Transcript BRANEWORLD COSMOLOGICAL PERTURBATIONS

BRANE-WORLD
COSMOLOGY
Revent reviews: Brax, Davis, vd Bruck, hep-th/0404011
RM, gr-qc/0312059
Roy Maartens
Porto 2004
University of
Portsmouth

standard
cosmology highly
successful
concordance model
= excellent fit

but – still a
paradigm seeking
a fundamental
theory
deep puzzles inflation,
dark energy,
dark matter, …
more to come
high-precision cosmology is
probing the limits of GR
 GR
breaks down
need quantum gravity
in the early universe

no QG theory as yet
but M theory is a
promising candidate
M theory needs extra
dimensions + branes

can also lower the Planck scale
explain ‘weakness’ of gravity
why don’t we see the extra dimensions?

conventional Kaluza-Klein idea:
internal extra dimension too small to be seen
4D spacetime
small extra
dimension

discovery of D-brane
 matter fields restricted
to lower dimensional brane
 external bulk felt only
through gravity
 extra dimension bigger
large extra
dimension
gravity
small extra dimensions
= moduli fields
mA(t,x)
visible
brane
shadow
brane
dilaton
D(t,x)
large extra dimension
= radion R(t,x)
THE BIG IDEA: M THEORY
WILL SOLVE PUZZLES
* dilaton/radion =
natural source of
brane inflation?
* more radical: no inflation brane-brane collision =
big bang (cyclic)?
* moduli = varying constants?
* shadow matter =
dark matter?
dark energy?
 the harsh reality …
 still no string/ M theory cosmology
 even inflation/ dark energy hard to get

2 parallel approaches
* hunt for string/ M theory cosmology
* use braneworld phenomenology

braneworld cosmology
use M theory ideas in cosmology
 use high-precision data to test &
constrain models

GR
phenomenology
QG
2 key features

braneworld gravity brings new features
KK modes of the graviton
new fields (moduli, dilaton,…)
shadow matter
holography, …

precision data constrains extra-dimensional gravity
dynamics – BBN, SNe
perturbations – CMB and LSS
start with simple models

similar to inflation and dark energy models

simplest models with predictive power

focus on one or two key aspects at a time

KK modes of graviton

scalar fields – radion, dilaton, moduli

….
Randall-Sundrum braneworlds

5D models

gravity itself is central
– warped extra dimension

4 
2 y /  
ds 2  dy 2  e 2| y|/ 
dx h dx



e

h

h
wave equation


 
(5)

separate

      h
put a small particle on brane

h  m ( x ) f m ( y), 
 m  m m
 
2
h  0   h
TT-gauge (4D)
4D
zero-mode
– only
tensor
 perturbed
5D field
equation
m=0: no normalizable scalar or vector


4
2 y /  
2


e
h

k
h

h

h
weak-field potential
 1
2 2
 ( r )   1 
 separate into modes
r 
3r 2
  0.1mm
h (t , y ) 

m
( t ) f m ( y ),
m
   (1 TeV ) 4 , M 5  105 TeV

  ...

h ( t , 0 )  0  h ( t , L )
m=0
m>0
gravitational waves
in high-energy radiation
- signature of braneworld?
adv LIGO
LISA
?
f  10 4 Hz (for =0.1mm)
stringy/quantum curvature corrections
Gauss-Bonnet (early universe)
S grav 
1
2
2
5

d 5 x  (5) g

( 5)
R  2 5  

( 5)

R 2  ...
  d 4x  g
induced gravity (late universe)
S grav 
1
2
2
5

d x  g
5
( 5)

( 5)

1 
R  2 5   d x  g   2 R
rC 


4