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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  106.6 M p
 Ms
H  M p
M
 p




9
1 / Ms
H  1060 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  1060 M p
Nonlocal String Scalar Field Dynamics: w<-1
Later oscillatio ns with a reasonable period : T  100Myr
String !
D-BRANE
!
SFT !!!