PolarizationIntro < Main

---+++ Polarization of the CMB

Introduction

Since around 1927, the dominating theory of the evolution of the universe has been what is affectionately called the Big Bang theory. I suspect the reader is already familiar with it, and if not, please refer to our good friends at Wikipedia.

While there is considerable experimental evidence for expansion of the universe, other details remain less well-proven. Probably the best evidence for the Big Bang theory so far has been the discovery and measurement of the Cosmic Microwave Background (CMB) radiation. It suggests, due to its uniformity, that every point was once in thermal contact, as well as a wealth of data about the early universe that has yet to be properly measured.

It has been proposed that there was a period of time in which the universe expanded at speeds greater than the speed of light, called inflation. Theoretically, inflation explains why space is Euclidean, a possible cause for the minute fluctuations on the CMB and why we have not seen magnetic monopoles. While extremely useful in the explanation of these observations, inflation has not been directly tested against competing theories. One key prediction of inflation theory is that it will leave a polarization pattern on the CMB, where we can detect it.

Gravity Waves

Gravity waves are ripples in spacetime that propagate at the speed of light. Basically, the Heisenberg uncertainty principle ensures that there will be quantum fluctuations, and these could lead to gravitational waves with wavelengths comparable to the size of the observable Universe.

Furthermore, the square of the amplitude of these waves is the density during inflation given in Planck units, thus measuring the gravitational wave power spectrum would provide direct measurement of the cosmic density during inflation. This would demonstrate something like inflation happened, and would provide information about physics of much higher energy than that accessible in a lab.

While there are considerable complexities in the prediction of the power spectrum of primordial gravitational waves, it is sufficient to say that it can be fit by a power law (that is a line on a log, log plot) of power versus frequency with slope n. There is some debate over what value n will take, though many theories predict n of around 0.96, implying slightly more large-scale variations than small-scale.

Theory of CMB polarization

To completely characterize the CMB one has to specify three numbers for every point in the sky. One to give the overall intensity of the radiation (or, equivalently the temperature of the blackbody spectrum) and two to describe the polarization properties. Two numbers are needed, one to describe the degree of polarization and one to describe the angle from a specified coordinate on the sky.

If circular polarization were present a fourth parameter would be needed, however, the CMB polarization is believed to arise only from Compton scattering, a mechanism that cannot generate circular polarization.

For the cosmic background radiation maps of the polarization field can be made. These resemble vector fields except that the polarization does not have one specified direction (meaning the "vectors" do not have arrows). These maps can be decomposed into two modes, the E modes (analogs of the gradient field) and the B modes (analogs of the curl component). Note that the E and B components are undefined at a single point, as they describe the the greater behavoir of the field.

In the non-relatavistic limit, photons can be treated as oscillating magnetic and electric fields and their scattering off of electrons is called Thomson scattering (a special case of Compton scattering). Polarization of the produced radiation occurs when the incident radiation field is anisotropic. Thus, in the case of the CMB, the incident radiation field should have contained anisotropies created by the random background of gravitational waves, as well as the anisotropies created by density perturbations, which lead to the stuctures we see today.

These two mechanisms of polarization can be separated as the spatial pattern of the anisotropies created by gravitational waves lacks reflection symmetry and thus provides the B component. Additionally, gravitational lensing can act as a source of B mode polarization patterns as the E mode CMB radiation behind gets bent into apparent B modes; however, it is possible to seperate this effect out as it is on much smaller scales than the primordial effect.

-- KevinMacDermid - 15 Jan 2007

This topic: Main > WebHome > EBEX > PolarizationIntro Topic revision: r1 - 2007-01-15 - KevinMacDermid