Cosmic Microwave Background Polarization Analysis

Abstract

With polarization of the cosmic microwave background (CMB) now detected, and confirmed by several independent experiments, the next goal is to characterise accurately its statistical properties. In these lecture notes we review the physical motivation for pursuing CMB polarization, and the basic statistical properties of the polarization fields. We then discuss some of the key aspects of the analysis of CMB polarization data, focusing on the additional complications that arise compared to temperature data due to the tensor character of the polarization field.

Invariant random fields in vector bundles and application to cosmology

“…Let η ℓ0 j , ℓ ≥ 0, 1 ≤ j ≤ 3 and η ℓm j , ℓ ≥ 1, 1 ≤ m ≤ ℓ, 1 ≤ j ≤ 6 be independent standard normal random variables. Put This formalism is also used by Cabella and Kamionkowski (2005), Challinor (2004Challinor ( , 2009, Challinor and Peiris (2009) among others. An excellent survey of different types of spherical harmonics may be found in Thorne (1980).…”

“…We explain both the mathematical and physical sense of the Stokes parameters I, Q, U , and V . The material of this Subsection is based on Cabella and Kamionkowski (2005), Challinor (2004), Challinor (2009), Challinor and Peiris (2009), Durrer (2008), and Lin and Wandelt (2006).…”

“…This form of the reality condition is used byCabella and Kamionkowski (2005),Challinor (2004Challinor ( , 2009, Challinor and Peiris (2009), Durrer (2008), Kamionkowski et al (1997), Lin and Wandelt (2006), among others. Introduce the following notation: m + = max{m, 0} = (|m| + m)/2, m − = max{−m, 0} = (|m| − m)/2.…”

The Berry phase in inflationary cosmology

“…4.4), which can only be sorted out once r is measured conclusively. But B mode polarized states can be contaminated with cosmic strings, primordial magnetic field etc, thereby making it difficult to measure r conclusively (for a lucid discussion see [43]). So, cosmological Berry phase may have the potentiality to play some important role in inflationary cosmology, since it is related to r and V via Eqns.…”

Techniques for Compact Source Extraction in CMB Maps

“…We would also like to point out that many polarisation experiments are currently planned (or already operating) which will provide with a wealth of information about our universe [19]. Given the weakness of the cosmological signal in polarisation and the current lack of knowledge regarding the foreground emissions, a careful process of cleaning of the CMB polarisation maps is even more critical than for the intensity case.…”