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Nonlocal Dynamics in String Field Theory and cosmological applications

Nonlocal Dynamics in String Field Theory and cosmological applications. Liudmila Joukovskaya, CTC, DAMTP, University of Cambridge. 14 April 2009, 2 nd Conference on String Field Theory and Related Aspects. Plan of the talk. General Motivations

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Nonlocal Dynamics in String Field Theory and cosmological applications

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  1. Nonlocal Dynamics in String Field Theory and cosmological applications Liudmila Joukovskaya, CTC, DAMTP, University of Cambridge 14 April 2009, 2nd Conference on String Field Theory and Related Aspects

  2. Plan of the talk • General Motivations • Construction of rolling solutions in the truncated SFT a) Truncated SFT (nonlocality) b) Space homogeneous rolling solutions • Cosmological motivations for nonlocal theories • SFT as a possible framework for cosmology • Rolling cosmological solutions

  3. Motivations • Cosmological Motivations • Theoretical Motivations • String Field Theory as a possible framework for Cosmology

  4. Witten’s Cubic Open String Field Theory E. Witten, Nucl. Phys. B 268 (1986) 253 V.A. Kostelecky, S.Samuel, Phys. Lett. B 207 (1988) 169 V.A. Kostelecky,S.Samuel, Phys. Lett. B 207 (1988) 169, P.West, Phys.Lett.B548:92-96,2002 N. Moeller, A. Sen, B. Zwiebach, JHEP, 08 (2000) 039 Cubic Fermionic String Field Theory I.Aref’eva, P.Medvedev, A.Zubarev Phys.Lett.B240 (1990)356 C.Preitschopf, C.Thorn, S.Yost, Nucl. Phys. B337 (1990) 363 I.Arefeva, D.Belov, A.Koshelev, P.Medvedev, Nucl.Phys.B638 (2002)3

  5. In the approximation u=U we have a more simple approximate action

  6. Level truncation Covariant String Field Theory

  7. Spatially-Homogeneous Configurations

  8. Stress Tensor N. Moeller, B. Zwiebach, JHEP, 10 (2002) 034 H. Yang, JHEP 11 (2002) 007 I. Aref’eva, L.J., A. Koshelev, JHEP, 09 (2003) 012

  9. Intuition about possible solutions

  10. Solution construction for Minkowski case Ya. Volovich, JPA, 2003; Ya. Volovich, V.S. Vladimirov, Theor. Math. Phys. 2004; L.J., Theor. Math. Phys. 2006 or arxiv: 0708.0642[hep-th]; V.S. Vladimirov, arxiv: 0705.4600 D. V. Prokhorenko, math-ph/0611068; G. Calcagni, G. Nardelli, arxiv: 0708.0366

  11. Solution of Equation of Motion

  12. Standard Cosmological Concordance Model is emerging during the last 10 years …

  13. Big Bang/Inflationary Cosmology Picture taken from:cosmology.berkeley.edu

  14. Cyclic/Ekpyrotic Cosmology N. Turok, P.J. Steinhardt, J. Khoury, B. Ovrut

  15. A great discovery of the last few years is the discoveryof the current accelerated expansion of the Universe Observations (1998) of very distant supernovae demonstrated that the Universe is expanding with an acceleration. Ia Supernovae: S.Perlmutter et al., A.Riess et al., 1998; This acceleration seems to be explicable by the presence of a new component of matter called dark energy (DE). DE is a special unknown form of matter with negative pressure and it provides universal repulsive forces (antigravity).

  16. Picture taken from: http:// map.gsfc.nasa.gov

  17. One more reason to work on new inflationary candidates

  18. Standard Cosmological Concordance Model is emerging during the last 10 years… String Field Theory as a possible cosmological framework

  19. Non-locality and Cosmology • Non-local gravity ad-hoc: Arkani-Hamed at al hep-th/0209227; Khoury, hep-th/0612052; T.Biswas,A.Mazumdar, W.Siegel, hep-th/0508194, G.Dvali, S. Hofmann, JKhoury,hep-th/0703027 S.Deser, R.Woodard, arXiv:0706.2151S. • Non-local SFT: I. Aref’eva, LJ, A. Koshelev, JHEP, 2003; Aref’eva AIP Conf Proc. 2004; I.Aref’eva, LJ, JHEP, 2005; I. Aref’eva, Koshelev, Vernov 2005; G.Calcagni, JHEP, 2005 LJ, PRD 2007; G. Calcagni,M.Montobbio, G.Nardelli; PRD 2007; N. Barnaby, T. Biswas, J.M. Cline, JHEP 2007 J.Lidsey, PRD 2007; D. Mulryne, N. Nunes, PRD 2008; A. Koshelev, S. Vernov; I. Aref’eva, N.Bulatov, LJ, S. Vernov 2009;

  20. Einstein equations FriedmannCosmology + Cosmological principle Isotropic Homogeneous K=+1 (3-sphere), k=0 (plane), k=-1 (3-hyperboloid)

  21. Intuition about possible solutions

  22. L.J., PRD 2007

  23. Two fields case

  24. Second possibility

  25. Numerical Scheme for Solution Construction II

  26. Numerical Scheme for Solution Construction II - continuation

  27. Numerical Solution

  28. Does there exist the rolling tachyon solution in the case of cubic potential?

  29. Coupling to the gravity / FRW case

  30. Do we have the rolling tachyon solution in this case?

  31. L.J., JHEP 2009

  32. Numerical solutions a. b.

  33. Energy and pressure for Rolling Tachyon Solutions a. b.

  34. Main results presented in this talk: • Construction of rolling cosmological solutions for: • Tachyon field describing non-BPS branes in Friedmann-Robertson-Walker background (Does exist in Minkowski case AJK) • Tachyon field of open bosonic string in Friedmann-Robertson-Walker background (Does not exist in the Minkowski case (Moeller, Zwiebach) )

  35. Conclusions and further directions

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