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3D weak lensing with spin wavelets on the ball

Leistedt, B; McEwen, JD; Kitching, TD; Peiris, HV; (2015) 3D weak lensing with spin wavelets on the ball. Physical Review D , 92 , Article 123010. 10.1103/PhysRevD.92.123010. Green open access

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Abstract

We construct the spin flaglet transform, a wavelet transform to analyze spin signals in three dimensions. Spin flaglets can probe signal content localized simultaneously in space and frequency and, moreover, are separable so that their angular and radial properties can be controlled independently. They are particularly suited to analyzing cosmological observations such as the weak gravitational lensing of galaxies. Such observations have a unique 3D geometrical setting since they are natively made on the sky, have spin angular symmetries, and are extended in the radial direction by additional distance or redshift information. Flaglets are constructed in the harmonic space defined by the Fourier-Laguerre transform, previously defined for scalar functions and extended here to signals with spin symmetries. Thanks to various sampling theorems, both the Fourier-Laguerre and flaglet transforms are theoretically exact when applied to bandlimited signals. In other words, in numerical computations the only loss of information is due to the finite representation of floating point numbers. We develop a 3D framework relating the weak lensing power spectrum to covariances of flaglet coefficients. We suggest that the resulting novel flaglet weak lensing estimator offers a powerful alternative to common 2D and 3D approaches to accurately capture cosmological information. While standard weak lensing analyses focus on either real- or harmonic-space representations (i.e., correlation functions or Fourier-Bessel power spectra, respectively), a wavelet approach inherits the advantages of both techniques, where both complicated sky coverage and uncertainties associated with the physical modeling of small scales can be handled effectively. Our codes to compute the Fourier-Laguerre and flaglet transforms are made publicly available.

Type: Article
Title: 3D weak lensing with spin wavelets on the ball
Open access status: An open access version is available from UCL Discovery
DOI: 10.1103/PhysRevD.92.123010
Publisher version: http://dx.doi.org/10.1103/PhysRevD.92.123010
Language: English
Additional information: This version is the version of record [delete as appropriate]. For information on re-use, please refer to the publisher’s terms and conditions.
Keywords: Science & Technology, Physical Sciences, Astronomy & Astrophysics, Physics, Particles & Fields, Physics, DIRECTIONAL SPHERICAL WAVELETS, POWER SPECTRUM, NON-GAUSSIANITY, COSMIC SHEAR, DARK ENERGY, COSMOLOGICAL CONSTRAINTS, COVARIANCE-MATRIX, CFHTLENS, CMB, RECONSTRUCTION
UCL classification: UCL
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Physics and Astronomy
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Space and Climate Physics
URI: https://discovery.ucl.ac.uk/id/eprint/1511258
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