Stealth Acceleration and Modified Gravity Tony Padilla, University of Nottingham Based on work with C. Charmousis and R. Gregory: 0706.0857 [hep-th]

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

Modified gravity and self acceleration u p o s e w h a v n c m r g y ( ½ = ) , 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 : ½ = ( 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

Self-acceleration and ghosts P 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/0604086 (Gregory, Charmousis, Kaloper, A.P) 0707.2666 [hep-th] (Gregory, Kaloper, Myers, A.P) hep-th/0512097 (Gorbunov, Koyama, Sibiryakov)

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 (0706.0857 [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.

Background solution and perturbations W e c a n m k t h v u b r M i o w s y ¯ g ¾ = ¡ 6 3 d S , ¤ 2 ( ) + x ¹ ; 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!

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 = ! ½ 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

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 ,

C H = An example of “Stealth Acceleration” standard 4D cosmo k ¼ 5 2 p l 3 1 H = standard 4D cosmo acceleration in matter universe acceleration in radiation universe

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

Magnitude-redshift plots b 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

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 ( ½ + c n ) ; < 3 (Freese and Lewis, astro-ph/0201229) This is achieved without introducing perturbative ghosts, unlike self accelerating models Plenty more to do. eg solar system tests, more cosmology