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

Blandton & Hogg

Hubble deep field

CfA survey

Sloan Digital Sky Survey

recombination WMAP website

CMB: cosmic microwave background

Sloan Digital Sky Survey

Gravitational Instability Interested quantity: overdensity

LANL

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

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

From: Obtain: Growing mode:

Gravitational Instability Interested quantity: overdensity

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.

Blandton & Hogg

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

WMAP

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.

Direct detection of WIMPs credit: U. Zaragoza

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.

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.

Hierarchical clustering: small things form first threshold

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

Rauch ☼ n=2 1216 Å n=1

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