1. Nonlocal Dynamics in String Field Theory and cosmological applications Liudmila Joukovskaya, CTC, DAMTP, University of Cambridge 21 January, Imperial College London

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. Cubic Fermionic String Field Theory Witten’s Cubic Open 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 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

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

6. Covariant String Field Theory Level truncation

7. Spatially-Homogeneous Configurations

10. 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

14. Intuition about possible solutions

15. 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

17. Solution of Equation of Motion

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

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

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

21. A great discovery of the last few years is the discovery of 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).

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

23. One more reason to work on new inflationary candidates

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

25. Non-locality and Cosmology Non-local gravity ad-hoc: Non-local SFT: 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 G.Dvali, S. Hofmann, J Khoury, hep-th/0703027 S.Deser, R.Woodard, arXiv0706.2151S. S.Deser, R.Woodard, arXiv:0706.2151S. I.Aref’eva, LJ, A.Koshelev, JHEP, 2003; I.Aref’eva, LJ, JHEP, 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

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

28. Intuition about possible solutions

29. L.J., PRD 2007

34. Two fields case

38. Second possibility

39. Numerical Scheme for Solution Construction II

40. Numerical Scheme for Solution Construction II - continuation

41. Numerical Solution

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

43. Coupling to the gravity / FRW case

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

45. L.J., arxiv: 0807.2065

47. Numerical solutions a. b.

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

49. 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) )

50. Conclusions and further directions

51. Thank you for the attention!