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

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

Cosmological Motivations

Theoretical Motivations

String Field Theory as a possible framework for Cosmology

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

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

Covariant String Field Theory

Level truncation

Spatially-Homogeneous Configurations

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

Intuition about possible solutions

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

Solution of Equation of Motion

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

Big Bang/Inflationary Cosmology

Picture taken from: cosmology.berkeley.edu

Cyclic/Ekpyrotic CosmologyN. Turok, P.J. Steinhardt,J. Khoury, B. Ovrut

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).

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

One more reason to work on new inflationary candidates

String Field Theory as a possible cosmological framework

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

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;

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)

Intuition about possible solutions

L.J., PRD 2007

Two fields case

Second possibility

Numerical Scheme for Solution Construction II

Numerical Scheme for Solution Construction II - continuation

Numerical Solution

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

Coupling to the gravity / FRW case

Do we have the rolling tachyon solution in this case?

L.J., JHEP 2009

Numerical solutions

a.

b.

Energy and pressure for Rolling Tachyon Solutions

a.

b.

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) )

Conclusions and further directions

Thank you for the attention!