1. Imprints of Nonlinear Super-Structures on Cosmic Microwave Background Nobuyuki Sakai (Yamagata U) in collaboration with Kaiki Inoue (Kinki U) Kenji Tomita (Kyoto U) Nobuyuki Sakai (Yamagata U) in collaboration with Kaiki Inoue (Kinki U) Kenji Tomita (Kyoto U)

2. Cold Spot in WMAP (Vielva et al. 2004) -spherical wavelet analysis size 〜 10° 、 ΔT ≒ー 70μK (3σ) Are non-Gaussianity Primordial?

3. Cold spot in NVSS radio (Rudnick et al.2007) Super-void?

4. ・ WMAP/SDSS cross-correlation (Granett et al. 2008) Identify 50 voids and 50 clusters in SDSS LRG catalog. (0.4<z<0.75) Average CMB cut-outs around them. cold spots appear in void stacks: radius 〜 4°, ΔT ≒ー 11μK hot spots appear in cluster stacks: radius 〜 4°, ΔT ≒ 8μK

5. Purpose of present work If non-Gaussian cold spots and hot spots really exist, it is important to clarify whether they are primordial fluctuations or generated by super-stuructures due to ISW effects. ↓ We model super-voids and super-clusters by LTB spacetime and analyze their nonlinear ISW effect. （ compare with thin-shell approximation & 2 nd order perturbations ）

6. Previous work on nonlinear ISW effects Spherical void (cluster) in Λ=0 Universe

7. Recent work on nonlinear ISW effects Spherical void/cluster in Λ≠0 Universe Thin shell void model (Inoue & Silk 2007) 2 nd order perturbation (Tomita & Inoue 2008) LTB spacetime (Sakai & Inoue 2008) only photons passing through center.

8. Modeling void/cluster by LTB metric f(r), m(r) ← density & velocity field at initial time Discritize radial coordinate ； at each grid point solve Einstein equations numerically. Geometrical quantities between grid points are evaluated by cubic interpolation using nearby 4 points.

9. Initial conditions for voids/clusters Universe model ： Ω 0 =0.26, λ 0 =0.74 At initial time: z i =100 –Velocity field =0 –Density (mass) distribution: Model parameters ： δ 0, R 0 、 shell with w 、 position z c open/closed FRW flat FRW

10. Density profile (examples)

11. Null geodesic equations (θ=π/2) 0

12. Numerical results Here we fix z c =0.5.

13. Voids Nonlinear effects generate hot ring. Large Ω (or high-z) enhances the effects      

14. Clusters Nonlinear effects generate dip in the center Large Ω (or high-z) enhances the effects

15. Comparison with 1 st and 2 nd order perturbation In LPT ΔT is monotonic and its sign is unchanged. 2 nd order effects are consistent with LTB results. VoidCluster

16. CMB stacked image by Granett et al.

17. Reconstruction of cold spot in stacked image.

19. Reconstruction of hot spots in stacked image.

20. Summary and discussions GR nonlinearity may distinguish ISW from primordial nG. –Super-void makes hot ring around cold spot. –Super-cluster makes dip in center of hot spot. Our void/cluster models are consistent with observed cold/hot spots. –Stacked image of 50 void and 50 clusters by Granett et al. R 〜 0.04/H, |δ| 〜 0.6, z~0.5, (Ω 0 =0.26, λ 0 =0.74) –The Cold Spot ←similar void around z=0.15 Further data of CMB (final WMAP, Planck, LiteBIRD) and galaxy survey will verify this conjecture. Cross-correlation analysis is important. What is origin of such a XL void and cluster as 〜 200Mpc?