imprints of nonlinear super-structures on cosmic microwave background nobuyuki sakai (yamagata u) in...
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Imprints of Nonlinear Super-Structures on Cosmic Microwave Background
Nobuyuki Sakai (Yamagata U)
in collaboration withKaiki Inoue (Kinki U)
Kenji Tomita (Kyoto U)
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• Cold Spot in WMAP (Vielva et al. 2004)- spherical wavelet analysis
size 〜 10° 、 ΔT≒ ー 70μK (3σ)
Are non-Gaussianity Primordial?
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Cold spot in NVSS radio (Rudnick et al.2007)Super-void?
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・ 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≒
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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 & 2nd order perturbations )
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Previous work on nonlinear ISW effects
Spherical void (cluster) in Λ=0 Universe
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Recent work on nonlinear ISW effects
Spherical void/cluster in Λ≠0 Universe• Thin shell void model (Inoue & Silk 2007)• 2nd order perturbation (Tomita & Inoue 2008)• LTB spacetime (Sakai & Inoue 2008)
only photons passing through center.
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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.
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Initial conditions for voids/clusters
• Universe model : Ω0=0.26, λ0=0.74• At initial time: zi=100
– Velocity field =0– Density (mass) distribution:
• Model parameters : δ0, R0 、 shell with w 、 position zc
open/closed FRW
flat FRW
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Density profile (examples)
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Null geodesic equations (θ=π/2)
0
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Numerical results
Here we fix zc=0.5.
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Voids
Nonlinear effects generate hot ring.
Large Ω (or high-z) enhances the effects
W0=0.26 d0=-0.4
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Clusters
Nonlinear effects generate dip in the center
Large Ω (or high-z) enhances the effects
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Comparison with 1st and 2nd order perturbation
In LPT ΔT is monotonic and its sign is unchanged.
2nd order effects are consistent with LTB results.
Void Cluster
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CMB stacked image by Granett et al.
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Reconstruction of cold spot in stacked image.
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Reconstruction of hot spots in stacked image.
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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, (Ω0=0.26, λ0=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?