Statistical Anisotropic Gaussian Simulations of the CMB Temperature Field

Abstract

Although theoretically expected to be Statistically Isotropic (SI), the observed Cosmic Microwave Background (CMB) temperature \& polarization field would exhibit SI violation due to various inevitable effects like weak lensing, Doppler boost and practical limitations of observations like non-circular beam, masking etc. However, presence of any SI violation beyond these effects may lead to a discovery of inherent cosmic SI violation in the CMB temperature \& polarization field. Recently, Planck presented strong evidence of SI violation as a dipolar power asymmetry of the CMB temperature field in two hemispheres. Statistical studies of SI violation effect require non-SI (nSI) Gaussian realizations of CMB temperature field. The nSI Gaussian temperature field leads to non-zero off-diagonal terms in the Spherical Harmonics (SH) space covariance matrix encoded in the coefficients of the Bipolar Spherical Harmonics (BipoSH) representation. We discuss an effective numerical algorithm, Code for Non-Isotropic Gaussian Sky (CoNIGS) to generate nSI realizations of Gaussian CMB temperature field of Planck like resolution with specific cases of SI violation. Realizations of nSI CMB temperature field are obtained for non-zero quadrupolar $(L=2)$ BipoSH measurements by WMAP, dipolar asymmetry (resembles $L=1$ BipoSH coefficients) with a \emph{scale dependent} modulation field as measured by Planck and for Doppler boosted CMB temperature field which also leads to $L=1$ BipoSH spectra. Our method, CoNIGS can incorporate any kind of SI violation and can produce nSI realizations efficiently.

18 pages, 14 figures. Matches the published version

References in corpus (5)

• Planck 2018 results. VII. Isotropy and Statistics of the CMB
• Asymmetric Beams and CMB Statistical Anisotropy
• A Large Sky Simulation of the Gravitational Lensing of the Cosmic Microwave Background
• Measuring Statistical Isotropy of CMB Anisotropy
• Simulating weak lensing on CMB maps

Cited by in corpus (11)

• Cosmology Intertwined: A Review of the Particle Physics, Astrophysics, and Cosmology Associated with the Cosmological Tensions and Anomalies
• Bayesian estimation of our local motion from the Planck-2018 CMB temperature map
• Direction dependence of cosmological parameters due to cosmic hemispherical asymmetry
• A novel approach to reconstructing signals of isotropy violation from a masked CMB sky
• Joint Bayesian analysis of large angular scale CMB temperature anomalies
• Cosmic topology. Part IIa. Eigenmodes, correlation matrices, and detectability of orientable Euclidean manifolds
• Orthogonal BipoSH measures : Scrutinizing sources of isotropy violation
• Bayesian inference on the sphere beyond statistical isotropy
• Estimating SI violation in CMB due to non-circular beam and complex scan in minutes
• Cosmic topology. Part IVa. Classification of manifolds using machine learning: a case study with small toroidal universes
• SIToolBox : A package for Bayesian estimation of the isotropy violation in the CMB sky