1. Update on String Cosmology Renata Kallosh Renata Kallosh Stanford, March 8, 2008

2. Outline Dark Energy and the Landscape of String Theory : Type IIA, Type IIB, Heterotic string theories Brane Inflation and Modular inflation What can fundamental physics learn from future detection or non-detection of B-modes from cosmic strings B-modes from inflation LHC: Tension between string cosmology and a TeV gravitino

3. Space of M/String Theory vacua Moduli Stabilization by fluxes and non-perturbative corrections in non- critical and type IIB superstring theory de Sitter vacua, models of inflation Until recently problems in type IIA superstring theory Heterotic string theory?

4. Type IIA string theory Stabilization of all moduli is possibble in a class of models in massive IIA. In these models there is the infinite number of AdS vacua, Lambda<0 DeWolfe, Giryavets, Kachru,Taylor, 2005 Cannot be uplifted to de Sitter vacua, Lambda>0, no-go theorem RK, M. Soroush, 2006 In these models inflation is not possible, no-go theorem Hertzberg, Kachru, Taylor, Tegmark, 2007 New type IIA models : extra dimensions with negative curvature, inflation with gravity waves, Silverstein, Westphal Cosmology as a selection principle?

5. 1998 CC > 0CC ~ 10 -120 SUPERSTRING THEORY : many AdS vacua with CC < 0 and Minkowski vacua with CC = 0, but no de Sitter vacua with CC > 0 2001-2003 Existence of Dark Energy is a real issue, supported not only by supernovae. It describes 70% of everything. Fundamental Physics has to explain it. First constructions of metastable de Sitter vacua in String Theory

6. It is possible to stabilize internal dimensions, and to obtain an accelerating universe. Eventually, our part of the universe will decay, but it will take a very long time Vacuum stabilization can be achieved in 10 100 - 10 1000 different ways. This means that the value of CC ~ 10 -120 in Planck units may not be impossible in the context of stringy landscape with anthropic reasoning W = - 1, CC=const, is in agreement with the data so far Metastable dS minimum V is the potential as the function of the volume of extra dimensions, described by 

7. What if CC=const will be definitely ruled out observationally as the explanation of Dark Energy? Most likely, it will not happen earlier than in 10 years from now (???) It may be difficult to explain it, as we will have to explain not only the height of the potential 10 -120 but also the slope ~ 10 -120 Allen at al

8. We focus on string theory (supergravity) models of inflation Generic class of inflationary models in talks of Lyth, Wise, Weinberg,…, Sasaki, …: “ Give me 2 fields and I will give you any level of non-gaussianity, any n s and any r=T/S which will agree with future experiments” “Give me a place to stand on, and I will move the earth.”

9. Thanks to Navin Sivanandam Stringy inflation models on WMAP5

10. Bevis, Hindmarsh, Kunz, Urrestilla January 2008 WMAP3-based 10% of cosmic strings For this model cosmic strings have to be detected!

11. B-modes from gravity waves from inflation B-modes from cosmic strings Pogosian, WymanFebruary 2008

12. Spergel: cosmic strings should be “eye-visible”

13. Inflation in string theory To produce a sensible cosmology in string theory it was necessary to stabilize all moduli but the inflaton. In 4d theory such moduli (scalar fields) have a runaway behavior. In string theory and supergravity they often have physical and geometrical meaning as volumes of extra dimensions and various cycles in topologically non-trivial extra dimensions. The inflaton can also be related to a distance between branes. If scalars have a geometric meaning in extra dimensions, what is their range in four-dimensional Planck units? In view of the Lyth bound on tensor to scalar fluctuation ratio r=T/S What has string theory to say on limits on r=T/S ? WMAP5+… Cosmic strings ?, Vilenkin Copeland, Myers, Polchinski Seeing cosmic strings on the sky would be a window of string theory into the real world

14. Brane Inflation in string theory KKLMMT brane-anti-brane inflation Hybrid D3/D7 brane inflation (Stringy D-term inflation) Dirac-Born-Infeld inflation Two-throat model

15. Modular Inflation models Kahler modular inflation Roulette inflation, Racetrack inflation

16. Cosmology, string theory and effective supergravity Generic potential of N=1 supergravity depends on a number of complex scalar fields which have a geometric meaning of coordinates in Kähler geometry + D-terms Kähler potential and the Superpotential

17. the first working model of the moduli inflation Blanco-Pilado, Burgess, Cline, Escoda, Gomes-Reino, Kallosh, Linde, Quevedo Superpotential: Kähler potential: Racetrack Inflation, KKLT Racetrack Inflation, KKLT KKLT Uplifting term: Rescaling (same slow-roll etc)

18. n s =0.95 No grav. waves No cosmic strings Spectral index as a function of the number of e-foldings (minus the total number of e-foldings) Racetrack Inflation

19. Update on KKLMMT brane inflation model: recent detailed studies of quantum corrections eta-problem quantum corrections do not remove terms, but add other terms to the potential. With fine-tuning one can find an inflection point and slow-roll inflation Baumann, Dymarsky, Klebanov, Maldacena, McAllister … 2007 Princeton group Accidental Inflation Linde, Wesphal Phenomenology? Cosmic strings, no GW

