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Lecture 2

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  1. Lecture 2 Temperature anisotropies cont: what we can learn CMB polarisation: what it is and what we can learn

  2. Announcements • Slides from lecture 1 now online (ppt and pdf), slides from this lecture available from tomorrow • Deadline for assessment is Thursday 18th March 5pm • Full instructions and suggestions, plus the paper for lecture 5 workshop will be circulated by email tomorrow

  3. Key point from Lecture 1:CMB map to Power Spectrum Amplitude of fluctuations as function of angular scale Wiggly line is a function of the cosmological parameters

  4. What can we learn? • Observe CMB over a wide range of scales, measure: • Compute in sensible bins • Use eg CMBFAST to generate theoretical power spectrum with parameter values • H0, ΩM, Ωb, Ω, Ωk, zre, t0….etc • Does it fit? • Tweak parameters, try again

  5. Parameter dependance • Positions and relative heights of the various peaks depend on parameter values • All inter-dependant and complicated • We’ll focus on three interesting points: • Position of the first peak • Ratio on 2nd/1st peaks • Height of the third peak

  6. First peak • Position of first peak gives the curvature of the Universe • In fact, other peaks are fixed to the first peak so this governs x-position of power spectrum

  7. First peak position: curvature • Decrease curvature, peaks shift right to smaller scales • If the Universe is not flat, it affects the apparent size of the anisotropies • Observations show Universe is almost perfectly flat

  8. 2nd/1st peak heights • Collapse driven by gravity: dark matter plus baryons (balls) • Rarefaction driven by photons (springs): coupled to baryons only • 2nd peak: comes from 1 compression and 1 rarefaction • Expect lower than 1st peak. • More baryons, difference is greater • In fact, expect all even peaks to be suppressed relative to odd peaks

  9. 2nd/1st peak heights • Increase Baryon density: • Odd/even peak height ratio increases • Also: • Baryons slow oscillations down: spectrum shifts to higher • Baryons increase the damping at high

  10. Third peak • Sensitive to ratio of dark matter to radiation • We know the radiation density from the physics of the early Universe, so really the only variable is the amount of dark matter • Smaller modes started oscillating earlier when the Universe was radiation dominated • Part of the gravitational potential came from the radiation itself • Mode at maximum compression, density stabilised, potential could dissipate, no longer resisted expansion • Expect high third peak and beyond (as oscillations started during radiation domination) BUT more dark matter will reduce this (plus silk damping)

  11. Third peak • Expect enhancement of higher peaks due to radiation driving • However, increase dark matter…. • Note growth of third peak with increasing matter density • All peak heights decrease (less radiation driving)

  12. Higher peaks / damping tail • Give consistency checks • Picture is actually complicated, effects all inter-related • Take home points: • 1st peak: tells us the curvature of the Universe • 2nd peak: height relative to 1st peak gives the baryon density • 3rd peak: height relative to 2nd peak gives the dark matter density • Thus we naturally have total matter density (baryons plus dark matter), and as we know the Universe is flat, we can also constrain dark energy

  13. Summary Expts: Pre-WMAP

  14. CMB Polarisation • The CMB is partially polarised • Two chances to polarise the CMB: • DURING recombination (short time, low level signal) • AFTER stars have reionised the Universe (ie a non-primordial signal, still interesting for cosmology) • Signal 10 times smaller than CMB temperature anisotropies (or less!) • WHY BOTHER?? • Constrain the redshift of reionisation, ie the time at which stars ‘turned on’ (E-modes) • Detect primordial gravity waves and thus confirm the theory of inflation (B-modes)

  15. Polarisation mechanism • Simple case: light reflected off a surface • Incoming radiation ‘shakes’ electrons on surface, this re-radiates the incident light • Electrons move most easily in the plane of the surface • Radiation polarised parallel to the plane of the suface • Analogy with CMB: photons ‘reflected’ by electrons via Thomson scattering

  16. Polarisation: Thomson scattering • Blue lines: E-field • Incoming light ‘shakes’ electron as shown • Radiation scattered at 90° • Light can not be polarised in direction of travel • One linear polarisation state is scattered

  17. Polarisation: Thomson scattering • Consider isotropic radiation • Incoming radiation from left and top have same intensity • Each is polarised as before • Outgoing radiation has no net polarisation • Need anisotropy to see a net polarisation

  18. Polarisation: Thomson scattering • ‘Quadropole’ anisotropy • Put simply: the two radiation sources, at 90° from each other, are at different temperatures • Still get both polarisation states but one is stronger than the other

  19. Polarisation modes • E-mode, or ‘electric’ mode • No curl • B-mode, or ‘magnetic’ mode • Has curl

  20. In practice: detect both modes Simulated data Pure E-mode Pure B-mode Decompose

  21. Polarisation modes • E-modes are produced by: • CMB primordial temperature anisotropies: ie we can place further constraints on the cosmological parameters already constrained by temperature anisotropies • Scattering after reionisation (discussed next) • Foregrounds (galaxy, instrumental) • B-modes are produced by: • Gravity waves during inflation (discussed next) • Lensing of E-modes by large scale structure • Foregrounds

  22. Aside: Reionisation • Post recombination, Universe was neutral…..until stars formed and produced ionising radiation • Charged particles (ions) can Thomson scatter CMB photons, although the probability is very low (~1%) • This produces E-mode polarisation on the largest scales

  23. Aside: Gravity waves • Inflation, explosive expansion made ‘ripples’ in space-time • Gravity waves: give B-mode polarisation in the CMB • Amplitude depends on expansion rate during inflation

  24. Aside: Cosmic shear • Two types of gravitational lensing: weak and strong • Strong: see arcs, multiple images • Weak: analyse ‘shear field’ • Cosmic shear: cumulative weak lensing • Lensing of E-mode CMB gives ‘fake’ B-modes

  25. Power spectra Temperature (as before) Correlation: T with E E-mode (10-100 times Fainter than T) B-mode (fainter still) Interesting info is on the larger scales

  26. E-mode detection TE correlation DASI - the first! 2002 Level consistent with Prediction from T anisotropy WMAP1: Confirmation Redshift of reionisation EARLY (when stars ‘turned on’)

  27. E-mode detection TE correlation DASI - the first! Level consistent with Prediction from T anisotropy WMAP3: TE correlation LATER RETRACTED!!

  28. E-mode detection y=0

  29. Effect of E-modes on P.S. Determine redshift of reionsation (birth of the first stars)

  30. B-modes….. • Primordial B-modes are produced by gravity waves (during inflation) • ISSUE: E-modes (as discussed previously) turn into B-modes via gravitational lensing • The CMB may be lensed by large scale structure on its journey towards us • Also: most primordial signal (the interesting bit) is on largest scales where galactic contamination is strongest

  31. B-modes….. Galatic contamination on large scales

  32. Effect of B-modes on P.S. Detect B-modes? Gravity waves. Prove inflation. If you’re sure it’s primordial signal!

  33. Summary: What the CMB can tell us • CMB temperature anisotropies: • 1st peak position: curvature • 2nd to 1st peak heights: baryon density • 3rd peak height: density of dark matter • CMB polarisation: • E-modes: cosmological parameters (as above), redshift of reionisation • B-modes: gravity waves (would prove inflation)