# On Minkowski Functionals of CMB polarization

## TL;DR

This paper investigates the use of Minkowski Functionals of Stokes parameters Q and U in CMB polarization data, revealing their invariance properties, differences from E modes in non-Gaussianity detection, and sensitivity to the tensor-to-scalar ratio.

## Contribution

It introduces the analysis of Minkowski Functionals of Q and U parameters for CMB polarization, highlighting their invariance under certain conditions and their potential in non-Gaussianity studies.

## Key findings

- MFs of Q,U are invariant under local rotations on the full sky.
- Non-Gaussian deviations in Q,U are an order of magnitude lower than in E modes.
- MF amplitudes decrease with increasing tensor-to-scalar ratio r.

## Abstract

CMB polarization data is usually analyzed using $E$ and $B$ modes because they are scalars quantities under rotations along the lines of sight and have distinct physical origins. We explore the possibility of using the Stokes parameters $Q$ and $U$ for complementary analysis and consistency checks in the context of searches for non-Gaussianity. We show that the Minkowski Functionals (MFs) of $Q,U$ are invariant under local rotations along the lines of sight even though $Q,U$ are spin-2 variables, for full sky analysis. The invariance does not hold for incomplete sky. For local type primordial non-Gaussianity, when we compare the non-Gaussian deviations of MFs for $Q,U$ to what is obtained for $E$ mode or temperature fluctuations, we find that the amplitude is about an order of magnitude lower and the shapes of the deviations are different. This finding can be useful in distinguishing local type non-Gaussianity from other origins of non-Gaussianity in the observed data. Lastly, we analyze the sensitivity of the amplitudes of the MFs for $Q$, $U$ and the number density of singularities of the total polarization intensity to the tensor-to-scalar ratio, $r$, and find that all of them decrease as $r$ increases.