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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Wittens 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.B54892-96,2002 N.
Moeller, A. Sen, B. Zwiebach, JHEP, 08 (2000) 039
Cubic Fermionic String Field Theory
I.Arefeva, 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
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In the approximation uU we have a more simple
approximate action
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Covariant String Field Theory
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Spatially-Homogeneous Configurations
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Stress Tensor
N. Moeller, B. Zwiebach, JHEP, 10 (2002) 034 H.
Yang, JHEP 11 (2002) 007 I. Arefeva, 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
  0708.0642hep-th
• V.S. Vladimirov, arxiv 0705.4600
• D. 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 Cosmology
N. 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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Standard Cosmological Concordance Model is
emerging during the last 10 years
String Field Theory as a possible cosmological
framework
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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, J Khoury,
hep-th/0703027 S.Deser, R.Woodard,
arXiv0706.2151S.

• Non-local SFT

I. Arefeva, LJ, A. Koshelev, JHEP, 2003
Arefeva AIP Conf Proc. 2004 I.Arefeva, LJ,
JHEP, 2005 I. Arefeva, 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. Arefeva, N.Bulatov, LJ, S. Vernov
2009
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Friedmann Cosmology
Cosmological principle
Isotropic
Homogeneous
K1 (3-sphere), k0 (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!