-Heisenberg-Institut)
Inflation = Era of accelerated expansion in the very early universe




                                                    picture from WMAP website

                                                Stefan Antusch
                                 2              MPI für Physik (Munich)
                           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




                                                  Stefan Antusch
                                 3                MPI für Physik (Munich)
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”




                                                     Stefan Antusch
                                   4                 MPI für Physik (Munich)
                                   The η-problem

‣ Challenge for realising inflation: Flat enough potential,

   •   Generic (effective field theory)

                V ⊂


   •   In supergravity (with K = ϕ*ϕ and V0 from F-term)




                                                                      with



 E.J Copeland, A.R. Liddle, D.H. Lyth, E.D. Stewart, D. Wands ('94)
                                                                      Stefan Antusch
                                                       5              MPI für Physik (Munich)
   Approaches to solve the η-problem:
             3 strategies
‣ Expansion of K in fields/MP:                    requires tuning of parameters!
                                                  (at 1%-level)




‣ 'Shift' symmetry:                               protects Im[ϕ] from obtaining
                                                  a SUGRA mass by symmetry!
                                                  (used in many works ...)




                                                  solves the η-problem for |ϕ| by
‣ Heisenberg symmetry:                            symmetry!




                                                  Gaillard, Murayama, Olive ('95),
                                                  S.A., Bastero-Gil, Dutta, King, Kostka (’08,’09)

  T: 'modulus field’ → has to be stabilised                  Stefan Antusch
                                              6              MPI für Physik (Munich)
   Approaches to solve the η-problem:
             3 strategies
‣ Expansion of K in fields/MP:



‣ 'Shift' symmetry:                  Remark:
                                     Symmetries have to be broken
                                     to allow for slope of V(ϕ)!
                                     → approximate symmetries

‣ Heisenberg symmetry:



                                                  Stefan Antusch
                                 7                MPI für Physik (Munich)
         Heisenberg symmetry solution to
                 the η-problem
‣ Example for K:
          }

                                                 K invariant under Heisenberg symmetry
    Example: No-scale form; More general: f(ρ)



   → 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

S.A., M. Bastero-Gil, K. Dutta,
S. F. King, P. M. Kostka ('08)                               Stefan Antusch
                                             8               MPI für Physik (Munich)
     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

                                                     Stefan Antusch
                                   9                 MPI für Physik (Munich)
                                           Modulus field ρ gets
                                           stabilized quickly and
                                           allows for >> 60 e-folds
      With V = Vtree + Vloop               of inflation!
ρ,ϕ




                                  ϕ




S.A., M. Bastero-Gil, K. Dutta,
S. F. King, P. M. Kostka ('08)             Stefan Antusch
                                      10   MPI für Physik (Munich)
              A new class of inflation models:
                      Tribrid Inflation
 ‣ Simple example (singlet fields, global SUSY to start with):




Driving superfield                             Waterfall superfield   Inflaton superfield

      •   Three fields, X, H and Φ relevant for the model → “Tribrid Inflation“




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)
                                                                      Stefan Antusch
                                                              11      MPI für Physik (Munich)
          A new class of inflation models:
                  Tribrid inflation
‣ Simple example (singlet fields, global SUSY to start with):




Driving superfield
(its F-term generates the                        V(H,Φ=0)

                                                        }
potential for H and provides
the vacuum energy V0;
During and after inflation:    |FX |2 ⇒                      V0
<X> = 0.)




                                                Stefan Antusch
                                     12         MPI für Physik (Munich)
          A new class of inflation models:
                  Tribrid inflation
‣ Simple example (singlet fields, global SUSY to start with):




Driving superfield                              Waterfall superfield
(its F-term generates the                       (contains the “waterfall field”
potential for H and provides                    (e.g. GUT- or Flavour-Higgs
the vacuum energy V0;                           field) that ends inflation by a
During and after inflation:                     2nd order phase transition and
<X> = 0.)
                                 V(H,Φ=0)       gives mass to ϕ after inflation)


