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

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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

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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

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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 –H 0, M, b,, k, z re, t 0 ….etc Does it fit? Tweak parameters, try again

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

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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

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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

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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

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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

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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)

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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)

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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

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Summary Expts: Pre-WMAP

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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)

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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

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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

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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

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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

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Polarisation modes E-mode, or electric mode –No curl B-mode, or magnetic mode –Has curl

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In practice: detect both modes Simulated dataPure E-modePure B-mode Decompose

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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

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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

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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

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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

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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

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E-mode detection DASI - the first! 2002 Level consistent with Prediction from T anisotropy WMAP1: Confirmation Redshift of reionisation EARLY (when stars turned on) TE correlation

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

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E-mode detection y=0

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

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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

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B-modes….. Galatic contamination on large scales

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Effect of B-modes on P.S. Detect B-modes? Gravity waves. Prove inflation. If youre sure its primordial signal!

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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)

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