On spin scale-discretised wavelets on the sphere for the analysis of CMB polarisation

A new spin wavelet transform on the sphere is proposed to analyse the polarisation of the cosmic microwave background (CMB), a spin $\pm 2$ signal observed on the celestial sphere. The scalar directional scale-discretised wavelet transform on the sphere is extended to analyse signals of arbitrary spin. The resulting spin scale-discretised wavelet transform probes the directional intensity of spin signals. A procedure is presented using this new spin wavelet transform to recover E- and B-mode signals from partial-sky observations of CMB polarisation.

[1]  Pierre Vandergheynst,et al.  S2LET: A code to perform fast wavelet analysis on the sphere , 2012, ArXiv.

[2]  P. Vielva,et al.  Detection of non-Gaussianity in the WMAP 1-year data using spherical wavelets , 2003 .

[3]  P. Baldi,et al.  Asymptotics for spherical needlets , 2006, math/0606599.

[4]  J. D. McEwen,et al.  A high-significance detection of non-Gaussianity in the Wilkinson Microwave Anisotropy Probe 1-yr data using directional spherical wavelets , 2004, astro-ph/0406604.

[5]  C. A. Oxborrow,et al.  Planck 2013 results. I. Overview of products and scientific results , 2013, 1502.01582.

[6]  M. P. Hobson,et al.  Cosmological Applications of a Wavelet Analysis on the Sphere , 2007, 0704.3158.

[7]  Matias Zaldarriaga,et al.  Cosmic Microwave Background Polarization as a Direct Test of Inflation , 1997, astro-ph/9705182.

[8]  O. Blanc,et al.  Exact reconstruction with directional wavelets on the sphere , 2007, 0712.3519.

[9]  Pierre Vandergheynst,et al.  Wavelets on the n-sphere and related manifolds , 1998 .

[10]  R. W. Ogburn,et al.  Detection of B-mode polarization at degree angular scales by BICEP2. , 2014, Physical review letters.

[11]  Gerard Kerkyacharian,et al.  Spin Needlets for Cosmic Microwave Background Polarization Data Analysis , 2008, 0811.2881.

[12]  Peter A. R. Ade,et al.  The Atacama Cosmology Telescope: CMB polarization at 200 < ℓ < 9000 , 2014, 1405.5524.

[13]  H. Peiris,et al.  First observational tests of eternal inflation. , 2010, Physical review letters.

[14]  Jean-Luc Starck,et al.  Wavelets, ridgelets and curvelets on the sphere , 2006 .

[15]  B Schulz,et al.  Detection of B-mode polarization in the cosmic microwave background with data from the South Pole Telescope. , 2013, Physical review letters.

[16]  G. W. Pratt,et al.  Planck 2013 results Special feature Planck 2013 results . XXV . Searches for cosmic strings and other topological defects , 2014 .

[17]  U. Seljak,et al.  An all sky analysis of polarization in the microwave background , 1996, astro-ph/9609170.

[18]  G. W. Pratt,et al.  Planck 2015 results - XVII. Constraints on primordial non-Gaussianity , 2014 .

[19]  J. D. McEwen,et al.  Probing dark energy with steerable wavelets through correlation of WMAP and NVSS local morphological measures , 2007, 0704.0626.

[20]  Matias Zaldarriaga.  Polarization of the microwave background in reionized models , 1997 .

[21]  P. Vielva,et al.  Steerable wavelet analysis of CMB structures alignment , 2006 .

[22]  J. Delabrouille,et al.  CMB power spectrum estimation using wavelets , 2008, 0807.1113.

[23]  P. Vielva,et al.  Detection of Non-Gaussianity in the Wilkinson Microwave Anisotropy Probe First-Year Data Using Spherical Wavelets , 2004 .

[24]  J.-L. Starck,et al.  Sparse component separation for accurate cosmic microwave background estimation , 2012, 1206.1773.

[25]  J. Starck,et al.  Polarized wavelets and curvelets on the sphere , 2009 .

[26]  Belgium,et al.  Correspondence principle between spherical and euclidean wavelets , 2005, astro-ph/0502486.

[27]  J. Aumont,et al.  Planck2018 results , 2013, Astronomy & Astrophysics.

[28]  Pierre Vandergheynst,et al.  On the computation of directional scale-discretized wavelet transforms on the sphere , 2013, Optics & Photonics - Optical Engineering + Applications.

[29]  Paolo Baldi,et al.  Spherical needlets for cosmic microwave background data analysis , 2008 .

[30]  Domenico Marinucci,et al.  Integrated Sachs-Wolfe effect from the cross correlation of WMAP 3 year and the NRAO VLA sky survey data: New results and constraints on dark energy , 2006 .

[31]  K. Gorski,et al.  HEALPix: A Framework for High-Resolution Discretization and Fast Analysis of Data Distributed on the Sphere , 2004, astro-ph/0409513.

[32]  H. Peiris,et al.  First Observational Tests of Eternal Inflation: Analysis Methods and WMAP 7-Year Results , 2010, 1012.3667.

[33]  Andrew H. Jaffe,et al.  MasQU: Finite Differences on Masked Irregular Stokes Q,U Grids , 2011, 1101.0520.

[34]  United Kingdom,et al.  Fast Directional Correlation on the Sphere with Steerable Filters , 2005, astro-ph/0508516.

[35]  Pencho Petrushev,et al.  Localized Tight Frames on Spheres , 2006, SIAM J. Math. Anal..

[36]  Jaiseung Kim,et al.  How to make a clean separation between CMB E and B modes with proper foreground masking , 2010, 1010.2636.

[37]  Anthony Challinor,et al.  Analysis of CMB polarization on an incomplete sky , 2001 .

[38]  J. D. McEwen,et al.  Non-Gaussianity detections in the Bianchi VIIh corrected WMAP one-year data made with directional spherical wavelets , 2005, astro-ph/0510349.

[39]  J. D. McEwen,et al.  A high-significance detection of non-Gaussianity in the WMAP 5-yr data using directional spherical wavelets , 2006, 0803.2157.

[40]  P. Baldi,et al.  Spherical Needlets for CMB Data Analysis , 2007, 0707.0844.

[41]  Matias Zaldarriaga,et al.  E/B decomposition of finite pixelized CMB maps , 2003 .