The influence of Dark Energy on the Large Scale Structure Formation Dec.02.2008 The influence of Dark Energy on the Large Scale Structure Formation International Workshop on Dark Matter, Dark Energy, and Matter-Antimatter Asymmetry November. 21th .2009 Seokcheon (sky) Lee Institute of Physics, Academia Sinica & LeCOSPA, NTU

Dec.02.2008 Outline 1. Linear perturbation of matter with dark energy when DE is the cosmological constant (Λ) or general DE 1-I. Exact Analytic solution of density perturbations (δ = D) 1-II. Growth index and its parameter (f and γ) 2. Non-linear perturbation of matter (SCM) with(out) curvature 3. Non-linear perturbation of matter with dark energy 4. Observational consequences. 5. Summary Nov.21th.2009 Sky Lee // IWDMDE

Dec.02.2008 Observations Nov.21th.2009 Sky Lee // IWDMDE

Linear perturbation theory.i Dec.02.2008 Linear perturbation theory.i Matter distribution in the Universe (Large scale) : Homogeneous Contains inhomogeneous structures (Small scale) : galaxies, clusters A small inhomogeneity grows due to gravitational instability At late times (z < 10), all interesting modes enter the horizon : sub-horizon scale(s) Nov.21th.2009 Sky Lee // IWDMDE

Linear perturbation theory.ii Dec.02.2008 Linear perturbation theory.ii Uniform growth (independent of k) due to the pressure-less DM : all modes evolves identically Figures from : Ma et.al. [arXiv:astro-ph/9506072] Nov.21th.2009 Sky Lee // IWDMDE

LPT Equations Perturbed equations Dec.02.2008 Nov.21th.2009 Sky Lee // IWDMDE

Dec.02.2008 Solve LPT 1. Numerical method : need to separate both the growing mode and decaying mode from 2. Analytic method : only true for cosmological constant or curvature with integral form. Nov.21th.2009 Sky Lee // IWDMDE

Analytic solution i-a For cosmological constant or curvature term Dec.02.2008 Analytic solution i-a For cosmological constant or curvature term Growth factor Growth index and its parameter Nov.21th.2009 Sky Lee // IWDMDE

Dec.02.2008 Analytic solution i-b Peculiar velocity : ~30% differences for 0.2 -0.4 matter Nov.21th.2009 Sky Lee // IWDMDE

Dec.02.2008 Analytic solution i-c Nov.21th.2009 Sky Lee // IWDMDE

Analytic solution ii-a Dec.02.2008 Analytic solution ii-a Solution for any general dark energy models Growth factor (growing mode solution) Growth index and its parameter Nov.21th.2009 Sky Lee // IWDMDE

Analytic solution ii-b Dec.02.2008 Analytic solution ii-b Nov.21th.2009 Sky Lee // IWDMDE

Dec.02.2008 Future Observations Nov.21th.2009 Sky Lee // IWDMDE

Dark matter and baryon I Dec.02.2008 Dark matter and baryon I DM dependence on matter density will confuse with the model dependence. Nov.21th.2009 Sky Lee // IWDMDE

Dark matter and baryon II Dec.02.2008 Dark matter and baryon II Baryon catch up the DM after the decoupling. Quite model independent and unique. If find anti-bias, then good for some coupling model (preparation with G-C Liu and K-W Ng) Nov.21th.2009 Sky Lee // IWDMDE

Spherical Collapse Model (SCM) Dec.02.2008 Spherical Collapse Model (SCM) Nov.21th.2009 Sky Lee // IWDMDE

Nonlinear matter perturbation Dec.02.2008 Nonlinear matter perturbation General method : Spherical collapse model (SCM) with and without curvature term Nov.21th.2009 Sky Lee // IWDMDE

SCM with(out) k .I Define new parameters Dec.02.2008 Nov.21th.2009 Sky Lee // IWDMDE

Dec.02.2008 SCM with(out) k .II Nov.21th.2009 Sky Lee // IWDMDE

SCM with(out) k .III Virial theorem Dec.02.2008 Nov.21th.2009 Sky Lee // IWDMDE

SCM with(out) k .IV Linear regime (critical threshold density) Dec.02.2008 SCM with(out) k .IV Linear regime (critical threshold density) Nov.21th.2009 Sky Lee // IWDMDE

Dec.02.2008 SCM with DE .I Nov.21th.2009 Sky Lee // IWDMDE

Dec.02.2008 SCM with DE .II Nov.21th.2009 Sky Lee // IWDMDE

Dec.02.2008 SCM with DE .III Nov.21th.2009 Sky Lee // IWDMDE

Dec.02.2008 SCM with DE .IV Nov.21th.2009 Sky Lee // IWDMDE

Observables CMB and Matter Power Spectrum (linear) Dec.02.2008 Observables CMB and Matter Power Spectrum (linear) Baryonic Acoustic Oscillation (linear + non-linear) SUBARU : Hyper Suprime-Cam (HSC) : ASIAA : Cluster abundances, Weak Lensing (WL), Nov.21th.2009 Sky Lee // IWDMDE

Dec.02.2008 Summary Linear perturbation theory in sub-horizon scales important for the structure formation. We are able to obtain the exact values of growth index and exact analytic solution of growth factor for any DE models. This simple and exact solution give the guidelines for future observations (sigma8, etc..) Nonlinear model can be used for probing cluster abundances, mass function, WL, and BAO. Exact solutions provide accurate tools for probing DE. Nov.21th.2009 Sky Lee // IWDMDE