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. 21 January, Imperial College London. Plan of the talk. General Motivations Construction of rolling solutions in the truncated SFT

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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

21 January, Imperial College London


Plan of the talk

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


Motivations

Motivations

  • Cosmological Motivations

  • Theoretical Motivations

  • String Field Theory as a possible framework for Cosmology


Nonlocal dynamics in string field theory and cosmological applications

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


Nonlocal dynamics in string field theory and cosmological applications

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


Nonlocal dynamics in string field theory and cosmological applications

Level truncation

Covariant String Field Theory


Nonlocal dynamics in string field theory and cosmological applications

Spatially-Homogeneous Configurations


Stress tensor

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


Intuition about possible solutions

Intuition about possible solutions


Solution construction for minkowski case

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


Nonlocal dynamics in string field theory and cosmological applications

Solution of Equation of Motion


Nonlocal dynamics in string field theory and cosmological applications

Standard Cosmological Concordance Model is emerging

during the last 10 years …


Big bang inflationary cosmology

Big Bang/Inflationary Cosmology

Picture taken from:cosmology.berkeley.edu


Cyclic ekpyrotic cosmology

Cyclic/Ekpyrotic Cosmology

N. Turok, P.J. Steinhardt,

J. Khoury, B. Ovrut


Nonlocal dynamics in string field theory and cosmological applications

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).


Nonlocal dynamics in string field theory and cosmological applications

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


Nonlocal dynamics in string field theory and cosmological applications

One more reason to work on new inflationary candidates


Nonlocal dynamics in string field theory and cosmological applications

Standard Cosmological Concordance Model is emerging

during the last 10 years…

String Field Theory as a possible cosmological framework


Non locality and cosmology

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;

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


Nonlocal dynamics in string field theory and cosmological applications

Einstein equations

FriedmannCosmology

+ Cosmological principle

Isotropic

Homogeneous

K=+1 (3-sphere), k=0 (plane), k=-1 (3-hyperboloid)


Intuition about possible solutions1

Intuition about possible solutions


Nonlocal dynamics in string field theory and cosmological applications

L.J., PRD 2007


Nonlocal dynamics in string field theory and cosmological applications

Two fields case


Second possibility

Second possibility


Numerical scheme for solution construction ii

Numerical Scheme for Solution Construction II


Numerical scheme for solution construction ii continuation

Numerical Scheme for Solution Construction II - continuation


Numerical solution

Numerical Solution


Does exist the rolling tachyon solution in the case of cubic potential

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


Coupling to the gravity frw case

Coupling to the gravity / FRW case


Do we have the rolling tachyon solution in this case

Do we have the rolling tachyon solution in this case?


Nonlocal dynamics in string field theory and cosmological applications

L.J., arxiv: 0807.2065


Numerical solutions

Numerical solutions

a.

b.


Energy and pressure for rolling tachyon solutions

Energy and pressure for Rolling Tachyon Solutions

a.

b.


Main results presented in this talk

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) )


Nonlocal dynamics in string field theory and cosmological applications

Conclusions and further directions


Thank you for the attention

Thank you for the attention!


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