BRANEWORLD COSMOLOGICAL PERTURBATIONS

1. BRANEWORLD COSMOLOGICALPERTURBATIONS Roy Maartens University of Portsmouth Tokyo IT October 2003

2. testing the braneworld scenario cosmology as a probe of theory braneworld observational signature?

3. t RS braneworld 5<0 >0 • why does gravity not leak into 5D? cosmological constant in bulk5 < 0 • how is brane protected against 4<0 ? brane tension >0 + 5  4 =0 Minkowski brane in anti de Sitter bulk 5D gravitons – effective mass m on brane (massive KK modes) nonlocal KK effects y x3

4. field equations • gravitational action • RS solution – 4-Minkowski in 5-AdS

5. massive KK modes • metric perturbation • TT-gauge (4D) • perturbed 5D field equation • separate into modes

6. solution • zero mode • massive modes RS1: m > 0 discrete spectrum RS2: m > 0 continuous spectrum • gravitational potential • m=0m>0

7. general braneworld • Gauss equation • Codazzi equation • junction equations

8. induced 4D Einstein tensor high-energy high or low energy 5D graviton -massive KK effects • KK/ Weyl anisotropic stress – • must be determined by 5D equations

9. KK stresses from brane matter matter obeys brane and bulk do not exchange energy not true if scalar field/radiation in bulk Bianchi identity KK stresses sourced by perturbations - inhomogeneity and anisotropic stress

12. inflation on the brane • 4D inflaton, high-energy inflation • high-energy assists slow-roll • brane slow-roll parameters • new possibility - steep inflation

13. brane matter perturbations decouple from bulk metric perturbation (large scales) • curvature perturbation can be found (large scales) then

14. tensor perturbations from inflation • perturbed de Sitter brane • wave equation separable (H constant)

15. solutions • mass gap above 0-mode • massive modes decay during inflation • 0-mode has increased amplitude at high energy • but tensor/ scalar is reduced!

16. spectrum of normalizable states • discrete zero mode (4D)m=0 • massive KK continuumm>3H/2 only zero-mode excited during inflation evolution after inflation • 0-mode re-enters Hubble – KK modes generated (5D gravitons bulk) loss of energy – damping (Koyama’s talk)

17. spectral indices scalar perturbations • same form as GR tensor perturbations • compare GR but consistency condition has the same form

18. RS2 + induced gravity • brane matter / bulk graviton coupling • quantum correction to gravitational action • curvature term induced on brane • modifies gravity at large scales/ low energies • but – also removes RS high-energy correction • early universe at high energy = GR + …

19. scalar perturbations less power since • need to check curvature perturbations

20. tensor perturbations from inflation same bulk equations – same modes but boundary conditions different: giving

21. RS2+Gauss-Bonnet gravity • most general 5D action with 2nd order equations • quantum/ stringy correction to gravity • modifies gravity at high energies • suggests lower scalar perturbations • but curvature perturbation must be checked

22. tensor perturbations from inflation bulk equation different but bulk wave equation has same form but boundary conditions different junction conditions cubic in extrinsic curvature! but same form of boundary condition as in IG: giving

26. Low energy approximation • gradient expansion curvature radius on the brane curvature radius in the bulk • To find - need boundary conditions - shadow/ regulator brane

27. background Friedmann equations dark radiation radion

28. radion low-energy solution

29. effective equations on +ve tension brane scalar-tensor theory

30. cosmological perturbations on large scales Weyl anisotropic stress given by radion

31. define new variables then

32. physical meaning of variables brane displacements bulk anisotropic perturbation

33. simple toy model • Weyl anisotropic stress • completely compensates entropy perturbation

37. further work • choose physical shadow matter • dark radiation in background • one-brane case: needs suitable boundary/ initial conditions