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1 COSMOLOGY PHYS COSMIC MICROWAVE BACKGROUND RADIATION Giampaolo Pisano - Jodrell Bank Centre for Astrophysics The University of Manchester - April giampaolo.pisano@manchester.ac.uk

2 COSMIC MICROWAVE BACKGROUND RADIATION Discovery and Observations Recombination Decoupling and Last Scattering Anisotropies Polarisation References: Ryden, Introduction to Cosmology - Par. 9.1 Serjeant, Observational Cosmology - Par. 2.1

3 CMB Discovery: Penzias & Wilson NASA Nobel price in Measuring reflected signals from communication satellites at λ=7.35 cmthey realised the existence of an excess noise pointing the antenna towards the sky - They tried everything to reduce the noise, even cleaning pigeons dielectric stuff.. - The excess signal was isotropic, unpolarised and constant with time: Not associated to any astronomical source -A possible explanation for the radiation was given by R. Dicke et al: A relic of an early, hot, dense and opaque state of the Universe -Note: the CMB existence was already predicted by Gamow et al in 1948

4 CMB Observations: COBE satellite NASA -The CMB peaks at ~2mm: Measurements at millimetre wavelengths required -At these wavelengths, the best way to observe is: High altitude dry sites, stratospheric balloons or satellites - The Comic Background Explorer (COBE) satellite had three instruments: - DIRBE (1<λ< λ<240um) Stars and dust in our galaxy - FIRAS (100um<λ< λ<10mm) Spectrum CMB -DMR (λ=3.3, 5.7, 9.6mm) Full sky CMB maps COBE achieved three main results (Mather & Smooth Nobel Price 2006)

5 CMB Observations: COBE Results 1/3 -At any position of the sky the CMB spectrum is very close to that of a Black Body: No deviations found at a level of The CMB mean temperature, averaged over all locations, is:

6 CMB Observations: COBE Results 2/3 T/T 10-3 T 3.4 mk -The CMB has a Dipole distortion in temperature : Doppler shift due to COBE motion relative to a frame where the CMB is isotropic - After correcting for the following orbital motions: COBE around Earth ~8 km/s Earth around Sun ~30 km/s Sun around Galactic centre ~220 km/s Our Galaxy relative to Local Group centre of mass ~80 km/s - Local Group moving towards Virgo Cluster and Hydra Centaurus supercluster: v=630±20 km/s

7 CMB Observations: COBE Results 3/3 T/T 10-5 T 30µK - Subtracting the Dipole distortion and the galactic emission contributions: Tiny temperature fluctuations still present - The temperature fluctuations at a given point is: - The root mean square temperature fluctuations was: -CMB as a nearly perfect Black Body + nearly isotropic Support Hot Bing Bang

8 The Hot Big Bang Model: Origin of the CMB Addison-Wesley Longman CMB

9 The origin of the CMB: Three epochs - To understand the origin of the CMB we need to distinguish between three different epochs: Recombination - Time when the ionised baryonic component becomes neutral: Defined as when number densities of ions and neutral atoms are equal Photon decoupling - Time when photons stop to interact with electrons, the Universe becomes transparent Rate photon-electron scattering << than Hubble parameter Last scattering - Time when a typical CMB photon has its last scattering from an electron Last scattering very close to photon decoupling epoch

10 Observing the CMB: The Last Scattering Surface - Surrounding every observer in the Universe is the Last Scattering Surface (LSS) Horizon 3000K 3K Last Scattering Surface Transparent Photons redshifted Opaque CMB photons have been travelling from the LSS without further scattering They have been continuosly redshifted

11 Observing CMB: Photons vs Baryons in the present Universe 1/2 - At mm wavelengths most of the light in the Universe comes from the CMB: The sky is uniformly bright at: T K 0 = - CMB average T - The current energy density of the CMB is: 4 3 ε γ, 0 = α T = MeVm - CMB energy density 3 ε c, 0 = 5200 MeVm 5 ε γ, 0 10 ε c,0 4 - However, the photon energy is very small: = 6 10 ev E γ,0 - So, the number density of CMB photons is very high: n 8 3 γ, 0 = m ε n γ,0 = E - CMB number density γ,0 γ,0 Let s compare these numbers to those of baryons

