Weak Gravitational Lensing

This chapter reviews the data mining methods recently developed to solve standard data problems in weak gravitational lensing. We detail the different steps of the weak lensing data analysis along with the different techniques dedicated to these applications. An overview of the different techniques currently used will be given along with future prospects.

[1]  Stephen F. Gull,et al.  Developments in Maximum Entropy Data Analysis , 1989 .

[2]  Stéphane Mallat,et al.  A Theory for Multiresolution Signal Decomposition: The Wavelet Representation , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[3]  N. Kaiser,et al.  Mapping the dark matter with weak gravitational lensing , 1993 .

[4]  Cluster lens reconstruction using only observed local data -- an improved finite-field inversion technique , 1994, astro-ph/9503096.

[5]  Nonlinear cluster lens reconstruction , 1994, astro-ph/9408092.

[6]  P. Schneider Detection of (dark) matter concentrations via weak gravitational lensing , 1996, astro-ph/9601039.

[7]  Jean-Luc Starck,et al.  Deconvolution of astronomical images using the multiscale maximum entropy method , 1996 .

[8]  G. A. Luppino,et al.  Detection of Weak Lensing by a Cluster of Galaxies at z = 0.83 , 1996, astro-ph/9601194.

[9]  J. Frieman,et al.  Nonlinear Evolution of the Bispectrum of Cosmological Perturbations , 1997, astro-ph/9704075.

[10]  Entropy-regularized Maximum-Likelihood cluster mass reconstruction , 1998, astro-ph/9803038.

[11]  H. Hoekstra,et al.  Weak Lensing Analysis of Cl 1358+62 Using Hubble Space Telescope Observations , 1998 .

[12]  A. Lasenby,et al.  A maximum‐entropy method for reconstructing the projected mass distribution of gravitational lenses , 1998, astro-ph/9802159.

[13]  Peter Schneider,et al.  A NEW MEASURE FOR COSMIC SHEAR , 1998 .

[14]  U. Seljak Weak Lensing Reconstruction and Power Spectrum Estimation: Minimum Variance Methods , 1997, astro-ph/9711124.

[15]  Wayne Hu,et al.  � 1999. The American Astronomical Society. All rights reserved. Printed in U.S.A. POWER SPECTRUM TOMOGRAPHY WITH WEAK LENSING , 1999 .

[16]  E. Candès,et al.  Ridgelets: a key to higher-dimensional intermittency? , 1999, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[17]  Y. Mellier Probing the Universe with Weak Lensing , 1998, astro-ph/9812172.

[18]  B. Jain,et al.  Statistics of Dark Matter Halos from Gravitational Lensing , 1999, The Astrophysical journal.

[19]  Gerard A. Luppino,et al.  Large scale cosmic shear measurements , 2000 .

[20]  Chung-Pei Ma,et al.  What Does It Take to Stabilize Gravitational Clustering? , 2000, astro-ph/0005233.

[21]  Chung-Pei Ma,et al.  Deriving the Nonlinear Cosmological Power Spectrum and Bispectrum from Analytic Dark Matter Halo Profiles and Mass Functions , 2000, astro-ph/0003343.

[22]  A. Cooray,et al.  Weak Gravitational Lensing Bispectrum , 2000, astro-ph/0004151.

[23]  Cosmic shear analysis in 50 uncorrelated VLT fields. Implications for $\Omega_0$, $\sigma_8$ , 2000, astro-ph/0011251.

[24]  Xiaoming Huo,et al.  Uncertainty principles and ideal atomic decomposition , 2001, IEEE Trans. Inf. Theory.

[25]  S. Gull,et al.  Maximum-entropy weak lens reconstruction: Improved methods and application to data , 2001, astro-ph/0112396.

[26]  M. Bartelmann,et al.  Weak gravitational lensing , 2016, Scholarpedia.

[27]  L. Wasserman,et al.  Fast Algorithms and Efficient Statistics: N-Point Correlation Functions , 2000, astro-ph/0012333.

[28]  Alexander S. Szalay,et al.  Fast Cosmic Microwave Background Analyses via Correlation Functions , 2001 .

[29]  Yannick Mellier,et al.  Cosmic shear analysis in 50 uncorrelated VLT fields. Implications for ? 0 , ? 8 , 2001 .

[30]  H. Couchman,et al.  A fitting formula for the non‐linear evolution of the bispectrum , 2000, astro-ph/0009427.

[31]  G. M. Bernstein,et al.  Shapes and Shears, Stars and Smears: Optimal Measurements for Weak Lensing , 2001 .

