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 requiring  In global susy, easy to obtain chaotic inflation  In supergravity the potential depends on K Kahler potential, W superpotential K Kahler potential, W superpotential easy to obtain Hybrid inflation, tricky Chaotic inflation 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 mass of the inflaton of the Hubble scale large value of large value of needs reappraisal 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…)