20. Update on D3/D7 brane inflation Work in Progress: Haack, RK, Krause, Linde, Luest, Zagermann The model is controlled by special geometry of N=2 supergravity The reason for the recent update was the observation by Hindmarsh et al than one can fit the data with n s =1 assuming the presence of light cosmic strings. (Summer Trieste workshop) This is in amazing agreement with the prediction from 2003 by RK and Linde that in D-term inflation one can have light cosmic strings for very small gauge couplings under condition that n s =1 In usual regime of D-term inflation n s ~ 0.98

21. D3/D7 Inflation Dasgupta, Herdeiro, Hirano, RK, 2001 This is a stringy version of hybrid D-term Inflation D3 is moving The mass of D3-D7 strings (hypers) is split due to the presence of the anti-self-dual flux on D7

22. Inflaton Trench SHIFT SYMMETRY, slightly broken by quantum corrections The motion of branes does not destabilize the volume The motion of branes does not destabilize the volume Hsu,RK,Prokushkin;Firouzjahi,Tye

23. n In F-theory compactifications on K3 x K3 one of the attractive K3 must be a Kummer surface to describe an orientifold in IIB, the second attractive K3 can be regular. Type IIB string theory on K3 x orientifold Aspinwall, RK Tripathy, Trivedi; Ferrara, Trigiante et al Bergshoeff, RK, Kashani-Poor, Sorokin,Tomasiello All moduli stabilized

24. How long is de Sitter valley in D3/D7 brane inflation model? Long thin pillow

25. A D3-brane and a D7-brane are placed on a rectangular, but ``asymmetrical'' (non-square) torus. The D3-brane (white circle) can travel at most the distance L 1 along the lower edge of the rectangle before it hits the D7-brane. This corresponds to the larger of the two topologically non-trivial circles (right figure) on the torus (red dashed lines). Making the torus very thin and long can thus yield, at least kinematically, a large field range. Enhancement factor, depends on the choice of fluxes K3 x

26. Pillow with 4 fixed points

27. What controls the breaking of shift symmetry in D3/D7 model on K3 x If these corrections are small, we derive the model with n s = 1, 10% of cosmic strings. If confirmed by data, we have a clear link to string theory.

28. What if tensor modes are detected? Current bound: r = T/S < 0.2 from WMAP5+… What this would mean for the fundamental physics, string theory and supergravity?

29. All relatively well developed brane inflation models and modular inflation models in string theory predict a non detectable level of tensor modes. New models, or new versions of known models, may lead to different results see Eva’s talk for the first example

30. Axion Valley Model: The first realization of `natural inflation’ (pNGb) in Supergravity  Shift symmetric quadratic Kähler potential  KKLT-type superpotential  The potential after the KKLT-type uplifting has a minimum at some value of the radial variable x 0. The radial direction is very steep. At this minimum the potential is that of natural inflation (pNGb) RK, Soroush, Sivanandam, 2007

31. Axion Valley Potential Sharp minimum in radial direction x, very shallow minimum for the axion The potential shows the periodic structure for pNGb potential is the slice at the bottom of the valley

32. There are models of inflation in supergravity which predict tensor modes with They have approximately shift-symmetric quadratic Kähler potentials

33. In string theory the computable K ä hler potentials in known cases of Calabi- Yau compactification have shift symmetry  However, they are logarithmic, not quadratic These models predict undetectably small tensor modes in inflation. RK, Soroush, Sivanandam KKLT, C 111 =1

34. Simplest example of KKLT potential  One modulus Axion is as steep as the radial modulus, there is no axion valley. No detectable GW in models with stringy logarithmic Kähler potentials

35. At fixed T and Hodge-Kahler manifold Will this string theory model provide the axion valley potential predicting GW ??? Less studied corners of the stringy landscape T. Grimm, N = 1 orientifold compactification with O3/O7 planes. R-R 2-forms The relevant moduli originate from hypermultiplets in both cases

36. In the context of inflation in string theory and supergravity, the detection (or non-detection) of the tensor modes from inflation is of crucial importance!  At the present level of understanding there seems to be a unique way to read the features of the geometry of extra dimensions from the sky.  No detection: Calabi-Yau 3-folds logarithmic Kähler potentials prediction, well studied corner of the stringy landscape  Detection: shift symmetric nearly quadratic Kähler potentials in effective supergravity. String theory?... Spaces of negative curvature of extra dimensions Additional problem: For most of the models based on the KKLT moduli stabilization, R.K., Linde 2003

37. Summary When we learned that our universe is accelerating, it was a creative crisis, which forced us to reconsider many issues in string theory, including the issue of moduli stabilization and metastable vacua. If tensor modes are detected, it may provide us with hints about the geometry of extra dimensions from the sky. Before the experiments will reach the level we may have more string theory models to test. If cosmic strings detected, it will give us an important selection principle for string theory confronting the data