Lecture 09

The Cosmic Microwave

BackgroundPart II

Features of the Angular Power Spectrum

PHYS 2961 Lecture 09 2

Angular Power Spectrum

● Recall the angular power spectrum

● Peak at l=200 corresponds to 1o structure

● Exactly the horizon distance at CMB release

● What is the origin of this structure?● What about the finer structure at higher l?● The explanation of the origin and the implications are based on Baryon

Acoustic Oscillations (BAO)

PHYS 2961 Lecture 09 3

Multipole Moment and Size

Larger l corresponds to smaller resolution (smaller angles)Peaks give good “focus”Lots of clear structure at that angular scale

PHYS 2961 Lecture 09 4

Simple Harmonic Oscillator

Recall from Physics ISimple Harmonic Oscillator

We can choose start time such that

PHYS 2961 Lecture 09 5

Matter and Photons during Recombination

● Cosmic fluid● Made of photons and baryons (photon baryon fluid)● We'll ignore electrons, since they have very little mass

● Consider a potential well● Matter is attracted to the well● Photons supply pressure, pushing baryons out of well

● Photon pressure scales with density● Increases as matter contracts, decreases as it expands

● Simple harmonic motion● Baryon acoustic oscillations

PHYS 2961 Lecture 09 6

BAOs

Characteristic frequency

● Spring constant k related to photon pressure● Photon to baryon ratio η● Defines how frequently photons “push” the matter apart● η depends on only baryonic matter, not dark matter

● m is sum of baryonic and non-baryonic (dark) matter

Characteristic wavelength

Speed of sound vac

is slower than c (about c/3)

PHYS 2961 Lecture 09 7

Source of BAOs

Remember what we discussed with inflation● Quantum fluctuations give local

disturbances● Local extrema in gravitational

potential● They are stretched out beyond the

horizon during inflation● Frozen in place

● These fluctuations exist at different length scales

● As the universe expands, larger and larger length scales “enter the horizon”

● When a fluctuation is accessible causally, BAOs begin

PHYS 2961 Lecture 09 8

Modes and Multipole Moment l

What can we access from the angular power spectrum?● Half modes

● Lowest mode (largest length scale, smallest l)● ½ oscillation

● Next mode● 1 full oscillation

● And so on...

Compression

Rarefaction

Time between entering horizon and last scattering

Compression:Maximum density (high T)½ integer number of oscillations

Rarefaction:Minimum density (low T)Integer number of oscillations

PHYS 2961 Lecture 09 9

1st Acoustic Peak

● Largest length scale accessible at recombination● Time for exactly one compression (½ oscillation)

PHYS 2961 Lecture 09 10

2nd Acoustic Peak

● Shorter length scale than first peak● Time for one full oscillation

For details see http://background.uchicago.edu/~whu/SciAm/sym1.html

PHYS 2961 Lecture 09 11

What do the peaks tell us?

Peak location sensitive to:● Amount of baryonic matter

● Shows up in spring constant k● Total matter density

● Shows up in frequency ω● Curvature of universe

● Relation of horizon distance to angular scale

● The CMB is the best probe we have of these three ingredients● Ω

tot, Ω

m, Ω

b

● Changing any of these drastically changes the shape

How Ωm

affects Angular Power Spectrum

Check out http://map.gsfc.nasa.gov/resources/camb_tool/

PHYS 2961 Lecture 09 12

ΛCDM Model

Cosmological standard model● Model cosmology with a minimum

of parameters (only 6)● Λ = Dark Energy (vacuum energy

● Comes from cosmological constant in Einstein Field Equations

● CDM = Cold Dark Matter● Makes up extra non-baryonic

matter that has to be there● Must be cold (non-relativistic)● More on CDM later

● CMB Anisotropies give us the energy content of the universe● They also constrain other parameters● Extensions to the cosmological standard model

PHYS 2961 Lecture 09 13

Reliability of Results

WMAP gave first measurement

Measurement repeated by Planck● Not identical results● Qualitatively similar● Numbers in slight disagreement

Consider the difficulties of this measurement● Build and deploy satellite● Collect data over many years● Complex data analysis

Agreement is actually quite good● ~ ¼ Dark Matter● ~ 70% Dark Energy● ~ 5% Normal Matter● Minimal amounts of radiation, neutrinos, etc