Lecture 2

Temperature anisotropies cont: what we can learn

CMB polarisation: what it is and what we can learn

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

Key point from Lecture 1:CMB map to Power Spectrum

Amplitude of fluctuations as function of angular scaleWiggly line is a function of the cosmological parameters

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

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

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

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

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

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

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)

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)

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

Summary

Expts:Pre-WMAP

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)

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

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

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

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

Polarisation modes

• E-mode, or ‘electric’ mode– No curl

• B-mode, or ‘magnetic’ mode– Has curl

In practice: detect both modes

Simulated data Pure E-mode Pure B-mode

Decompose

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

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

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

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

Power spectraTemperature(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

E-mode detection

DASI - the first! 2002Level consistent withPrediction from T anisotropy

WMAP1: ConfirmationRedshift of reionisation EARLY(when stars ‘turned on’)

TE correlation

E-mode detection

DASI - the first!Level consistent withPrediction from T anisotropy

WMAP3: TE correlationLATER RETRACTED!!

TE correlation

E-mode detection

y=0

Effect of E-modes on P.S.

Determineredshift of reionsation(birth of thefirst stars)

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

B-modes…..

Galatic contamination on large scales

Effect of B-modes on P.S.

Detect B-modes?Gravity waves.Prove inflation.

If you’re sureit’s primordialsignal!

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)