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Deformation, non-commutativity and cosmological constant problem

Deformation, non-commutativity and cosmological constant problem. Renata Kallosh. Stanford. Davis, May 16, 2004. Outline. 1. Observational data on DARK ENERGY and INFLATION  CC PROBLEM 2. String Theory- Cosmology: KKLT model of de Sitter space,

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Deformation, non-commutativity and cosmological constant problem

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  1. Deformation, non-commutativity and cosmological constant problem RenataKallosh Stanford Davis, May 16, 2004

  2. Outline 1. Observational data on DARK ENERGY and INFLATION  CC PROBLEM 2.String Theory- Cosmology: KKLT model of de Sitter space, Warping  small parameter from deformed conifold. Problems with warping in KKLMMT model of inflation 3. Hybrid Inflation/Acceleration in D3/D7 Brane System 4. Deformed non-linear instanton, Nekrasov-Schwarz non-commutative instanton 5. Irrational deformation (non-commutativity) parameter in 6,7,8,9 space  CC in 0,1,2,3 space.

  3. Replace D0/D4 by D3/D7 Non-commutative in the space orthogonal to D3 Cosmological Constant in effective 4d

  4. Cmbgg OmOl

  5. How much dark energy is there? Closed Open

  6. How much dark energy is there? Cmbgg OmOl closed CMB flat open

  7. How much dark energy is there? Cmbgg OmOl closed CMB flat + open LSS WMAP + SDSS: lots

  8. How much dark energy is there? Cmbgg OmOl closed CMB flat + open LSS

  9. How much dark energy is there? Cmbgg OmOl closed CMB flat + open LSS Tegmark et al, 2004

  10. Early Universe Inflation Near de Sitter space 13.7 billion years ago During 10^{-35} sec Current Acceleration Near de Sitter space Now During few billion years Cosmological Concordance Model

  11. DARK ENERGY • Total energy in 3d flat FRW universe O • 70% of the total energy of the universe is DARK

  12. Cosmological Constant (CC) Problem • The simplest form of dark energy: CC

  13. String Theory and Cosmology • All observations fit 4d Einstein GR: how to get this picture from the compactified fundamental 10d string theory or 11d M-theory and supergravity How to get de Sitter or near de Sitter 4d space?

  14. Towards cosmology in type IIB string theory Dilaton stabilization Giddings, Kachru and Polchinski 2001 Volume stabilization, KKLT Kachru, R. K, Linde, Trivedi 2003 Landscape Susskind Flux Vacua Douglas Kachru, R. K., Maldacena, McAllister, Linde and Trivedi 2003

  15. Deformed Conifold Copeland, Myers, Polchinski picture The throat geometry has a highly warped region

  16. Volume stabilization • Warped geometry of the compactified space and nonperturbative effects allows to obtain AdS space with unbroken SUSY and stabilized volume • One can uplift AdS space to a metastable dS space by adding anti-D3 brane at the tip of the conifold

  17. The role of warping factor inuplifting AdS vacuum to dS • Small z (resolution of conifold singularity) In our example C was 10-9 Small C is necessary for dialing the anti-D3 energy to AdS scale to preserve and uplift the minimum

  18. The redshift in the throat plays the key role in • Advantage: source of small parameters • Disadvantage: highly warped region of KS geometry corresponds to conformal coupling of the inflaton field (position of D3-brane in the throat region) Flatness of the Inflaton Potential and of the Perturbation Spectrum Require Few possibilities to improve the model are known

  19. Supersymmetry and Inflation Linde, 91 • Hybrid Inflation F-term, D-term Inflation Copeland, Liddle, Lyth, Stewart, Wands; Dvali, Shafi, Shafer, 94 Binetruy, Dvali; Halyo, 96; Dvali, Tye, 99 D3/D7 Brane Inflation as D-term Inflation Dasgupta, Herdeiro, Hirano, R.K., 2002 Burgess, Kallosh, Quevedo, 2003 Include Volume Stabilization: F-term for KKLT+ Shift Symmetry slightly broken by quantum corrections Hsu, R. K., Prokushkin, 2003-2004 Ferrara et al, 2003 Practically D-term Inflation

  20. Inflaton Trench Supersymmetric Ground State of Branes in Stabilized Volume SHIFT SYMMETRY The motion of branes does not destabilize the volume

  21. Cosmology, Supersymmetry and Special Geometry • In familiar case of Near Extremal Black Holes DUALITY SYMMETRY protects exact entropy formula from large quantum corrections DUALITY SYMMETRY (shift symmetry) protects the flatness of the potential in D3/D7 inflation model from large quantum corrections

  22. The Potential of the Hybrid D3/D7 Inflation Model is a hypermultiplet is an FI triplet: resolution of the singularity

  23. Same Potential without Fayet-Iliopoulos term Flat direction corresponding to the singularity in the moduli space of instantons in D3/D7

  24. D3/D7 BRANE INFLATION MODEL The mass of D3-D7 strings (hypers) is split due to the presence of the deformed flux on D7

  25. De Sitter stage- Waterfall- Ground State DeSitter: Inflation or current acceleration Ground state: D3/D7 bound state Higgs branch: non-commutative instantons NS non-commutative instantons: Higgs branch, bound state of D0/D4

  26. D3 can move away from D7 when the deformationparameter vanishes, the moduli space is singular: there isno de Sitter space Resolution of singularity of the moduli space of instantons in D3/D7 Higgs branch requires that the Coulomb branch has a non-vanishing D-term potential Deformation-non-commutativity-resolution of singularity de Sitter space

  27. DBI kappa-symmetric action and non-linear deformed instantons Seiberg,Witten, 99; Marino, Minassian, Moore, Strominger, 99 D3/D7 bound state and unbroken supersymmetry Bergshoeff, R. K., Ortin, Papadopoulos, 97 Deformed flux on the world-volume Non-linear deformed instanton

  28. D-term volume stabilization Instead of anti-D3 add D7 with flux. The D-term potential depends on the ASD deformed flux and volume modulus 2 possibilities to make this mechanism working 1) Place D7 in highly warped region of space Burgess, R. K., Quevedo 2) Use deformation: irrational quantized cannot be gauged away into Deformation parameter (non-commutativity) is not quantized, it can be small!

  29. Discussion In the context of non-commutative instantons (Nekrasov-Schwarz, 1998) and Dirac-Born-Infeld non-linear instantons (Seiberg-Witten, 1999) FI terms are necessary to make the Abelian instantons non-singular. It is tempting to speculate that in D3/D7 cosmological model with volume stabilization mechanism there is an explanation of the non-vanishing effective cosmological constant Non-commutativity parameter (FI term in effective theory) is needed to remove the instanton moduli space singularity in the description of the supersymmetric D3/D7 bound state when D3 has dissolved into D7. The same cosmological model must have a non-supersymmetric de Sitter stage when D3 is separated from D7

  30. Can we measure the non-commutativity parameters of the internal space by looking at the sky ? Hopefully, with the further development of the theory we will find an answer to this question

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