# Cosmic Microwave Background polarization

Usually when we study the CM8B we focus on the temperature anisotropies of it and we say that $\delta T/T \sim O(10^{-5})$

For the temperature anisotropies I know that the definition is $\delta T(\hat{n})=T(\hat{n})-T_0$ where $T_0$ is the average temperature.

I saw on the internet that there are maps of the CMB polarization ANISOTROPIES. I want to ask: how are those anisotropies defined and of what order are they.

• This uses the Stokes parameters $Q$ and $U$. Are you versed in those? – user154997 Oct 22 '17 at 21:51
• Yes, I know Q,U and V. – Saladino Oct 22 '17 at 22:24

The analysis of the CMBR polarisation uses the Stokes parameters. Only $Q$ and $U$ play any role: the reference value, by that I mean the equivalent of your $T_0$, is 0 here, i.e. a lack of polarisation. More precisely, $Q+iU$ and $Q-iU$ are expanded on the basis of spherical harmonics. I have the recollection there is a subtlety related to the transformation of $Q$ and $U$ under rotation. A classic paper introducing the analysis of the CMBR polarisation is [1], and I will refer you to it.
• I know this description(and the fact that $Q+iU$ is a 2 spin field). What I don't understand is why people talk about polarization anisotropies. I know that CMB (linear) polarization is due to Thompson scattering coming from the quadrupole part of the radiation field. So lets imagine that I have a particular direction of polarization for the scattered photon. What does it mean polarization anisotropy? – Saladino Oct 22 '17 at 23:03
• $Q$ and $U$ are functions of the direction of observation in the sky, i.e. the unit vector $\hat{n}$ in your question. The anisotropy is their variation as $\hat{n}$ varies. What else would you have had in mind? – user154997 Oct 22 '17 at 23:13
• Ok, so it makes sense to take a mean value and calculate two type of anisotropies $\delta U$ and $\delta Q$...Thanks. My last question is: $\delta U/U$ is of the same order as temperature anisotropies? – Saladino Oct 22 '17 at 23:35