The cosmic microwave background radiation

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1 The cosmic microwave background radiation László Dobos Dept. of Physics of Complex Systems É 5.60 May 18, 2018.

2 Origin of the cosmic microwave radiation Photons in the plasma are scattered constantly 380 thousand years after the Big Bang: recombination temperature falls (well) below the ionization energy of H around 3000 K (determine from the Saha equation) protons combine with electron into neutral H atoms the Universe becomes gradually transparent for thermal photon Surface of the last scattering photons are scattered for the very last time in the plasma average free path becomes larger than size of the horizon free streaming, in a mere 13.8 bn years, they reach us today its temperature is redshifted to 2.7 K, microwave Spectrum of the cosmic microwave background same as at the time of last scattering but redshifted Planck curve but varies from direction to direction

3 Surface of last scattering The farthest surface we can ever observe via EM radiation temperature anisotropies in the order of δt /T 10 5 temperature fluctuations follow density fluctuations even here where we are, was plasma at early times structure visible around us must come from density fluctuations of the early plasma

4 COBE - dipole

5 COBE

6 WMAP

7 Map of the cosmic microwave radiation Source: Planck Consortium (2013)

8 Acoustic oscillations and the surface of last scattering Before photon decoupling fluctuations inside the horizon oscillate amplitude of a plane wave changes with time early universe: no crosstalk between wave numbers Surface of the last scattering imprint of the oscillating modes at decoupling each mode catches decoupling at different phase imprint of each mode with corresponding amplitude density is from the combination of all modes temperature depends on density only adiabatic modes After decoupling photo pressure disappears fluctuations are affected by gravity only linear grows on large, non-linear growth on small scales

9 Amplitude of adiabatic modes

10 Modes with maximum amplitudes When is the amplitude of a mode with wave number k maximal? if it had enough time to fully it had exactly enough time to compress fully 1/4 period or 3/4 period wavelength equal to the size of the acoustic horizon and all the harmonics of them k 1 = v s t Amplitude of other wavelengths depend on the phase they were caught in recombination.

11 What do we see from the early fluctuations? Sachs Wolfe effect (primordial) fluctuations just before decoupling with different amplitudes when plasma denser, a bit hotter but also deeper gravitational potential photons have to climb out of potential wll lose energy, photons from denser regions will appear colder denser regions will appear slightly colder in CMB Projection effects fluctuations are treated as plane waves surface of last scattering appears as surface of a sphere how do we see plane waves intersected by a sphere?

12 Projection of a plane wave ϑ ϑ

13 Map of the cosmic microwave background Source: Planck Consortium (2013)

14 Power spectrum of the CMB Express temperature fluctuations by spherical harmonics T (θ, φ) T 0 = l l=0 m= l Power spectrum is averaging by directions C l = 1 2l + 1 a (lm) Y (lm) (θ, φ) l a lm 2 m= l

15 Power spectrum as measured by Planck Angular scale Dl[µK 2 ] Multipole moment, l Source: Planck Consortium (2013)

16 Peaks of the power spectrum First acoustic peak wave number which had enough time to reach maximal amplitude (1/4 period) by t wavelength equal to the size of the acoustic horizon r s at t its redshift z can be measured from temperature of CMB compare r s with D A (z)-vel Ω = 1 Second acoustic peak wavelength reaching 3/4 period by t baryons fell into the potential formed by dark matter a foton barion interaction 1 depends in wavelength of fluctuation second peak has smaller amplitude as first one measures the amount of baryonic matter 1 baryon drag

17 Other peaks and the plateau Third acoustic peak sensitive to the baryon-dark matter ratio Higher harmonics with decreasing amplitude due to Silk damping Plateau at large angles (small l-s) we would not expect any correlations similar to horizon problem evidence for cosmic inflation inflation measurements with large error (Poisson noise) The problem of cosmic variance CMB can only be measure from a single point of the U for small l-s, statistical sample is very small causes significant shot noise

18 Interaction of the background radiation with the foreground The background photons right after decoupling stream freely in the tenuous neutral universe First stars and quasars reionize hydrogen by this time the universe is even less dense CMB photons are scattered but not as much that their original pattern could be washed out

