A comprehensive study of Modulation effects on CMB Polarization

Abstract

The Cosmic Microwave Background is characterized by temperature and linear polarization fields. Dipole modulation in the temperature field has been extensively studied in the context of hemispherical power asymmetry. In this article, we show that a dipole modulation, and in general, any kind of modulation isn't allowed in the $E$ and $B$ modes. This is the main result of this paper. This result explains why no evidence of modulation in $E$ mode has been found in the literature. On the contrary, the linear polarization fields $Q$ and $U$ have no such restrictions. We show that modulation under certain situations can be thought of as local $U(1)$ gauge transformations on the surface of a sphere. As far as the modulation function is concerned, we show that physical considerations enforce it to be (i) a spin $0$ field and (ii) a scalar under parity. As masking is a specific type of modulation, our study suggests that direct masking of $E$ mode isn't also possible. Masking in the $E$ map can only be applied through $Q$ and $U$ fields. This means that in principle, leaking of $E$ and $B$ mode powers into each other is unavoidable.

Matches with the (to be) published version in GERG

References in corpus (14)

• Planck 2018 results. VII. Isotropy and Statistics of the CMB
• Hemispherical power asymmetry in the three-year Wilkinson Microwave Anisotropy Probe sky maps
• Cosmic Microwave Background Statistics for a Direction-Dependent Primordial Power Spectrum
• Broken Isotropy from a Linear Modulation of the Primordial Perturbations
• Direction-Dependent CMB Power Spectrum and Statistical Anisotropy from Noncommutative Geometry
• Probing Cosmic Inflation with the LiteBIRD Cosmic Microwave Background Polarization Survey
• Expected dipole asymmetry in CMB polarization
• CMB circular and B-mode polarization from new interactions
• Probing statistical isotropy of cosmological radio sources using SKA
• Generation of circular polarization in CMB radiation via nonlinear photon-photon interaction
• Generation of Circular Polarization of CMB via Polarized Compton Scattering
• Exact joint likelihood of pseudo-$C_{\ell }$ estimates from correlated Gaussian cosmological fields
• A Pixel Space Method for Testing Dipole Modulation in the CMB Polarization
• Anisotropic power spectrum and the observed low-l power in PLANCK CMB data

Cited by in corpus (2)

• Hemispherical Power Asymmetry in intensity and polarization for Planck PR4 data
• A Pixel Space Method for Testing Dipole Modulation in the CMB Polarization