Post on 28-Sep-2020
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