Inflation, String Theory,

1. Inflation, String Theory, and Origins of Symmetry • AndreiLinde

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. Inflation as a theory of a harmonic oscillator

4. Equations of motion: • Einstein: • Klein-Gordon: Compare with equation for the harmonic oscillator with friction:

5. Logic of Inflation: Large φ largefriction largeH field φ moves very slowly, so that its potential energy for a long time remains nearly constant No need for false vacuum, supercooling, phase transitions, etc.

6. Add a constant to the inflationary potential - obtain two stages of inflation

7. A photographic image of quantum fluctuations blown up to the size of the universe

8. How important is the gravitational wave contribution? For these two theories the ordinary scalar perturbations coincide:

9. Is the simplest chaotic inflation natural? • Often repeated (but incorrect) argument: Thus one could expect that the theory is ill-defined at However, quantum corrections are in fact proportional to and to These terms are harmless for sub-Planckian masses and densities, even if the scalar field itself is very large.

10. Chaotic inflation in supergravity Main problem: .. Canonical Kahler potential is Therefore the potential blows up at large |φ|, and slow-roll inflation is impossible: Too steep, no inflation…

11. A solution: shift symmetry Kawasaki, Yamaguchi, Yanagida 2000 Equally legitimate Kahler potential and superpotential The potential is very curved with respect to X and Re φ, so these fields vanish But Kahler potential does not depend on The potential of this field has the simplest form, without any exponential terms:

12. Inflation in String Theory The volume stabilization problem: Consider a potential of the 4d theory obtained by compactification in string theory of type IIB Here is the dilaton field, and describes volume of the compactifiedspace The potential with respect to these two fields is very steep, they run down, and V vanishes Giddings, Kachru and Polchinski 2001 The problem of the dilaton stabilization was solved in 2001, but the volume stabilization problem was most difficult and was solved only recently (KKLTconstruction) Kachru, Kallosh, Linde, Trivedi 2003 Burgess, Kallosh, Quevedo, 2003

13. Volume stabilization Basic steps: • Warped geometry of the compactified space and nonperturbative effectsAdS space (negative vacuum energy) with unbroken SUSY and stabilized volume • Uplifting AdS space to a metastabledS space (positive vacuum energy) by adding anti-D3 brane (or D7 brane with fluxes) AdS minimum Metastable dS minimum

14. 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 Hsu, Kallosh , Prokushkin 2003 Koyama, Tachikawa, Watari 2003 Firouzjahi, Tye 2003 Hsu, Kallosh 2004 Alternative approach: Modifications of kinetic terms in the strong coupling regime Silverstein and Tong, 2003

15. String inflation and shift symmetry Hsu, Kallosh , Prokushkin 2003

16. Why shift symmetry? It is not just a requirement which is desirable for inflation model builders, but, in a certain class of string theories, it is an unavoidable consequence of the mathematical structure of the theory Hsu, Kallosh, 2004

17. The Potential of the Hybrid D3/D7 Inflation Model is a hypermultiplet is an FI triplet

18. In many F and D-term models the contribution of cosmic strings to CMB anisotropy is too large • This problem disappears for very small coupling g • Another solution is to add a new hypermultiplet, and a new global symmetry, which makes the strings semilocal and topologically unstable

19. Semilocal Strings are Topologically Unstable Achucarro, Borill, Liddle, 98

20. D3/D7 with two hypers Dasgupta, Hsu, R.K., A. L., Zagermann, hep-th/0405247 • Detailed brane construction - D-term inflation dictionary Brane construction of generalized D-term inflation models with additional global or local symmetries due to extra branes and hypermultiplets. Resolving the problem of cosmic string production: additional global symmetry, no topologically stable strings, only semilocal strings, no danger Confirmation ofUrrestilla, Achucarro, Davis; Binetruy, Dvali, R. K.,Van Proeyen

21. Bringing it all together:Double Uplifting KKL, in progress First uplifting: KKLT

22. Second uplifting in D3/D7 model

23. Inflationary potential at as a function of S and Shift symmetry is broken only by quantum effects

24. Potential of hybrid inflation with a stabilized volume modulus

25. For two hypers: Inflaton potential: Symmetry breaking potential:

26. Can we have eternal inflation in such models? Yes, by combining these models with the ideas of string theory landscape

27. String Theory Landscape 100 Perhaps 10 different vacua

28. de Sitter expansion in these vacua is eternal. It creates quantum fluctuations along all possible flat directions and provides necessary initial conditions for the low-scale inflation

29. Landscape of eternal inflation

30. Self-reproducing Inflationary Universe

31. Finding the way in the landscape • Anthropic Principle: Love it or hate it but use it • Vacua counting: Know where you can go • Moduli trapping: Live in the most beautiful valleys

32. Beauty is Attractive Kofman, A.L., Liu, McAllister, Maloney, Silverstein: hep-th/0403001 also Silverstein and Tong, hep-th/0310221 • 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

33. Basic Idea is related to the theory of preheating after inflation Kofman, A.L., Starobinsky 1997 Consider two interacting moduli with potential It can be represented by two intersecting valleys Suppose the field φ moves to the right with velocity .Can it create particles c ? Nonadiabaticity condition:

34. When the field φpasses the (red) nonadiabaticity region near the point of enhanced symmetry, it created particles χ with energy density proportional to φ. Therefore the rolling fieldslows down and stops at the point when Then the field falls down and reaches the nonadiabaticity region again… V φ

35. When the field passes the nonadiabaticity region again, the number of particles c (approximately) doubles, and the potential becomes two times more steep. As a result, the field becomes trapped at distance that is two times smaller than before. V φ

36. Trapping of a real scalar field

37. Thus anthropic and statistical considerations are supplemented by a dynamical selection mechanism, which may help us to understand the origin of symmetries in our world.