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SHIFT SYMMETRY and INFLATION in SUPERGRAVITY

SHIFT SYMMETRY and INFLATION in SUPERGRAVITY. Ph. Brax and J. Martin hep/th0504168 to appear in PRD. Outline. The flatness problem in supergravity Mutated chaotic inflation. Inflation and Supergravity. Inflation requires flat potentials Almost scale invariant spectrum requiring

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SHIFT SYMMETRY and INFLATION in SUPERGRAVITY

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  1. SHIFT SYMMETRY and INFLATION in SUPERGRAVITY Ph. Brax and J. Martin hep/th0504168 to appear in PRD

  2. Outline The flatness problem in supergravity Mutated chaotic inflation

  3. 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 easy to obtain Hybrid inflation, tricky Chaotic inflation

  4. 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 needs reappraisal

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

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

  7. Sugra implementation Small arguments Shift symmetry

  8. 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

  9. 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

  10. The scalar potential

  11. Curved inflationary trajectory • Scalar potential • Curved trajectory Inflationary valley • End of inflation

  12. Mutated vs Hybrid

  13. Spectral Index • Comparison with chaotic inflation • Mutated chaotic inflation • Proviso: need to take into account the entropy perturbations (two field inflation)

  14. 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…)

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