void宇宙における構造形成

Report
Structure formation in Void Universes
?
Osaka City University (OCU)
Ryusuke Nishikawa
collaborator
Ken-ichi Nakao (OCU) ,Chul-Moon Yoo (YITP)
1/15
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.
2/15
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)
3/15
Observational Tests
consistency
•CMB acoustic peak positions
Clarkson, Regis (2010), Yoo, Nakao, Sasaki (2010) ・・・
○
•Radial BAO
△
•redshift drift
?
•kSZ effect Yoo, Nakao, Sasaki (2011)
×?
Zibin, Moss, Scott (2008), Garcia-Bellido, Haugbolle (2008)
Yoo, Kai, Nakao (2008)
etc.
The symmetry of the background LTB is less than FLRW.
Tests using the large-scale structure evolution have
not been performed.
4/15
Void structure
density contrast :
nonlinear
Clarkson, Regis model
(2010)
5/15
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).
6/15
Linear approximation for the void universe
density
linear perturbation
background FLRW
linear growing factor
The relative error is within 20%.
7/15
Hubble parameter
blue line : linear approximation
black line : exact LTB
8/15
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), ・・・
9/15
Non-spherically symmetric density perturbation
sub-horizon scale :
Fourier transform
10/15
Angular power spectrum & Effective growth rate
effective growth rate
3D power spectrum in FLRW.
We assume
In linear approximation,
11/15
Effective growth rate
ΛCDM
Open FLRW
Void model (CR model)
summary
If we observe the growth rate of
, we can test the void model.
12/15
Future work
13/15
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.
14/15
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.
15/15
参考
redshift space distortions
空間曲率無視
redshift space distortions
redshift space distortions
FLRW + void effect
FLRW
19/15
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
・
・
known function
は座標を選ぶ自由度.
を仮定.
(宇宙初期は一様等方時空)
second-order perturbation
linear perturbation equations
second-order perturbation
second-order perturbation equation
density contrast on past light-cone
Garcia-Bellido & Haugbolle model (2008)
(遠方はEinstein de-Sitter universeに近づくvoid model)
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
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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