1. Cosmic Microwave Radiation Anisotropies in brane worlds K. Koyama astro-ph/030310 K. Koyama PRD 66 084003(2002) Kazuya Koyama Tokyo University

2. Brane World picture Standard model lives on a brane Gravity can propagate into bulk Observational signatures Extra-dimension can be “observed” only through gravitational interactions Can we observe extra-dimension using CMB experiments ? 1. Introduction gravity Standard model bulk brane

3. Gravity on the brane in AdS 5 carries the information in the bulk 4D Equations for on the brane Randall Sundrum model (Randall, Sundrum) (Shiromizu, Maeda, Sasaki)

4. Cosmology Background universe Perturbations 4D equations can determine the behavior of At large scales, Weyl anisotropic stress cannot be determined only by 4D equations

5. Red shift photon (Langlois, Maartens, Sasaki, Wands) CMB anisotropies (SW effect) We cannot predict CMB anisotropies unless the behavior of Weyl anisotropic stress is known In this talk, we calculate Weyl anisotropic stress in two branes model at low energies Impact of dark radiation perturbation on CMB anisotropies

6. Anisotropy on the brane anisotropy in the bulk anisotropy on the brane Bulk and brane is coupled ２． Large scale anisotropy on the brane Black Hole Brane Moving brane in BH geometry Homogeneity and isotropy = AdS Schwartzshild bulk

7. We know the metric for Ads-Schwartzsild We know the metric for Ads-Schwartzsild metric near the brane: metric near the brane: Consider the perturbation of dark radiation Consider the perturbation of dark radiation AdS spacetime + perturbations (TT gauge) anisotropic shear

8. In TT gauge, anisotropic perturbation In TT gauge, anisotropic perturbation can exist (5D graviton) can exist (5D graviton) In TT gauge, the brane location is perturbed In TT gauge, the brane location is perturbed

9. Junction condition relates matter perturbation on the brane to and perturbations Junction condition relates matter perturbation on the brane to and perturbations Adiabatic condition on matter perturbations Adiabatic condition on matter perturbations equation for equation for

10. Solution for : integration constant Solution for : integration constant Metric perturbations on the brane Curvature perturbation

11. Curvature perturbation is determined Curvature perturbation is determined independently of independently of Curvature perturbation = brane dynamics Curvature perturbation = brane dynamics ( FRW equation = brane dynamics) ( FRW equation = brane dynamics) Solution for curvature perturbation can be derived exactly at large scales (including, at high energies) Solution for curvature perturbation can be derived exactly at large scales (including, at high energies) Anisotropic stress Anisotropic stress anisotropic stress on the brane anisotropic stress on the brane coupled to anisotropic perturbation coupled to anisotropic perturbation

12. Evolution equation for Evolution equation for Junction condition at the brane Junction condition at the brane Gradient expansion Gradient expansion

13. Junction condition on the brane Junction condition on the brane One more boundary condition is needed to One more boundary condition is needed to specify specify Anisotropic stress is nothing but Anisotropic stress is nothing but Behavior of anisotropic stress completely depends on the boundary condition in the bulk Behavior of anisotropic stress completely depends on the boundary condition in the bulk

14. The simplest case where we can determine The simplest case where we can determine another brane in the bulk another brane in the bulk Junction conditions Junction conditions

15. Solution for, Solution for, Anisotropic stress Anisotropic stress

16. Two branes model Two branes model Shadow matter, radion affect the anisotropy of the brane at large scales Shadow matter, radion affect the anisotropy of the brane at large scales CMB anisotropies provide CMB anisotropies provide useful constraints on the model useful constraints on the model Realistic model should be considered Realistic model should be considered case is interesting case is interesting Anisotropic stress associated with dark Anisotropic stress associated with dark radiation does not depend on radiation does not depend on Toy model for anisotropic stress (Rhodes, van der Bruck, Brax, Davis)

17. 3.Effect of dark radiation on CMB anisotropies Dark radiation perturbation induces the isocurvature perturbation Weyl anisotropic stress gives distinguishable features to CMB anisotropies We use the result for to investigate the effect of dark radiation on CMB anisotropies

18. Covariant formalism Radion

19. Parameter amplitude of dark radiation perturbation isocurvature perturbation, anisotropic stress Due to Weyl anisotropic stress, the resultant CMB spectrum is different from simple mixtures of adiabatic and isocurvature perturbations Likelihood analysis Malkov Chain Monte Calro approach (K. Koyama and K Ichiki in preparation)

22. Summary Two branes model Two branes model Shadow matter, radion affect large scale CMB anisotropies Shadow matter, radion affect large scale CMB anisotropies Extensions to general cases Extensions to general cases Construct realistic models Construct realistic models stabilization mechanism stabilization mechanism or time dependent fundamental constant or time dependent fundamental constant (K. Koyama, R. Maartens, work in progress)

23. One brane model One brane model We should carefully investigate the We should carefully investigate the boundary condition in the bulk boundary condition in the bulk Anisotropic stress boundary condition Anisotropic stress boundary condition Validity of our modeling ? Validity of our modeling ? – Anisotropic AdS-Schwartzshild spacetime – Toy model where the above relation can be analytically examined in a whole spacetime analytically examined in a whole spacetime (KK and K. Takahashi hep-th/0307073) (KK and K. Takahashi hep-th/0307073)