19 Sunyaev Zel dovich effect Hot intracluster medium emits light in x-ray several millions of Kelvin temperature high energy electrons Inverse Compton scattering interaction of high energy electrons with photons electrons give energy to photons can give a small kick from back Effect on the photons of the CMB with the CMB radiation traverses cluster a part of the photons gains extra energy slightly increases the temperature of the radiation

20 Szunyajev Zeldovics-effektus

21 The integral (late time) Sachs Wolfe effect 2 If a photon falls into a potential well gains energy climbs out of a potential well loses energy while traversing gravitationally bound systems E = 0 in the presence of Λ there s always an effect CMB photons traverse huge voids and super clusters light crossing time is very long dark energy and expansion changes the potential well during the traversal potential gets flatter photons might gain/lose some energy during crossing hot/cold spots in the CMB pattern 2 Called the Rees Sciama effect when calculated to non-linear order

22 First evidence for the integral Sachs Wolfe effect Have to stack CMD data for lots of voids Granett, Neyrinck & Szapudi (2008)

23 Polarization of electromagnetic radiation Monochromatic electromagnetic plane wave propagating in the z direction: E x = a x (t)e i(ω 0t θ x (t)) E y = a y (t)e i(ω 0t θ y (t)) the CMB is not coherent, nor monochromatic such radiation is polarized if the two components correlate can be described by the coherence matrix I ij = E xex Ex Ey Ex E y Ey Ey

24 Stokes-paraméterek Good quantities to measure polarization relative intensity in different direction of polarization Stokes parameters: I = Ex 2 + E 2 y Q = Ex 2 E 2 y U = 2Re( E x Ey ) V = 2Im( E x E y ) U and V don t seem to be easily measurable, but I = I (0 ) + I (90 ) Q = I (0 ) I (90 ) U = I (45 ) I (135 ) V = I R I L

25 Stokes parameters

26 Source of linear polarization Incident photons are scattered via Thomson scattering can cause linear polarization but if incoming radiation is isotropic, there is no net polarization

27 Source of linear polarization Quadrupole moment of incident radiation can cause net liner polarization.

28 Covariance tensor of linear polarization The Stokes parameters describing linear polarization can be written in tensor form: ( ) Q U P ab = 1 2 U Q Polarization of the CMB is measured on the surface of the sphere: P ab = P ab (θ, φ)

29 E and B mode Similarly to Helmholtz decomposition of the electromagnetic field P ab (θ, φ) can be written as the sum of a curl-free and a div-free term these can be written as multipole series P ab (θ, φ) T 0 = Y E l l=2 m= l [ a E (lm) Y E (lm)ab (θ, φ) + ab (lm) Y B (lm)ab (θ, φ) ] (lm) and Y (lm) B come from the derivatives of ordinary spherical harmonics The cross-correlation spectrum is defined from the coefficients C AB l = 1 2l + 1 l m= l a A lm ab lm

30 Quadrupole anisotropy Three kinds of perturbations can cause quadrupole anisotropy m = 0: scalar perturbations : only E mode m = ±1: vector perturbations : B mode dominates m = ±2: gravitational waves : E and B with similar strength This is always true locally, for a singla plane wave but have to sum over all wave numbers what is inherited into the final polarization pattern? parity, i.e. E and B modes, don t mix but correlations with the multipole modes of the temperature are inherited

31 Why is measuring the polarization important? B modes originating from the early universe vector perturbations decay quickly only tensor perturbations can cause B modes early time gravity waves or later effect from the foreground Temperature anisotropies are significantly affected by the foreground: Sunayev Zel dovich effect Rees Schiama effect (integrated Sachs Wolfe effect) Polarization is less sensitive to the foreground gravitational lensing can cause E B mixing galactic sources can produce B modes

32 The BB cross-correlation spectrum

33 The galactic foreground Source: Planck Konzorcium (2013)

Really, really, what universe do we live in?

Really, really, what universe do we live in? Fluctuations in cosmic microwave background Origin Amplitude Spectrum Cosmic variance CMB observations and cosmological parameters COBE, balloons WMAP Parameters