SHIFT SYMMETRY and INFLATION in SUPERGRAVITY

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SHIFT SYMMETRY and INFLATION in SUPERGRAVITY

• Ph. Brax and J. Martin
• hep/th0504168
• to appear in PRD

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Outline

• The flatness problem in supergravity
• Mutated chaotic inflation

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Inflation and Supergravity

• Inflation requires flat potentials
• Almost scale invariant spectrum
• requiring
• In global susy, easy to obtain chaotic inflation
• In supergravity the potential depends on
• K Kahler potential, W superpotential

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KKLT Stabilisation and Inflation

• In string theory Moduli (volume of the
  compactifying manifold)
• Stabilisation
• Inflation motion of D3 branes
• Brane-antibrane potential lifts the potential
• Around the stabilised modulus
• mass of the inflaton of the Hubble scale
• large value of

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The flatness problem

• In supergravity models of inflation, the scalar
  potential
• For canonically normalised fields, large mass for
  the inflaton
• Generically, scalar index

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Shift Symmetry

• Inflaton flat direction
• Lifted by interactions
• Along the flat direction shift symmetry
• Natural in string theory motion of D3/D7

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• Sugra implementation
• Small arguments
• Shift symmetry

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Special form of the superpotential
After a Kahler transformation
Inflation obtained by breaking shift symmetry in
the superpotential
Does not generate large values of the mass
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Mutated chaotic inflation

• Superpotential for modulus
• Leads to AdS susy vacuum
• Introduce a lifting term breaking susy
  and
• Superpotential for inflation
• Chaotic inflation superpotential
• Can be obtained in the condensed phase of
• D3/D7 system
• COBE normalisation

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The scalar potential
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Curved inflationary trajectory

• Scalar potential
• Curved trajectory
• Inflationary valley
• End of inflation

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Mutated vs Hybrid
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Spectral Index

• Comparison with chaotic inflation
• Mutated chaotic inflation
• Proviso need to take into account the entropy
  perturbations (two field inflation)

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Conclusions

• Inflationary model combining modulus
  stabilisation and chaotic inflation
• Shift symmetry alleviates the flatness problem of
  F-term supergravity inflation
• Curved inflationary trajectory necessitates a
  special treatment for perturbations (spectral
  index)