The Cosmic Microwave Background 1
Photons and Charge Remember the lectures on particle physics Photons are the bosons that transmit EM force Charged particles interact by exchanging photons But since they are massless, they can propagate indefinite distances Consider a plasma Free charged objects Photons exchanged continuously But they do not propagate indefinitely High cross section means short mean free path for photons Consider neutral atoms Effective charge density goes to zero Photons do propagate freely Must get close to atoms to interact 2
Photosphere Inner region of the sun is plasma kt >> 13.6 ev Photons are bound to plasma Outer region of sun is cooler kt < 13.6 ev Photons propagate freely, and leave the sun Transition region: Photosphere The region where photons decouple and propagate freely Effective photon emission point We see the photosphere as the surface of the sun Opaque inside, transparent outside 3
Photosphere of the Universe The same phenomenon happens in the evolution of the universe Early universe was hot and ionized Free charge everywhere (like interior of sun) Universe cooled below 13.6 ev Photons propagate freely Surface of last scattering Cosmic Microwave Background (CMB) Predicted in 1948 by Alpher & Herman Based on these simple principles 4
CMB and Redshift The CMB release should give ~ 13.6 ev photons That was the temperature at its release But recall: the expansion of the universe cools photons via redshift Consider a matter dominated universe Most of the evolution of the CMB fits this model Beginning, transition from Radiation to Matter End, transition from Matter to Vacuum Energy We can ignore these for now, since they are perturbations to the result Relationship of energy density and temperature There is a mathematical relationship between density and temperature Based on Thermodynamics and Statistical Mechanics For this course, let's just accept that we can convert from redshift to temperature This will be much clearer when you've studied stat mech At release T = 13.6 ev = 1.57 X 105 K Occurred at redshift z = 1100 Today T = 2.35 X 10-4 ev = 2.73 K 5
Blackbody Radiation A blackbody is an object in complete thermal equilibrium Absorbs all light that hits it Radiates light according to its temperature Spectrum of wavelengths Recall the cosmological principle Uniform and isotropic universe Ideal candidate for a blackbody The CMB release should have a blackbody spectrum T = 13.6 ev when released Measurement of CMB should be a blackbody spectrum Based on expansion of matter dominated universe Should be at microwave wavelengths Length scale ~ cm Temperature scale ~ K 6
Discovery of CMB Penzias and Wilson Microwave observations of cosmic rays in 1964 Accidentally discovered CMB as noise in their instrument Couldn't get noise to disappear On closer inspection realized it corresponded to a uniform T source Did their homework and saw prediction of Alpher and Herman One of the most important discoveries in cosmology! Awarded Nobel Prize in physics in 1978 7
Dedicated CMB Measurement After discovery, questions about spectrum Is it a blackbody? At what temperature? What is directional distribution? COsmic Background Explorer (COBE) Satellite telescope launched in 1989 Full sky survey of the CMB Measured spectrum at cm wavelength Most precise blackbody ever measured! Error bars smaller than line width T = 2.73 K Measured dipole (hotter in one direction than the other) Due to motion of earth 8
Results of COBE T of universe today = 2.73 K Dipole anisotropy Origin of Horizon Problem T the same to very high level in every direction Implies causal connection Led to model of inflation Smaller anisotropies also observed at 7o resolution 9
A Closer Look: WMAP Wilkinson Microwave Anisotropy Probe (WMAP) Designed to investigate features seen in COBE Satellite telescope measuring different bands in microwave range Full sky survey with finer angular resolution Few arcmin vs few degrees Results: Measured same blackbody T Same dipole observed T fluctuations of smaller anisotropies measured 10
What about the Pattern of the Anisotropies? Performed a detailed analysis of the pattern of the anisotropies Angular Power Spectrum Fit angular distribution with series of spherical harmonics Found characteristic length scale Angular Power Spectrum 11
Angular Power Spectrum of CMB Y axis is amplitude of correlation function Proportional to c(θ) Peak in spectrum shows dominant angular scale of anisotropy pattern Peaks at higher l due to smaller structure Lower l due to larger structure Peaks tell us the length scale of T fluctuations at CMB release Hotter regions released later (less redshift) Cooler regions released earlier (more redshift) Very sensitive to matter distribution 12
Ruler on the Sky The Friedmann Equation tells us how far away things are Horizon distance Using the redshift measurement of the CMB (peak wavelength today relative to release at 13.6 ev) From the angular measurement and the distance, we know the physical size of these fluctuations 13
Size of Fluctuations The horizon distance at z = 1100 comes from integrating I(z) Then we can calculate the angular size This corresponds very precisely with the peak in the CMB angular power spectrum L = 200 is roughly 1o Size of fluctuations is the horizon distance when CMB was released! Causally connected regions at that time Anisotropies due to local physics at CMB release 14
Multipole Moment and Size Larger l corresponds to smaller resolution (smaller angles) Peaks give good focus Lots of clear structure at that angular scale 15
Simple Harmonic Oscillator Recall from Physics I Simple Harmonic Oscillator We can choose start time such that 16
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 17
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) 18
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 19
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... Rarefaction Time between entering horizon and last scattering Compression: Maximum density (high T) ½ integer number of oscillations Compression Rarefaction: Minimum density (low T) Integer number of oscillations 20
st 1 Acoustic Peak Largest length scale accessible at recombination Time for exactly one compression (½ oscillation) 21
nd 2 Acoustic Peak Shorter length scale than first peak Time for one full oscillation For details see http://background.uchicago.edu/~whu/sciam/sym1.html 22
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, Ω, Ω tot m 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/ 23
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 See animation at http://map.gsfc.nasa.gov/resources/camb_tool/ 24
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 25