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Inflation, String Theory,

Contents:. Inflation as a theory of a harmonic oscillatorInflation and observationsInflation in supergravityString theory and cosmologyEternal inflation and string theory landscapeOrigins of symmetry: moduli trapping. Various models of inflation. Starobinsky model Starobinsky 1979Old Inflation Guth 1981New Inflation A.L., Albrecht, Steinhardt 1982Chaotic Inflation A.L. 1983Hybrid Inflation A.L. 1991.

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Inflation, String Theory,

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    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:

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