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Structure formation in Void Universes

Structure formation in Void Universes. ?. Osaka City University (OCU) Ryusuke Nishikawa. collaborator Ken- ichi Nakao (OCU) , Chul -Moon Yoo (YITP). Dark Energy & Copernican Principle. Standard cosmological model. General Relativity 　＋　 Copernican Principle 　＋　 Observations.

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Structure formation in Void Universes

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  1. Structure formation in Void Universes ? Osaka City University (OCU) RyusukeNishikawa collaborator Ken-ichiNakao (OCU) ,Chul-Moon Yoo (YITP)

  2. Dark Energy & Copernican Principle Standard cosmological model General Relativity　＋　Copernican Principle　＋　Observations (homogeneous and isotropic spacetime) Dark Energy Inhomogeneous cosmological model Tomita (2000) , Celerier (2000) General Relativity　＋　Copernican Principle　＋　Observations (inhomogeneous and isotropic spacetime) Dark Energy We live close to the center in spherically symmetric spacetime.

  3. Void cosmological models dust, spherically symmetric Lemaitre-Tolman-Bondi (LTB) solutions two functional degree (growing mode and decaying mode) Homogeneous Big Bang time only growing mode We consider homogeneous Big Bang Void models. large void Clarkson, Regis (2010)

  4. Observational Tests consistency • CMB acoustic peak positions • Radial BAO • redshift drift • kSZ effect • etc. ○ △ ？ ×? Clarkson, Regis (2010), Yoo, Nakao, Sasaki (2010) ・・・ Zibin, Moss, Scott (2008), Garcia-Bellido, Haugbolle (2008) Yoo, Kai, Nakao (2008) Yoo, Nakao, Sasaki (2011) The symmetry of the background LTB is less than FLRW. • Tests using the large-scale structure evolution have not been performed.

  5. Void structure density contrast : nonlinear Clarkson, Regis model (2010)

  6. density contrast on past light-cone We can use perturbative analysis for void structure inside the past light-cone. This was first pointed out by Enqvist, Mattsson, Rigopoulos (2009).

  7. Linear approximation for the void universe density background FLRW linear perturbation linear growing factor The relative error is within 20%.

  8. Hubble parameter blue line : linear approximation black line : exact LTB

  9. Perturbation in the approximated void universe synchronous comoving gauge Spherically symmetric： (we consider only scalar-scalar coupling) Non-spherically symmetric： We assume and neglect terms. Second order perturbations in homogeneous and isotropic spacetime We can solve. Tomita (1967), ・・・

  10. Non-spherically symmetric density perturbation sub-horizon scale : Fourier transform

  11. Angular power spectrum & Effective growth rate 3D power spectrum in FLRW. effective growth rate We assume In linear approximation,

  12. Effective growth rate ΛCDM Open FLRW Void model (CR model) summary If we observe the growth rate of , we can test the void model.

  13. Future work

  14. redshift space distortions redshift space real space Kaiser (1987) Matsubara, Suto (1996) 2-parameter の摂動の場合： Guzzo et al. (2005) 線形摂動でヴォイドの効果が入る． この図にヴォイドモデルを 書き入れたい．

  15. redshift space distortions voidの効果 real space redshift space 視線方向 >0 視線方向の相関を強める．

  16. 参考

  17. redshift space distortions 空間曲率無視

  18. redshift space distortions

  19. redshift space distortions FLRW + void effect FLRW

  20. LTB solution 球対称 、ダスト時空はLTB (Lemaitre-Tolman-Bondi) 解で記述される. 任意関数は ・　　　　　は座標を選ぶ自由度． ・　　　　　　　　　　を仮定． known function （宇宙初期は一様等方時空）

  21. second-order perturbation linear perturbation equations

  22. second-order perturbation second-order perturbation equation

  23. density contrast on past light-cone Garcia-Bellido & Haugbolle model (2008) （遠方はEinstein de-Sitter universeに近づくvoid model）

  24. 近似してLTB摂動方程式を解いた例 Zibin (2008) Dunsby et al. (2010) silent approximation neglecting the coupling between density perturbations and gravitational waves

  25. メモ RedshiftはFLRWのredshift用いて書く． ２次摂動まで入れると，１次の効果まで取り入れたredshiftを考える必要があるか． 球対称ゆらぎのみ存在するときにdistortionsはどうみえるか？ 固有速度は（一様等方時空に比べて）外に行くほど小さくなる． ->redshift spaceでは集まるようにみえる．

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