CMB Polarization Jack Replinger Observational Cosmology Lab Professor Peter Timbie University of Wisconsin-Madison

CMB Basics The early universe was hot, dense and opaque Radiation was constantly absorbed and emitted by the early charged particles (electrons and protons) The universe cooled as it expanded, and became transparent At T=3000K, there were just enough high energy (high frequency) photons to ionize the particles As the temperature continued to drop, neutral hydrogen atoms formed, the photons could travel without interaction This occurred virtually simultaneously throughout the universe, these photons that reach observers today compose the CMB This occurred at 3000K due to the 1100 fold expansion of the universe these photons have been red-shifted such that they are detected as a blackbody with a temperature of 2.73K graph courtesy of http://athene.as.arizona.edu/~lclose/teaching/a202/CMB_blackbody.gif

CMB Temperature Fluctuations largest fluctuations ~200µK It is important to note the large scale smoothness and the small scale variations. The fact that photons from opposite sides of the universe of have nearly identical energies is surprising since according to the standard big bang model they were never in causal contact (could have exchanged photons / information). The size of the small scale variations can help us determine the geometry of the universe. Image from courtesy of www.aip.de/~gallery/cosmology/WMAP.jpg

Inflation Era: Pre-Inflation Decoupling Present ctdc*(1100) c(to-tdc) Θ ctdc cti causally connected region in very early universe These regions appear 1100 times larger on our sky because of the expansion of the universe from decoupling to the present. For photons to reach an observer on earth they will have traveled a distance of the speed of light times the time interval between decoupling and the present. We then can use simple geometry to determine the angle of these regions on our sky, which work out to about one degree for a flat universe (this angle would be larger for a close universe and smaller for and open universe). The small regions of the CMB that have the same temperature are formed by regions that could have communicated after inflation. These regions have a diameter ~ the speed of light times the time interval between inflation and decoupling. The size of the universe increased so fast and became so large, that our entire observable universe is made up of a region that was causally connected in the pre-inflation universe Era: Pre-Inflation Decoupling Present

Inflation Solves Three Cosmology Problems The Horizon Problem Inflation explains overall smoothness (how opposite sides of the universe could have been in causal contact, and thus be the nearly the same temperature). The Flatness Problem Inflation causes the universe to be nearly flat, which is consistent with Θ measured by the power spectrum (at left). The Structure Problem Inflation increases quantum mechanical fluctuations to macroscopic scales Temperature fluctuations from densities graph courtesy of http://kicp.uchicago.edu/~davemilr/ISW/wmap_p_spec.JPG The inflation model explains these problems but does it make predictions that we can test? (This will be explained by the end of this presentation!)

Image courtesy of http://www.physics.nyu.edu/matiasz/THESIS/tqu2.jpg CMB Polarization The temperature fluctuations have been measured by COBE and WMAP, but we can also study the polarization of the light CMB Polarization Can verify the WMAP density conclusions Provide additional information Image courtesy of http://www.physics.nyu.edu/matiasz/THESIS/tqu2.jpg

Polarization: Assumptions and Notation ABSORPTION AND EMISSION Light constantly being absorbed and emitted by charged particles, in all directions POLARIZATION The incident light is randomly polarized MODEL In our model four unpolarized (shown with same magnitude electric field perpendicular directions) photons interact with electron from four sides perpendicular to line of sight of observer direction to observer E-fields direction of propagation electron photon(s) high energy photon(s) low energy photon(s)

How to Scatter Light: Uniform Scattering Note that the polarization of the scattered photon is only effected by the strength of the E-fields perpendicular to its direction of propagation

How to Polarize Light: Quadrupole Scattering The incident photons could be high or low energy depending on the motion of the particles scattering them. A particle moving toward this central electron will emit a photon that is blue shifted (having a higher frequency and thus higher energy). A particle moving away from this central electron will emit a photon that is red shifted (having a lower frequency and thus lower energy). The scattered light is polarized in the direction of blue (higher energy) electric field

overdense visualization screen is surface of last scattering, therefore we are interested in the polarization of the light propagating out of the screen

underdense visualization Note that we have only considered gravitational effects, in reality when matter condenses to a certain point in an overdense region the matter will be forced outward due to thermal pressure. The motion of the charged particles will be the same as what was just shown for an underdense region so the polarization pattern will also be the same. These can be distinguished from polarization patterns due to a different mechanism as will be discussed. screen is surface of last scattering, therefore we are interested in the polarization of the light propagating out of the screen

Gravitational Waves Predicted by Inflation Example of orientation Inflation theory predicts that a large scale gravitational wave propagated across the surface of last scattering Example of orientation Propagating in z-direction Peaks compress space in x-direction Troughs compress space in y-direction As shown by color of the arrows, light received by a charged particle in the path of the gravitational wave will blue shifted in opposite directions (high energy), and red shifted in the perpendicular directions (low energy). Again we have a quadrupole, the light scattered out of the screen will be polarized in the direction that the oval is compressed.

Gravitational Wave Propagating Across Surface of Last Scattering peak trough Direction of Gravitational Wave: Into Screen

Gravitational Wave Propagating Across Surface of Last Scattering View of Cross Section Since an observer on earth is at the center of the spherical shell that makes up the surface of last scattering this is what we see on the sky The gravitational wave reaches the outer most (closest) matter of the shell first expanding them horizontally. Then strikes the matter on the red circle a half wave length later. And finally the innermost matter. Recall the polarization is in the direction the matter is compressed. Direction of Gravitational Wave: Into Screen

E-modes Polarizations due to densities (or thermal pressure) have gradient, are known as E-modes B-modes Polarizations due to gravitational waves are the only source of curl, are known as B-modes

MBI The Observational Cosmology Lab at UW-Madison Headed by Professor Peter Timbie Current project: Millimeterwave Bolometric Interferometer (MBI) Procedure: measure the polarization of the CMB Data: look for E-modes and B-modes Purpose: Better understand the origins of our universe.