                                       }   V0


                                                  Stefan Antusch
                                 13               MPI für Physik (Munich)
      A new class of inflation models:
              Tribrid inflation
‣ Simple example (singlet fields, global SUSY to start with):




                                                 Inflaton superfield
                                                 (contains the inflaton field
                                                 as scalar component;
                                                 For <ϕ> > ϕcrit it stabilises
                                                 H at <H> = 0)
                                 V(H,Φ=0)

                                       }   V0


                                                Stefan Antusch
                                14              MPI für Physik (Munich)
               A new class of inflation models:
                       Tribrid inflation
  ‣ Simple example (singlet fields, global SUSY to start with):




→ Inflaton candidates are e.g.:
                                                        Inflaton superfield
i) Right-handed Sneutrino                               (contains the inflaton field
(in ‘Tribrid Inflation’-type scenario):                 as scalar component;
S.A., Bastero-Gil, King, Shafi (‘04)                    For <ϕ> > ϕcrit it stabilises
                                                        H at <H> = 0)
ii) Unified Matter Sparticle
   (16 of SO(10) SUSY GUT)
                                          V(H,Φ=0)
S.A., Bastero-Gil, Baumann,
Dutta, King, Kostka (‘10)
                                               }   V0


                                                        Stefan Antusch
                                          15            MPI für Physik (Munich)
      A new class of inflation models:
              Tribrid inflation
‣ Simple example (singlet fields, global SUSY to start with):



                      During inflation:
                                                 Inflaton superfield
                                                 (contains the inflaton field
                                                 as scalar component;
                                                 For <ϕ> > ϕcrit it stabilises
                                                 H at <H> = 0)




                                                Stefan Antusch
                                     16         MPI für Physik (Munich)
      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 field
                                                 as scalar component;
                                                 For <ϕ> > ϕcrit it stabilises
                                                 H at <H> = 0)




                                                Stefan Antusch
                                     17         MPI für Physik (Munich)
      A new class of inflation models:
              Tribrid inflation
‣ Simple example (singlet fields, global SUSY to start with):



                      After inflation:
                                                 Inflaton superfield
                                                 (contains the inflaton field
                                                 as scalar component;
                                                 For <ϕ> > ϕcrit it stabilises
                                                 H at <H> = 0)




                                                Stefan Antusch
                                         18     MPI für Physik (Munich)
      A new class of inflation models:
              Tribrid inflation
‣ Simple example (singlet fields, global SUSY to start with):



                      After inflation:
                                                      Non-thermal
                                                      leptogenesis after
                                                      sneutrino inflation:
                                                      very efficient way of
                                                      generating the observed
                                                      baryon asymmetry!


                                              Recent study within ‘hybrid-like’ models:
                                              ‘Sneutrino Hybrid Inflation and Leptogenesis’
                                              S.A., Baumann, Domcke, Kostka (‘10)


                                                         Stefan Antusch
                                         19              MPI für Physik (Munich)
            Tribrid inflation in Supergravity

‣ Example model in SUGRA:
                                                       breaks the Heisenberg
                                                       symmetry




                                          K invariant under Heisenberg symmetry



  → η-problem solved:
   Flat potential for ϕ at tree-level
   Slope from V1-loop


S.A., M. Bastero-Gil, K. Dutta,                      Stefan Antusch
S. F. King, P. M. Kostka (‘08)       20              MPI für Physik (Munich)
                                                                       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 ...
                                                                        Stefan Antusch
                                                         21             MPI für Physik (Munich)
  Can the inflaton be a Gauge Non-Singlet?

    ‣ Example model of GNS inflation in SUGRA:




     Many additional
                                                        Example: SO(10) GUTs
        challenges
        for GNS inflation
        ... all resolved!
                                                         i = (1,...,4)




S.A., Bastero-Gil, Baumann, Dutta, King, Kostka (‘10)
                                                                         Stefan Antusch
                                                        22               MPI für Physik (Munich)
                 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




                                                 Stefan Antusch
                               23                MPI für Physik (Munich)
           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)




                                                      Stefan Antusch
                                   24                 MPI für Physik (Munich)

				
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