1. Dark Matter and the Large Scale Structure of the Universe 暗物質及宇宙建構
Lam Hui 許林
Columbia University

2. This is the second in a series of 3 talks.
July 5: Dark energy and the homogeneous
universe
Today: Dark matter and the large scale
structure of the universe
July 18: Inflation and the early universe

3. Outline
Review: the inhomogeneous universe
Basic mechanism: gravitational instability
Basic ingredient: dark matter
Basic statistical tool: correlation function
Basic problem: mass

4. Blandton & Hogg

5. Hubble deep field

6. CfA survey

7. Sloan Digital Sky Survey

8. recombination
WMAP website

9. CMB: cosmic microwave background

12. Sloan Digital Sky Survey

13. Gravitational Instability
Interested quantity: overdensity

14. LANL

16. Scale factor a(t)
time = t’
time=t
x=0
x=1
x=2
x=0
x=1
x=2
distance = a(t)Δx
distance = a(t’)Δx

17. Fundamental equations
mass conservation:
momentum conservation
i.e. F = ma :
Poisson’s equation:

18. From:
Obtain:
Growing mode:

19. Gravitational Instability
Interested quantity: overdensity

20. Problem:
There is not enough time for structure
to grow from recombination to today! γ γ e- p+ H
Solution:
Dark matter - no/little interaction with
photons; pressureless.

21. Blandton & Hogg

22. Evidence from rotation curve (Vera Rubin)
Credit: Richard Pogge

23. WMAP

24. naturally get the right left over abundance.
What makes up dark matter?
Most plausible candidate:
Weakly Interacting Massive Particle (WIMP)
If annihilation cross section ,
naturally get the right left over abundance.

25. Direct detection of WIMPs
credit: U. Zaragoza

26. Current structure formation paradigm:
Pressureless (cold) dark matter, which makes up about 20% of the universe,
forms structure via gravitational instability.
To understand the quantitative success
of this model, we need to learn one
statistical tool: the 2 point correlation
function.

27. quantifies amplitude of fluctuations
Two-point correlation function ξ
and power spectrum P r
Common to plot:
quantifies amplitude of fluctuations
at scale 1/k.

28. Hierarchical clustering: small things form first
threshold

30. Problem: usually don’t observe mass directly.
CMB: observe temperature
Galaxies: observe counts
Want: mass

31. Rauch ☼
n=2
1216 Å
n=1

32. deflection angle = 4GM/r
Gravitational lensing
image ☀ ☀
lens
source
observer
image ☀
deflection angle = 4GM/r

35. Jain

36. Tegmark

37. Summary
- Structure formation occurs via the
gravitational instability of cold dark
matter.
- Small galaxies form first, which then
merge to form bigger things.
- A major goal of observational cosmology
is to measure the mass fluctuations.
- We still don’t know what dark matter is.