12 Observing CMB: Photons vs Baryons in the present Universe 2/2 - We know tha the current baryons density parameter is: Ω bary, = So, the baryons energy density is: 0,0, 0 ε = Ω ε bary, bary c 0 3 ε bary, MeVm - Baryons energy density ε ε bary, γ,0 - However, the rest energy of protons/neutrons is very high: E bary 939 MeV - So, the number density of baryons is very small: 3 nbary, 0 = 0.22 m n bary,0 ε = E bary,0 bary - Baryons number density - In conclusion: η = n bary,0 n γ, Baryons to Photons ratio In the present Universe there are ~ two billion photons per baryon

13 COSMIC MICROWAVE BACKGROUND RADIATION Discovery and Observations Recombination Decoupling and Last Scattering Anisotropies Polarisation References: Ryden, Introduction to Cosmology - Par. 9.2, 9.3

14 Recombination: Hydrogen 1/2 - Let s assume the baryonic component before recombination consisting only of Hydrogen (We will see that Nucleosynthesis generates also He) - Hydrogen can be in the form: Neutral atom H Ionised (nucleus) p n = - For the Universe charge neutrality: p e n - The degree of baryonic ionisation is defined: n n X = n + n n p p e = = - Baryons fractional p H bary n n bary ionisation X =1 fully ionised X =0 entirely neutral

15 Recombination: Hydrogen 2/2 - The ionisation energy of Hydrogen is: Q =13.6 ev - A photon with h ν > Q can ionise an H atom: H + γ p + e - Hydrogen photoionisation - A proton and an electron can undergo: p + e H + γ - p-e radiative recombination In a Universe made of electrons, protons and photons the fractional ionisation X will depend on the balance between photoionisation and radiative recombination

16 Before Recombination: Thomson Scattering - Lets choose a period before the epoch of recombination: a =10-5 z =10 5 T rad 3x10 5 E γ = hν = 2.7kT 60 ev >> Q - Given the high photon energy and the high photon/baryon ratio (1/η): The Universe was fully ionised X = 1 - In such a Universe, photons interacted mainly with electron via: γ + e γ + e - The mean free path of a photon is: λ 1 n σ e e - Thomson scattering 2 = where = m σ e γ e - - Thomson scattering Cross section

17 Before Recombination: Thomson Scattering rate - On average photons will scatter from electrons every: t sc λ = c - So, the rate of interaction photons-electrons is: Γ = c λ = neσ e c γ e - e - - Full ionisations means: X = 1 n = n = e p n bary - The number density of conserved particles, like baryons, goes as: n bary = n bary,0 3 a - So, the scattering rate becomes: Γ = n σ ec bary,0 3 a - Thomson scattering rate

18 Coupling and Decoupling: Thomson Scattering vs Expansion - Photons remain coupled to electrons as long as: Γ > H - Photon-electron coupling condition Scattering rate larger than expansion rate of the Universe λ < c H - Equivalently: Mean free path < Hubble distance Photons, electrons and protons in thermal equilibrium at the same T ( Protons are coupled to electrons via Coulomb interaction) - If the expansion dilution is more rapid than photon-electron scattering rate: Γ < H - Decoupling condition Photon decouple from electrons and the Universe become transparent ( Baryons and photon temperatures evolve differently ) - Decoupling is not a gradual process, rather relatively sudden process

19 Before Recombination: Radiation era Example a =10-5 a < a rm Radiation era - The Friedmann equation was: 2 H Ω H r,0 0 Ω r,0 = H = H 0 a a = s - The scattering rate was: Γ = n ec baryσ 6 1 = s 3 a - Comparing the two: Γ > H Photons coupled to electrons and protons

20 Epoch of Recombination: Temperature derivation 1/5 - A very rough estimate of T rec can be obtained equating the mean energy of a CMB photon with the hydrogen ionisation energy: 2.7 ~ Q kt rec T rec ~ Q 2.7k ~ K This temperature is wrong by more than a factor This happens for two reasons: 1) BB spectrum has an exponential tail of high energy γ (tiny fraction) 2) However, the number of photons compared to baryons is enormous Photoionisation can still occur at much lower temperatures ( A proper calculation of T rec requires statistical mechanics )

