Dark Matter and the Large Scale Structure of the Universe

暗物質及宇宙建構

Lam Hui 許林Columbia University

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

Outline

Basic mechanism: gravitational instability

Basic ingredient: dark matter

Review: the inhomogeneous universe

Basic problem: mass

Basic statistical tool: correlation function

Blandton & Hogg

Hubble deep field

CfA survey

Sloan Digital Sky Survey

WMAP website

recombination

CMB: cosmic microwave background

Sloan Digital Sky Survey

Gravitational Instability

Interested quantity: overdensity

LANL

Scale factor a(t)

x=0 x=2x=1

x=0 x=1 x=2

time=t

time = t’

distance = a(t)Δx

distance = a(t’)Δx

Fundamental equations

mass conservation:

momentum conservation

Poisson’s equation:

i.e. F = ma :

From:

Obtain:

Growing mode:

Gravitational Instability

Interested quantity: overdensity

Problem:

There is not enough time for structureto grow from recombination to today!

p+

e-γ

Solution:

γ

H

Dark matter - no/little interaction with photons; pressureless.

Blandton & Hogg

Credit: Richard Pogge

Evidence from rotation curve (Vera Rubin)

WMAP

What makes up dark matter?

Most plausible candidate: Weakly Interacting Massive Particle (WIMP)

If annihilation cross section naturally get the right left over

abundance.

,

credit: U. Zaragoza

Direct detection of WIMPs

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 successof this model, we need to learn one statistical tool: the 2 point correlationfunction.

Two-point correlation function ξand power spectrum P

r

Common to plot:quantifies amplitude of

fluctuations at scale 1/k.

threshold

Hierarchical clustering: small things form first

Problem: usually don’t observe mass directly.

CMB: observe temperature Galaxies: observe counts

Want: mass

Rauch

☼

n=2

n=11216 Å

Gravitational lensing

☀lens

observer

source

☀

☀image

image

deflection angle = 4GM/r

Jain

Tegmark

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.