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#### Presentation Transcript

**1. ** Inflation, String Theory, Andrei Linde

**2. ** Contents: Inflation as a theory of a harmonic oscillator
Inflation and observations
Inflation in supergravity
String theory and cosmology
Eternal inflation and string theory landscape
Origins of symmetry: moduli trapping

**3. **Various models of inflation Starobinsky model Starobinsky 1979
Old Inflation Guth 1981
New Inflation A.L., Albrecht, Steinhardt 1982
Chaotic Inflation A.L. 1983
Hybrid Inflation A.L. 1991

**4. ** Inflation as a theory of a harmonic oscillator

**5. **Einstein:
Klein-Gordon:

**6. ** Logic of Inflation:

**7. ** Phase portrait of chaotic inflation

**8. **Add a constant to the energy of a harmonic oscillator - obtain 2 stages of inflation

**9. ** WMAP and the temperature of the sky

**12. **Comparing different inflationary models: Chaotic inflation can start in the smallest domain of size 10-33 cm with total mass ~ Mp (less than a milligram) and entropy O(1)
New inflation can start only in a domain with mass 6 orders of magnitude greater than Mp and entropy greater than 109
Cyclic inflation can occur only in the domain of size greater than the size of the observable part of the universe, with mass > 1055 g and entropy > 1087

**13. ** Chaotic inflation in supergravity

**14. ** A solution: shift symmetry

**16. ** Volume stabilization Warped geometry of the compactified space and nonperturbative effects AdS space (negative vacuum energy) with unbroken SUSY and stabilized volume
Uplifting AdS space to a metastable dS space (positive vacuum energy) by adding anti-D3 brane (or D7 brane with fluxes)

**17. ** Implications for dark energy:

**18. ** Inflation with stabilized volume Use KKLT volume stabilization
Kachru, Kallosh, Linde, Maldacena, McAllister, Trivedi 2003
Introduce the inflaton field with the potential which is flat due to shift symmetry
Break shift symmetry either due to superpotential or due to radiative corrections

**19. **String inflation and shift symmetry

**20. ** Why shift symmetry?

**22. ** Landscape of eternal inflation

**23. ** Self-reproducing Inflationary Universe

**25. ** Two possible regimes: Resurrection: From any dS minimum one can always jump back with probability e?S, and experience a stage of inflation
Eternal youth: A much greater fraction of the total volume is produced due to eternal jumps in dS space at large energy density, and subsequent tunneling followed by chaotic inflation

**26. **Solutions for Stochastic Equations:

**27. ** From discretuum to continuum

**28. **Quantum effects lead to particle production which result in moduli trapping near enhanced symmetry points
These effects are stronger near the points with greater symmetry, where many particles become massless
This may explain why we live in a state with a large number of light particles and (spontaneously broken) symmetries

**29. ** Basic Idea

**35. **Interesting features of moduli trapping: ESP with greater symmetry (with larger number of fields becoming massless at these points) are more attractive
Symmetry may grow step by step
Example: