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CMB continued …

This article explores the Integrated Sachs-Wolfe (ISW) Effect and its three different stages: Early, Late, and General. It also discusses the polarization of the Cosmic Microwave Background (CMB) and its origins from density fluctuations and gravitational waves. Additionally, it covers the polarization fluctuations during the Epoch of Reionization (EoR) and their contributions to the CMB power spectrum.

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CMB continued …

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  1. CMB continued…

  2. Integrated Sachs-Wolfe Effect All Sachs-Wolfe effects are due to photons going through density fluctuations (potential wells and peaks). SW Effect: super-horizon scales during the epoch of recombination Early Integrated SW Effect: just after recombination, at z~1000, photons (now decoupled from electrons/baryons) stream out of potential wells, and towards potential peaks. This reduces the amplitude of potential wells/peaks Late Integrated SW Effect: If the Universe is matter dominated during recent epochs, z<1, on very large spatial scales, linear growth of density perturbations, d implies no change in the potential. However, if L dominates at late times, gravitational potential wells and peaks will be decaying in amplitude, inducing temperature changes. These can be detected by cross-correlating CMB temp. maps with (i) large scale structure, LSS, traced by the distribution of galaxies, or (ii) lensing potential extracted from the CMB itself. ~ (integration is over comoving length)

  3. Polarization of the CMB General requirements for linear polarization to be produced by Thomson scattering – applies to primary anisotropy and reionization induced polarization incoming radiation is isotropic; radiation scattered by electron is not polarized incoming radiation is from one direction; radiation scattered by electron is polarized

  4. Polarization of the CMB General requirements for linear polarization to be produced by Thomson scattering – applies to primary anisotropy and reionization induced polarization Needed for polarization: component of the radiation field where radiation seen by the election is modulated on 90 degrees angular scales: this is the property of quadrupole distribution m=0 m=1 m=2 Electron is in the middle of these quadrupoles; red and blue are radiation of different intensities

  5. Polarization of the CMB from density fluctuations potential well: Convergent/divergent velocity field is set up in the potential wells/peaks as the baryon-photon fluid oscillates. Then, these are projected on to the plane of the observer’s sky. Result: E-mode, curl-free pattern. electron electrons are bunching up in tangential direction Electrons neighboring will Thomson scatter photons: * tangentially scattered photons will be blueshifted; * radially scattered photons will be redshifted electrons getting dispersed in radial direction electron sees l=2, m=0 spherical harmonic

  6. Fluid oscillations in a potential well Maximum fluid rarefication Maximum velocity – maximum contribution to the Doppler term Maximum fluid compression Largest amplitude polarization will be seen on scales that correspond to max. fluid velocity, i.e. at 90deg from max. fluid compression. In the power spectrum, polarization peaks will be between the temperature fluctuation peaks. Graphic – Wayne Hu

  7. Polarization of the CMB from gravitational waves electron sees l=2, m=2 spherical harmonic John Kovac Thesis Result: E-mode and B-mode patterns.

  8. Two modes of polarization electron sees radiation pattern of l=2 m=2 due to tensor (GW) perturbations electron sees radiation pattern of l=2 m=0 due to scalar (density) perturbations what we see on the sky tensor (i.e. gravity waves) perturbations produce E-modes and B-modes, depending on how the quadrupole is oriented with respect to the observer scalar (i.e. density) perturbations produce E-modes only

  9. Planck 2015 results cross-correlation of the temperature and E-mode polarization signal auto-correlation of the E-mode polarization signal (troughs correspond to peaks in the temperature power spectrum)

  10. Polarization fluctuations – Epoch of Reionization At z ~ 10-15, first stars and quasars formed, releasing UV ionizing radiation in to the Inter Cluster Medium  EoR Newly freed electrons saw the quadrupole of the CMB radiation field, and emitted polarized radiation. The linear scale is that of Hubble horizonat the time of reionization. Because this happened recently, we see the corresponding signal at large angular scales, or small l. Polarization from the reionization epoch at z~10 (amplitude depends on optical depth) Primary CMB polarization, z~1000

  11. Temp, EE polarization, lensing, and BB polarization contributions to the CMB power spectrum EE auto-correlation BB auto-correlation

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