21 Epoch of Recombination: Temperature derivation 2/5 - When photons and baryons are coupled, the reactions will be in statistical equilibrium: H + γ p + e Photoionisation rate will balance the radiative recombination rate - When a reaction is in statistical equilibrium at temperature T the number density of particles with mass m x is given by: n x = g x 3/ 2 m xkt exp 2 2πh mxc kt 2 - Maxwell-Boltzmann equation kt << m x c 2 Non-relativistic particles g x : Particle statistical weight To calculate T rec we need to determine X as a fucntion of (η,t )

22 Epoch of Recombination: Temperature derivation 3/5 - The relation between number densities of H, p and e - in equilibrium is: nh n n p e = g H =4 g H g g p e mh mpm e 3/ 2 kt 2πh 2 3/ 2 exp Q (binding energy) [ m + m m ] p e kt H c 2 g p =g e =2 m H m p - That becomes: nh n n p e = mekt 2 2πh 3/ 2 exp Q kt - Saha equation This equation relates the number densities of particles in the two states of the hydrogen atom: neutral and ionised - It is possible to convert the equation in terms of (X, T, η): 3/ 2 1 X kt Q = 3.84η exp (see Ryden) 2 2 X mec kt

23 Epoch of Recombination: Temperature derivation 4/5 - Solving for the fractional ionisation X and plotting as a function of redshift z: X Ryden Fig.9.4 Recombination z Recombination is not an istantaneous process, it last for ~70,000yr - However, we define the Time of recombination when X =1/ 2

24 Epoch of Recombination: Temperature derivation 5/5 - Solving the equations, we finally have: Recombination T rec = 3740 K - Temperature Q T rec = 42k z rec = Redshift t rec = 240,000 yr - Time Recombination happens at much lower temperatures than initially estimated

25 COSMIC MICROWAVE BACKGROUND RADIATION Discovery and Observations Recombination Decoupling and Last Scattering Anisotropies Polarisation References: Ryden, Introduction to Cosmology - Par. 9.3

26 Epoch of Decoupling: Derivation 1/2 - During recombination the number density of electrons drops rapidly: The photon decoupling process happens soon after recombination - When the hydrogen is partially ionised, the photon scattering rate is function of the redshift: Γ = n e ( z) σ c e - Remembering that: ne ( z) X ( z) = ne ( z) = X ( z) nbary ( z) nbary ( z) nbary,0 3 nbary ( z) = = n 3 bary, 0( 1+ z) a - Substituting: Γ = X ( z)(1 + z) 3 n bary,0 σ c e - Photon scattering rate during Recombination

27 Epoch of Decoupling: Derivation 2/2 - During recombination the Universe is matter dominated and the Friedmann equations is: H H = Ω a m,0 3 2 = Ω m + H = H Ω ( 1 z 3/ - Hubble parameter m + 3, 0( 1 z) 0,0 ) during Recombination - We define the Time of photon decoupling when Γ = H - Solving the equations we have: T dec = 3000 K Photon decoupling - Temperature z dec t dec ,000 yr - Redshift - Time

28 Last Scattering Epoch - The CMB photons we detect have travelled straight to us since they last scattered from an electron - In the time interval (t, t+dt) the probability for a photon to scatter an e - is: dp = Γ( t) dt - If today, t 0, we detect a photon, the number of scattering it had since t is: t 0 τ ( t ) = Γ ( t ) dt t - Optical depth - We define the Time of last scattering when τ = 1 T ls = 3000 K Last scattering - Temperature - Calculations give: z ls Redshift t ls 350,000 yr - Time

29 Epochs Summary Event Redshift Temperature (K) Time (yr) Radiation-matter equality ,000 Recombination ,000 Photon decoupling ,000 Last scattering ,000 Notes - The Last Scattering Surface is actually thick z ( ) - Before Decoupling: - single photon-baryon fluid - photons tend to smooth any fluid fluctuations smaller than the horizon - After Decoupling: - Independent photon and neutral hydrogen gases - Hydrogen gas free to collapse under self-gravity and dark matter

30 COSMIC MICROWAVE BACKGROUND RADIATION Discovery and Observations Recombination Decoupling and Last Scattering Anisotropies Polarisation References: Ryden, Introduction to Cosmology - Par. 9.4, 9.5 Serjeant, Observational Cosmology - Par. 2.10, 2.12

