1. The influence of Dark Energy on the Large Scale Structure Formation
Dec
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

2. Dec
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
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3. Dec
Observations
Nov.21th.2009
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4. Linear perturbation theory.i
Dec
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

5. Linear perturbation theory.ii
Dec
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/ ]
Nov.21th.2009
Sky Lee // IWDMDE

6. LPT Equations Perturbed equations Dec.02.2008 Nov.21th.2009
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7. Dec
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

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

9. Dec
Analytic solution i-b
Peculiar velocity : ~30% differences for matter
Nov.21th.2009
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10. Dec
Analytic solution i-c
Nov.21th.2009
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11. Analytic solution ii-a
Dec
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

12. Analytic solution ii-b
Dec
Analytic solution ii-b
Nov.21th.2009
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13. Dec
Future Observations
Nov.21th.2009
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14. Dark matter and baryon I
Dec
Dark matter and baryon I
DM dependence on matter density will confuse with the model dependence.
Nov.21th.2009
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15. Dark matter and baryon II
Dec
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

16. Spherical Collapse Model (SCM)
Dec
Spherical Collapse Model (SCM)
Nov.21th.2009
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17. Nonlinear matter perturbation
Dec
Nonlinear matter perturbation
General method : Spherical collapse model (SCM) with and without curvature term
Nov.21th.2009
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18. SCM with(out) k .I Define new parameters Dec.02.2008 Nov.21th.2009
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19. Dec
SCM with(out) k .II
Nov.21th.2009
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20. SCM with(out) k .III Virial theorem Dec.02.2008 Nov.21th.2009
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21. SCM with(out) k .IV Linear regime (critical threshold density)
Dec
SCM with(out) k .IV
Linear regime (critical threshold density)
Nov.21th.2009
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22. Dec
SCM with DE .I
Nov.21th.2009
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23. Dec
SCM with DE .II
Nov.21th.2009
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24. Dec
SCM with DE .III
Nov.21th.2009
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25. Dec
SCM with DE .IV
Nov.21th.2009
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26. Observables CMB and Matter Power Spectrum (linear)
Dec
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

27. Dec
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