[32]  Imaging the 3-D cosmological mass distribution with weak gravitational lensing , 2001, astro-ph/0111605.

[33]  Peter Schneider,et al.  Suppressing the contribution of intrinsic galaxy alignments to the shear two-point correlation function , 2002, astro-ph/0208256.

[34]  Peter Schneider,et al.  Separating cosmic shear from intrinsic galaxy alignments: Correlation function tomography , 2002 .

[35]  Jean-Paul Kneib,et al.  BAYESIAN GALAXY SHAPE ESTIMATION , 2002 .

[36]  Detection of non-Gaussian signatures in the VIRMOS-DESCART lensing survey , 2002, astro-ph/0201032.

[37]  C. Keeton,et al.  Three-dimensional mapping of dark matter , 2002, astro-ph/0205412.

[38]  Y. Mellier,et al.  Astronomy & Astrophysics manuscript no. (will be inserted by hand later) Likelihood Analysis of Cosmic Shear on Simulated and VIRMOS-DESCART Data ⋆ , 2002 .

[39]  H. Hoekstra,et al.  Constraints on Ωm and σ8 from Weak Lensing in Red-Sequence Cluster Survey Fields , 2002 .

[40]  Constraints on Omega_m and sigma_8 from weak lensing in RCS fields , 2002, astro-ph/0204295.

[41]  Ue-Li Pen,et al.  Fast n-point correlation functions and three-point lensing application , 2003, ArXiv.

[42]  G. Bernstein,et al.  The skewness of the aperture mass statistic , 2003 .

[43]  E. Candès,et al.  Astronomical image representation by the curvelet transform , 2003, Astronomy & Astrophysics.

[44]  3D weak lensing , 2003, astro-ph/0304151.

[45]  New Dimensions in Cosmic Lensing , 2003, astro-ph/0306239.

[46]  Catherine Heymans,et al.  Weak gravitational lensing: reducing the contamination by intrinsic alignments , 2002, astro-ph/0208220.

[47]  A. Réfrégier Weak Gravitational Lensing by Large-Scale Structure , 2003, astro-ph/0307212.

[48]  The three-point correlation function of cosmic shear: I. The natural components , 2002, astro-ph/0207454.

[49]  Mapping the 3D dark matter potential with weak shear , 2002, astro-ph/0212266.

[50]  M. White,et al.  Simulating Weak Lensing by Large-Scale Structure , 2003, astro-ph/0303555.

[51]  Masahiro Takada,et al.  Three-point correlations in weak lensing surveys: Model predictions and applications , 2003, astro-ph/0304034.

[52]  Edinburgh,et al.  Evolution of the dark matter distribution with three-dimensional weak lensing , 2004, astro-ph/0403384.

[53]  Martin White,et al.  Tomography of Lensing Cross-Power Spectra , 2003, astro-ph/0311104.

[54]  Mapping the 3D dark matter with weak lensing in COMBO-17 , 2004, astro-ph/0402095.

[55]  R. Massey,et al.  Polar Shapelets , 2004, astro-ph/0408445.

[56]  Naoki Yoshida,et al.  Searching for massive clusters in weak lensing surveys , 2003, astro-ph/0310607.

[57]  Dipak Munshi,et al.  Cosmology with weak lensing surveys. , 2005, Philosophical transactions. Series A, Mathematical, physical, and engineering sciences.

[58]  The three-point correlation function of cosmic shear II. Relation to the bispectrum of the projected mass density and generalized third-order aperture measures , 2003, astro-ph/0308328.

[59]  Roger Y. Tsien,et al.  Insulin disrupts β-adrenergic signalling to protein kinase A in adipocytes , 2005, Nature.

[60]  D. Donoho,et al.  Simultaneous cartoon and texture image inpainting using morphological component analysis (MCA) , 2005 .

[61]  R. Massey,et al.  An enlarged cosmic shear survey with the William Herschel Telescope , 2004, astro-ph/0404195.

[62]  P. Fosalba,et al.  Cosmological Three-Point Function: Testing the Halo Model against Simulations , 2005, astro-ph/0504305.

[63]  Shears from shapelets , 2005, astro-ph/0601011.

[64]  Adam Amara,et al.  Optimal Surveys for Weak Lensing Tomography , 2006, astro-ph/0610127.

[65]  Wendy L. Freedman,et al.  Report of the Dark Energy Task Force , 2006, astro-ph/0609591.

[66]  Laurent Demanet,et al.  Fast Discrete Curvelet Transforms , 2006, Multiscale Model. Simul..