31 CMB Observations: BOOMERanG (also DASI and Maxima) 1998 Boomerang - First high resolution map down to 10 arcmin. Results: Angular diameter distance to LSS and the geometry of the Universe = Flat

32 Cosmic Microwave Background: WMAP satellite NASA - Instrument: - Channels: GHz - Resolution: arcmin -Goal: -Full sky CMB anisotropies - Temperature anisotropy - Polarisation correlation

33 CMB Anisotropies: Spherical Harmonics Expansion - To describe the temperature anisotropy distribution we use: δt T 0 ( θ, φ) = l l= 0 m= l a Y lm lm( θ, φ) l = 0,1, Multipole expansion m = l,... + l ( 2l+1 values for each l ) where: Y lm ( θ, φ ) - Spherical Harmonics - Across the sphere, they form an orthonormal set of functions: Y * lm( θ, φ) Yl ' m' ( θ, φ) dω = δll' δ mm' - Orthogonality relations Let s visualise some examples of spherical harmonics

34 Spherical Harmonics: Examples ( Plots: Re Y lm ) Y 0,0 Monopole Y 1,0 Y 1,1 ϑ λ = o 360 l Dipoles Y 10,6 Y 2,0 Y 2,1 Y 2,2 Quadrupoles Y 3,0 Y 3,1 Y 3,2 Y 3,3 Octopoles

35 CMB Anisotropies: Angular Power Spectrum - The anisotropies expansion coefficients can be calculated: a * δt = Ylm ( θ, φ) ( θ, φ dω T lm ) 0 - Multipole coefficients ( Analogous to Fourier coefficients ) l = 0 Monopole Y = const CMB average T a00 l =1 Dipole l 2 Primordial dominated 00 = by Doppler effect motion Solar System Fluctuations at the time of 0 Last Scattering - Primordial perturbations are Gaussian, and this implies: a lm = 0 C = - We then define: - Angular power spectrum l a lm 2 ( Theoretical expected values over a statistical ensemble of modelled universes) Because of the isotropic nature of the random processes the angular power spectrum is expressed only in terms of l (no preferred directions)

36 CMB Anisotropies: Observed Power Spectrum 1/2 - We observe only one CMB temperature distribution and so we define: ~ C = 1 2l + 1 l a lm m 2 - Observed power spectrum All the statistical information of the CMB anisotropies is contained in the C l - C l is a measure of temperature fluctuations on the angular scale: o 180 ϑ ~ l - Power spectra are normally plotted in terms of l l + 1) C / on log l scales: 2 ~ T l( l + 1) = T 0 2π ( l This way, scale-invariant spectra look horizontal in these plots C l 2π

37 CMB Anisotropies: Observed Power Spectrum 2/2 - Pre-Planck experiment results: First peak at l~200, corresponding to an angular scale of ~1

38 CMB anisotropies: Angular size 1/2 - The relation between angular and physical size of a CMB fluctuations is: d A = l δθ where: d A = dl /( 1+ z) dl = d p ( t 0 )(1 + z) 2 - The LSS is at a redshift: z ls =1100 >>1 t e = 0 d p ( t0) dhor ( t0) Current Horizon distance d A = d p ( t 0 (1 + )(1 + z) 2 z) d hor ( t 0 ) z ls = 14,000 Mpc Mpc - LSS angular diameter distance - A fluctuation δθ on the LSS had a physical size: δθ lls = d A δθ = 0.22 Mpc o 1 - LSS fluctuation proper size

39 CMB anisotropies: Angular size 2/2 - Observed fluctuations are in the range: δθ = (0.2 o 1 o ) l ls ( )Mpc (At the time of Last Scattering) - Today, they correspond to a physical size of: l l ls ( z + 1) (44 0 = ls 240 )Mpc - Fluctuation present proper size The low end size of these primordial fluctuations is comparable with the size of present large-scale structures, such as superclusters and voids

40 CMB anisotropies: Small vs Large Angular Scales - The Hubble distance at the time of last scattering was: c H ( z ls ) 0.2 Mpc - A patch of this size on the LSS corresponds to an observed angular size: θ H c / H ( z d ls = d A ) 0.2 Mpc 13 Mpc o 1 Coincident with the peak in the anisotropies power spectrum - The origin of the temperature fluctuation is different for: θ > l < 180 θ H θ < l > 180 θ H - Large angular scales - Small angular scales

