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Structure formation in Void UniversesOsaka City University (OCU)Ryusuke NishikawacollaboratorKen-ichi Nakao (OCU) ,Chul-Moon Yoo (YITP)

?1/15Dark Energy & Copernican PrincipleStandard cosmological modelGeneral RelativityCopernican PrincipleObservationsDark Energy(homogeneous and isotropic spacetime)Inhomogeneous cosmological modelTomita (2000) , Celerier (2000) We live close to the center in spherically symmetric spacetime. General RelativityCopernican PrincipleObservationsDark Energy(inhomogeneous and isotropic spacetime)2/15

Void cosmological modelsdust, spherically symmetricLemaitre-Tolman-Bondi (LTB) solutionsHomogeneous Big Bang time

only growing modetwo functional degree (growing mode and decaying mode)We consider homogeneous Big Bang Void models.

large voidClarkson, Regis (2010)

3/15Observational TestsCMB acoustic peak positions

Radial BAO

redshift drift

kSZ effect

etc.consistency

?Tests using the large-scale structure evolution have not been performed. 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.4/15

Void structureClarkson, Regis model (2010)

nonlinear

density contrast :5/15density contrast on past light-coneThis was first pointed out by Enqvist, Mattsson, Rigopoulos (2009).

We can use perturbative analysis for void structure inside the past light-cone.6/15

Linear approximation for the void universe

background FLRWThe relative error is within 20%.linear perturbationlinear growing factor

density7/15FLRWREDSHIST7Hubble parameter

blue line : linear approximationblack line : exact LTB8/15Perturbation in the approximated void universe

Second order perturbations in homogeneous and isotropic spacetimeWe can solve.Spherically symmetric

synchronous comoving gauge

We assume and neglect terms.Tomita (1967), (we consider only scalar-scalar coupling)Non-spherically symmetric

9/159Non-spherically symmetric density perturbation

sub-horizon scale :

Fourier transform

10/15Angular power spectrum & Effective growth rate

3D power spectrum in FLRW.

effective growth rate

We assumeIn linear approximation,

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Effective growth rateIf we observe the growth rate of , we can test the void model. summaryVoid model (CR model)CDMOpen FLRW

12/15Future work13/15

redshift space distortionsGuzzo et al. (2005)Kaiser (1987)Matsubara, Suto (1996)14/15

redshift spacereal space2-parameter

redshift space distortions15/15

redshift spacereal spacevoid>015

redshift space distortions

redshift space distortions

redshift space distortions19/15

FLRWFLRW + void effect

LTB solution LTB (Lemaitre-Tolman-Bondi) .

known function

second-order perturbation

linear perturbation equations

second-order perturbation

second-order perturbation equation

density contrast on past light-cone

Garcia-Bellido & Haugbolle model (2008)Einstein de-Sitter universevoid modelLTBZibin (2008)silent approximationneglecting the coupling between density perturbations and gravitational waves Dunsby et al. (2010)RedshiftFLRWredshiftredshiftdistortions

->redshift space