1. Stealth Acceleration and Modified Gravity
Tony Padilla,
University of Nottingham
Based on work with C. Charmousis and R. Gregory: [hep-th]

2. Why/how to modify gravity?
Effective field theory methods have so far failed to give a satisfactory
explanation for dark energy I n t h e w o r s c a i , v u m g y p d b Q F T 1 2 l !
Ignoring anthropic arguments, and hidden UV physics,
Weinberg’s “no-go” theorem states that no effective 4D theory can solve the CCP
Perhaps cosmic speed up is actually a sign of
new dimensions opening up at large distances
Extra dimensions must be infinite or else one can still apply
Weinberg’s arguments
But modifying GR in this way is tough.
Typically we run into problems of theoretical consistency,
and disagreement with solar system tests

3. Modified gravity and self accelerationu p o s e w h a v n c m r g y ( = ) , t i 4 D G R F d q b : 6 M 2 l H I n a m o d i e t h r y f g v s p l c b F q u : = ( H 2 ) I n 4 D G R , t h e v a c u m s o l i b f ( H = ) . d g r y w
> T p x F
COSMIC ACCELERATION IS ENTIRELY DUE TO MODIFICATION OF GRAVITY

4. Self-acceleration and ghostsP m o d e l : F ( H 2 ) = 6 M 4 1 5 T h i n u s b r a c f t g x 3 w .
Perturbations about the self-accelerating solution contain a scalar ghost
It has negative kinetic energy and if it couples to ordinary fields, will
destabilise the solution by continually transferring energy into those fields
Five dimensional energy unbounded from below
hep-th/ (Gregory, Charmousis, Kaloper, A.P)
[hep-th] (Gregory, Kaloper, Myers, A.P)
hep-th/ (Gorbunov, Koyama, Sibiryakov)

5. M R 2 l p A possible alternative to self-acceleration The CGP model 5
Vacuum is flat rather than de Sitter but can still
get acceleration due to modification of gravity at some stage in cosmic evolution
The CGP model
( [hep-th]
Charmousis, Gregory, Padilla)
5D anti de Sitter
(retain adS boundary)
5D Minkowski M 2 p l R 5 D P l a n c k s e d i r o t h f b ( M S 6 = m )
Large curvature term “induced”on brane by loop corrections
to brane stress-energy, or by finite width corrections.

6. Background solution and perturbationsW e c a n m k t h v u b r M i o w s y g = 6 3 d S , 2 ( ) + x ; 1
<
> l
Bulk volume is infinite c Fluctuations about this vacuum do not contain a zero mode
c gravity is only quasilocalised. It is modified in the IR
Scalar radion (perhaps surprisingly) decouples from matter on the brane
and the induced metric, to linear order (at least)
No ghosts
in linearised theory!

7. Cosmological behaviour
As is well known in braneworld gravity, cosmological branes correspond
to branes moving through the bulk.
Exact solutions can be easily found by
gluing bulk solutions together across the moving brane
Without going into too much detail…. P u t s o m e a r n h b , w i q f p = ! y g S E C : ; + 3
We get a modified Friedmann equation F ( H 2 ) = 6 M p l 3 a d S + k m i n

8. What do we need for acceleration?p m , q
< w = 1 + 3 2 C ( H ) ! ; F A c e l r a t i o n w u f m ( ! = ) C H 2 s b 3 . d 1 4 D g y ,

9. C H = An example of “Stealth Acceleration” standard 4D cosmok 5 2 p l 3 1 H =
standard
4D cosmo
acceleration in matter universe
acceleration in radiation universe

10. k t k t Comoving Hubble radius vs proper time A c e l r a t i o n w h
Matter
Radiation k a H k a H k t k t A c e l r a t i o n w h : 5 k . 3 2
More like “coasting”
Model naturally explains why acceleration can only occur after matter domination

11. Magnitude-redshift plotsb t r a c i o n f p e d m g s C D M ( = : 3 ; 7 ) R e d c u r v s : o m l w i t h k = H n a G r e n c u v : O p m a t i s ( = 3 ; )
Purple curve:
DGP model, normal branch

12. Summary L e s a c l r t i o n h ¤ C D M , b u v g m . E d ¯ p H = ( ½
Can get power law acceleration at late times due to modification of gravity L e s a c l r t i o n h C D M , b u v g m . E d p
Acceleration only occurs when matter dominates. Vacuum brane is Minkowski!
In fact, model realises a Cardassian cosmology H 2 = 1 6 M p l ( + c n ) ;
< 3
(Freese and Lewis, astro-ph/ )
This is achieved without introducing perturbative ghosts,
unlike self accelerating models
Plenty more to do. eg solar system tests, more cosmology