[67]  I. Tereno,et al.  Cosmic shear analysis with CFHTLS deep data , 2005, astro-ph/0511090.

[68]  Y. Mellier,et al.  First Cosmic Shear Results from the Canada-France-Hawaii Telescope Wide Synoptic Legacy Survey , 2006 .

[69]  H. Hoekstra,et al.  The Shear Testing Programme – I. Weak lensing analysis of simulated ground-based observations , 2005, astro-ph/0506112.

[70]  Jean-Luc Starck,et al.  Weak lensing mass reconstruction using wavelets , 2005, astro-ph/0503373.

[71]  H. Hoekstra,et al.  Very weak lensing in the CFHTLS Wide: Cosmology from cosmic shear in the linear regime , 2007, 0712.0884.

[72]  Y. Mellier,et al.  COSMOS: Three-dimensional Weak Lensing and the Growth of Structure , 2007, astro-ph/0701480.

[73]  R. Ellis,et al.  The Shear TEsting Programme 2: Factors affecting high precision weak lensing analyses , 2006, astro-ph/0608643.

[74]  R. Ellis,et al.  Dark matter maps reveal cosmic scaffolding , 2007, Nature.

[75]  Yannick Mellier,et al.  Cosmological constraints from the 100-deg2 weak-lensing survey , 2007 .

[76]  Sarah Bridle,et al.  Dark energy constraints from cosmic shear power spectra: impact of intrinsic alignments on photometric redshift requirements , 2007, 0705.0166.

[77]  T. Kitching,et al.  Bayesian galaxy shape measurement for weak lensing surveys – I. Methodology and a fast-fitting algorithm , 2007, 0708.2340.

[78]  The ring statistics - how to separate E- and B-modes of cosmic shear correlation functions on a finite interval , 2006, astro-ph/0605084.

[79]  J. Fadili,et al.  FAst STatistics for weak Lensing (FASTLens): fast method for weak lensing statistics and map making , 2008, 0804.4068.

[80]  Bayesian Galaxy Shape Measurement for Weak Lensing Surveys -II. Application to Simulations , 2008, 0802.1528.

[81]  P. Schneider,et al.  The removal of shear-ellipticity correlations from the cosmic shear signal via nulling techniques , 2008 .

[82]  P. Schneider,et al.  The removal of shear-ellipticity correlations from the cosmic shear signal , 2008, 0905.0393.

[83]  John Shawe-Taylor,et al.  HANDBOOK FOR THE GREAT08 CHALLENGE: AN IMAGE ANALYSIS COMPETITION FOR COSMOLOGICAL LENSING , 2008, 0802.1214.

[84]  Gary M. Bernstein,et al.  COMPREHENSIVE TWO-POINT ANALYSES OF WEAK GRAVITATIONAL LENSING SURVEYS , 2008, 0808.3400.

[85]  Simon Prunet,et al.  Full-sky weak-lensing simulation with 70 billion particles , 2008, 0807.3651.

[86]  Andy N. Taylor,et al.  Unfolding the matter distribution using three-dimensional weak gravitational lensing , 2009, 0907.0016.

[87]  Jean-Luc Starck,et al.  Cosmological model discrimination with weak lensing , 2009 .

[88]  Yannick Mellier,et al.  Evidence of the accelerated expansion of the Universe from weak lensing tomography with COSMOS , 2009, 0911.0053.

[89]  A. Amara,et al.  OPTIMAL CAPTURE OF NON-GAUSSIANITY IN WEAK-LENSING SURVEYS: POWER SPECTRUM, BISPECTRUM, AND HALO COUNTS , 2009, 0909.0529.

[90]  Argelander-Institut fur Astronomie,et al.  Simultaneous measurement of cosmology and intrinsic alignments using joint cosmic shear and galaxy number density correlations , 2009, 0911.2454.

[91]  David Spergel,et al.  Shear power spectrum reconstruction using the pseudo-spectrum method , 2010, 1004.3542.

[92]  J. P. Dietrich,et al.  Cosmology with the shear-peak statistics , 2009, 0906.3512.

[93]  Morgan May,et al.  Probing cosmology with weak lensing peak counts , 2009, 0907.0486.

[94]  Andrew Connolly,et al.  THREE-DIMENSIONAL RECONSTRUCTION OF THE DENSITY FIELD: AN SVD APPROACH TO WEAK-LENSING TOMOGRAPHY , 2010, 1008.2396.

[95]  P. Schneider,et al.  COSEBIs: Extracting the full E-/B-mode information from cosmic shear correlation functions , 2010, 1002.2136.