Nonlocal Dynamics in String Field Theory and cosmological applications
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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
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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
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Motivations
Cosmological Motivations
Theoretical Motivations
String Field Theory as a possible framework for Cosmology
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Cubic Fermionic String Field Theory
Witten’s Cubic Open String Field Theory
I.Aref’eva, P.Medvedev, A.ZubarevPhys.Lett. B240 (1990)356C.Preitschopf, C.Thorn, S.Yost, Nucl. Phys. B337 (1990) 363I.Arefeva, D.Belov, A.Koshelev,
P.Medvedev, Nucl.Phys.B638 (2002)3
E. Witten, Nucl. Phys. B 268 (1986) 253V.A. Kostelecky, S.Samuel, Phys. Lett. B 207 (1988) 169V.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
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In the approximation u=U we have a more simple approximate action
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Covariant String Field Theory
Level truncation
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Spatially-Homogeneous Configurations
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Stress Tensor
N. Moeller, B. Zwiebach, JHEP, 10 (2002) 034H. Yang, JHEP 11 (2002) 007I. Aref’eva, L.J., A. Koshelev, JHEP, 09 (2003) 012
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Intuition about possible solutions
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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: 0705.4600D. V. Prokhorenko, math-ph/0611068; G. Calcagni, G. Nardelli, arxiv: 0708.0366
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Solution of Equation of Motion
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Standard Cosmological Concordance Model is emerging during the last 10 years …
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Big Bang/Inflationary Cosmology
Picture taken from: cosmology.berkeley.edu
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Cyclic/Ekpyrotic CosmologyN. Turok, P.J. Steinhardt,J. Khoury, B. Ovrut
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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).
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Picture taken from: http:// map.gsfc.nasa.gov
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One more reason to work on new inflationary candidates
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String Field Theory as a possible cosmological framework
Standard Cosmological Concordance Model is emerging during the last 10 years…
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Non-locality and Cosmology
Non-local gravity ad-hoc:
Non-local SFT:
Arkani-HamedArkani-Hamed at al at al hep-th/0209227hep-th/0209227;;KhouryKhoury, , hep-th/0612052hep-th/0612052;;T.Biswas,T.Biswas, A.Mazumdar, W.Siegel, A.Mazumdar, W.Siegel, hep-th/0508194 hep-th/0508194,,G.Dvali,G.Dvali, S. Hofmann, J S. Hofmann, J KhouryKhoury,, hep-th/0703027hep-th/0703027S.Deser, R.Woodard, S.Deser, R.Woodard, arXivarXiv:0706.21510706.2151S.S.
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, 2005LJ, PRD 2007; G. Calcagni, M.Montobbio, G.Nardelli; PRD 2007; N. Barnaby, T. Biswas, J.M. Cline, JHEP 2007J.Lidsey, PRD 2007; D. Mulryne, N. Nunes, PRD 2008;A. Koshelev, S. Vernov; I. Aref’eva, N.Bulatov, LJ, S. Vernov 2009;
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Friedmann Cosmology
TGgRR 821
Einstein equations
)1
)(( 222
2222 dr
krdr
tadtds
+ Cosmological principle
Homogeneous Isotropic
K=+1 (3-sphere), k=0 (plane), k=-1 (3-hyperboloid)
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Intuition about possible solutions
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L.J., PRD 2007
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Two fields case
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Second possibility
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Numerical Scheme for Solution Construction II
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Numerical Scheme for Solution Construction II - continuation
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Numerical Solution
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Does there exist the rolling tachyon solution in the case of cubic potential?
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Coupling to the gravity / FRW case
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Do we have the rolling tachyon solution in this case?
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L.J., JHEP 2009
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Numerical solutions
a.
b.
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Energy and pressure for Rolling Tachyon Solutions
a.
b.
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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) )
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Conclusions and further directions
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Thank you for the attention!