41 Large angular scales: Sachs-Wolfe effect 1/2 - The energy density of non-baryonic dark matter, baryonic matter and photons at the time of last scattering were: ε dm( z ls ) = Ωdm, 0ε c,0(1 + zls ) MeV m = - Dark matter ε bary ( z ls ) = Ωbary, 0ε c,0(1 + zls ) MeV m = - Baryonic matter ε 4 γ ( z ls ) Ω γ, 0 c,0 (1 + z ls ) = ε 11 3 = MeV m - Photons ε ε > > bary dm (6.4 : 1.4 : 1) ε γ At the time of last scattering the non-baryonic dark matter dominated the energy density and so the gravitational potential Dark matter will drive the gravitational collapse of baryonic matter

42 Large angular scales: Sachs-Wolfe effect 2/2 - Any energy density fluctuation in the dark-matter δε spatially varying gravitational potential δφ : δφ δε δφ dm δε dm will give rise to a - Imagine, at the time of last scattering, a photon at a potential: - Local minimum Climbing out will lose energy Redshifted - Local maximum Falling down will gain energy Blueshifted - Relativistic calculations give: δ T = T 1 δφ 2 3 c Sachs-Wolfe effect Temperature fluctuations from variation in the gravitational potential Fluctuations at θ > θ H provide a map of the potential fluctuations at LS

43 Small angular scales: Acoustic peaks 1/3 - Consider the baryon-photon fluid just before decoupling moving under the influence of dark matter - If the fluid is in a potential well: fall to the centre of the well pressure increase pressure enough to expand back expansion continues until pressure drops fluid falls invard again by gravity Acoustic Oscillations /fizisist/isw/spring_peaks.jpg Compression and expansion continue until photon decoupling

44 Small angular scales: Acoustic peaks 2/3 - At the time of decoupling, if the photon-baryon fluid is: Main peak - at maximum compression Photons hotter than average - at maximum expansion Photons cooler - expanding or contracting Doppler effect: hotter/cooler - Potential wells where the fluid just reached max compression at LS - Proper size at LS: c / H ( z ) - Today angular size: ~ ls θ l 180 θ H - Location peak depend on curvature Universe: θ θ θ peak peak peak < 1 o 1 o > 1 o κ = 1 κ = 0 The observations are consisten with a flat Universe κ = + 1 Second peak Provides information about Ω bary

45 Small angular scales: Acoustic peaks 3/3 - Fluctuation size at LS Hotter Cooler Doppler Additional information is provided by the smaller angular scales peaks

46 COSMIC MICROWAVE BACKGROUND RADIATION Discovery and Observations Recombination Decoupling and Last Scattering Anisotropies Polarisation References: Serjeant, Observational Cosmology - Par. 2.16

47 CMB Polarisation: Thomson Scattering - In the elastic scattering between photon and electrons it is possible to generate linear polarisation G. Pisano PhD Thesis 2001 Incoming unpolarised light will emerge completely polarised in the case of 90 degrees scattering

48 CMB Polarisation generation on the Last Scattering Surface - Imagine distributions of photons scattering off an electron on the LSS: G. Pisano PhD Thesis 2001 Monopole Null Pol Dipole Pol Null Quadrupole Pol not null Only a quadrupolar distribution of photons will produce a polarised signals

49 CMB Polarization: E-Modes and B-Modes - Linear polarisation patterns can be decomposed into two components: E-modes B-modes Due to scalar (density) or tensor (gravity waves) perturbations Due to primordial tensor (gravity waves) perturbations

50 Cosmic Microwave Background: Planck satellite ESA 2009 PLANCK -Two instruments: -LFI: GHz -HFI: GHz Resolution arcmin Resolution 5-10 arcmin - Goal: Full sky CMB anisotropies and E-mode polarisation

51 CMB Anisotropies: From COBE to Planck Best angular resolution: Anisotropies resolved with high accuracy

52 Planck: Anisotropies Power Spectrum ESA Best spectrum ever measured: Data just released!

53 Planck: Polarisation Results ESA Work on progress: Not yet released!

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