Lecture 09. The Cosmic Microwave Background. Part II Features of the Angular Power Spectrum

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1 The Cosmic Microwave Background Part II Features of the Angular Power Spectrum

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) 2

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 3

4 Simple Harmonic Oscillator Recall from Physics I Simple Harmonic Oscillator We can choose start time such that 4

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 5

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) 6

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 7

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... 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 8

9 st 1 Acoustic Peak Largest length scale accessible at recombination Time for exactly one compression (½ oscillation) 9

10 nd 2 Acoustic Peak Shorter length scale than first peak Time for one full oscillation For details see 10

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, Ω, Ω tot m b Changing any of these drastically changes the shape How Ωm affects Angular Power Spectrum Check out 11

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 12

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 13