Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
STRINGY NON-LOCAL COSMOLOGY I. Aref'eva Steklov Mathematical Institute, Moscow 43rd Rencontres de Moriond 15-22 March, 2008 STRINGY NON-LOCAL COSMOLOGY • Cosmological constant why it is now so small • Dynamical DE w<-1 periodic crossing the w=-1 barrier STRINGY NON-LOCAL COSMOLOGY • Cosmology FRW metric • Start from the flat space-time Zero vacuum energy consistence theory w < - 1 periodic crossing the w=-1 barrier STRINGS in FLAT SPACE-TIME Zero vacuum energy • SUSY • Sen mechanism = Energy of the true vacuum is compensated by the brane tension (in classical and quantum levels) STRINGS INFINITE number of FIELDS , Am , B mn , ... Sen’s mechanism STRINGS INFINITE number of FIELDS { ( x), BM ( x), B( x), BMN ( x), ... } Vacuum { 0 , 0, B0 , 0, ... } Vacuum energy is negative Take D-brane Total energy = Vacuum + D-brane tension =0 Result of calculations! (or a theorem!) D-brane String Field Theory 1+9 { ( x), BM ( x), B( x), BMN ( x),... } x t , x1 , x2 , x3 1+3 M 0, 1, 2, 3,.....D 1 d 4 x 2 1 2 1 4 S NSR GSO [ ] 2 g4 2 2 4 tachyon 1 g 42 v 6M s M s 2 go M c 4 ' L 2 string f 6 1/ M ( x) exp[( 'log ) ] ( x) 2 string , 2 are numbers Sen’s conjecture : f=1/4, I.A, D.Belov,A.Koshelev,P.Medvedev, Nucl.Phys.(2000), Ohmori (2001) Rolling for NSR GSO- Tachyon 2 ( 1) e 3 3 K ( t t ') ( t ') dt ' (t ) 2 2 Boundary problem () 1 2 0 Solution: kink 1 2 Later oscillations ( 1) 2 Effective local approximation AK-talk 3 Ghost I.A., L.Joukovskaya, A.Koshelev (2002); Vladimirov, Ya.Volovich, D.Prokhorenko (2006) NSR Tachyon + Gravity 1 1 M 1 4 g d x g g42 ( 2 F ( M s2 ) 4 f ) 2 R 2 p 4 F (z ) ( z 1)e 2 New conjecture: (t ) z 1 f 4 t Effective cosmological constant I.A., astro-ph/0410443 Nonlocal Dynamics in the Friedmann Metric 2 D 1 e 2 H DH2 3 D 3H 2 H 2 1 2 2 2 ( 1 ) D DH 1 1 H 2 2 2 2 2 H 2 d ( DH 1) e e m p 2 20 e DH2 via a diffusion equation Numerical results L.Joukovkaya, Phys.Rev, (2007) Exact Solution for Toy Model 3H V 0 3H 2 1 1 2 V ( ) m 2p 2 1 2 2 V ( ) (1 ) 4 1 2 2 2 (3 ) 2 12m p (t ) tanh t H 1 3m p2 I.A., A. Koshelev, S.Vernov, PRD,2005, Hubble Parameter H m M p go M c mp 2 M s v6 M s 2 2 1/ Mp 2 p 6 2 M c M p M s 106.6 M p Ms H M p M p 9 1 / Ms H 1060 M p M s string scale , M P Planck scale Nonlocal Models in Cosmology I. Nonlocality in Matter (mainly string motivated) 2 M 1 1 g p 4 d x g g42 ( 2 F ( M s2 ) V ( )) 2 R Later cosmology Inflation Bouncing solutions I.A., astro-ph/0410443 I.A., L.Joukovkaya, JHEP,05109 (2005) 087 I.A., A.Koshelev, JHEP, 07022 (2007) 041 I.A., L.Joukovskaya, S.Vernov, JHEP 0707 (2007) 087, L.Joukovskaya, PR D76(2007) 105007; arXiv:0710.0404 G. Calcagni, M.Montobbio,G.Nardelli JHEP, 0605 (2006) 012 0705.3043; 0712.2237; N. Barnaby, T. Biswas, J.M. Cline, hep-th/0612230; J.Lidsey, hep-th/0703007 II. Nonlocality in Gravity 2 M 1 1 p 4 d x g g42 ( 2 M s2 V ( )) 2 G F ( M , ...) R 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, arXiv:0706.2151S. UV - completion Summary Assumptions: Universe as slowly decaying D3-brane D-brane dynamics is described in the SFT framework Dark Energy dynamics by Open String Tachyon Back reaction by closed string dilaton Hubble Parameter H 1060 M p Nonlocal String Scalar Field Dynamics: w<-1 Later oscillatio ns with a reasonable period : T 100Myr String ! D-BRANE ! SFT !!!