Weak Gravitational Lensing and Its Cosmological Applications

Weak gravitational lensing is a unique probe of the dark side of the universe: It provides a direct way to map the distribution of dark matter around galaxies and clusters of galaxies as well as on cosmological scales. Furthermore, the measurement of the weak lensing–induced distortions of the shapes of distant galaxies is a potentially powerful probe of dark energy. In this review we discuss how this challenging measurement is made and interpreted. We describe the various systematic effects that can hamper progress and how they may be overcome. We review some of the recent results in weak lensing by galaxies, galaxy clusters, and cosmic shear and discuss the prospects for dark energy measurements from planned surveys.

[1]  S. Refsdal.  On the possibility of determining Hubble's parameter and the masses of galaxies from the gravitational lens effect , 1964 .

[2]  M. Milgrom.  A modification of the newtonian dynamics as a possible alternative to the hidden mass hypothesis , 1983 .

[3]  John Dubinski,et al.  The structure of cold dark matter halos , 1991 .

[4]  The distortion of distant galaxy images by large-scale structure , 1991 .

[5]  Nick Kaiser,et al.  Weak gravitational lensing of distant galaxies , 1992 .

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

[7]  OBSERVATIONAL AND THEORETICAL CONSTRAINTS ON SINGULAR DARK MATTER HALOS , 1994, astro-ph/9402004.

[8]  W. Kells,et al.  A search for weak distortion of distant galaxy images by large-scale structure , 1994 .

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

[10]  B. Moore.  Evidence against dissipation-less dark matter from observations of galaxy haloes , 1994, Nature.

[11]  Mapping cluster mass distributions via gravitational lensing of background galaxies , 1994, astro-ph/9406052.

[12]  MEASURING GALAXY MASSES USING GALAXY-GALAXY GRAVITATIONAL LENSING , 1995, astro-ph/9503073.

[13]  T. Broadhurst,et al.  A Method for Weak Lensing Observations , 1994, astro-ph/9411005.

[14]  N. Kaiser,et al.  Unbiased Cluster Lens Reconstruction , 1995, astro-ph/9512094.

[15]  S. White,et al.  The Structure of cold dark matter halos , 1995, astro-ph/9508025.

[16]  F. Bernardeau,et al.  Weak lensing statistics as a probe of Omega and power spectrum , 1996 .

[17]  Uros Seljak,et al.  Cosmological Model Predictions for Weak Lensing: Linear and Nonlinear Regimes , 1996, astro-ph/9611077.

[18]  STEPS TOWARDS NONLINEAR CLUSTER INVERSION THROUGH GRAVITATIONAL DISTORTIONS. III. INCLUDING A REDSHIFT DISTRIBUTION OF THE SOURCES , 1996, astro-ph/9601079.

[19]  R. Blandford,et al.  Weak Gravitational Lensing by Galaxies , 1996 .

[20]  S. White,et al.  A Universal Density Profile from Hierarchical Clustering , 1996, astro-ph/9611107.

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

[22]  H. Dahle,et al.  Galaxy-Galaxy Lensing in the Hubble Deep Field: The Halo Tully-Fisher Relation at Intermediate Redshift , 1997, astro-ph/9711341.

[23]  A new finite-field mass reconstruction algorithm , 1998, astro-ph/9802051.

[24]  S. McGaugh,et al.  Testing the Dark Matter Hypothesis with Low Surface Brightness Galaxies and Other Evidence , 1998, astro-ph/9801123.

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

[26]  Max Tegmark,et al.  Weak Lensing: Prospects for Measuring Cosmological Parameters , 1998, astro-ph/9811168.

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

[28]  Weak Gravitational Lensing and Cluster Mass Estimates , 1999, astro-ph/9904156.

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

[30]  George Lake,et al.  Cold collapse and the core catastrophe , 1999 .

[31]  Uros Seljak,et al.  Ray-tracing Simulations of Weak Lensing by Large-Scale Structure , 1999, astro-ph/9901191.

[32]  Cambridge,et al.  Detection of weak gravitational lensing by large-scale structure , 2000 .

[33]  R. Croft,et al.  Weak-Lensing Surveys and the Intrinsic Correlation of Galaxy Ellipticities , 2000, astro-ph/0005384.

[34]  Ue-Li Pen,et al.  Spin-induced Galaxy Alignments and Their Implications for Weak-Lensing Measurements , 2000, astro-ph/0009052.

[35]  Spergel,et al.  Observational evidence for self-interacting cold dark matter , 1999, Physical review letters.

[36]  David M. Wittman,et al.  Detection of weak gravitational lensing distortions of distant galaxies by cosmic dark matter at large scales , 2000, Nature.

[37]  P. Schneider,et al.  Detection of correlated galaxy ellipticities on CFHT data: first evidence for gravitational lensing by large-scale structures , 2000, astro-ph/0002500.

[38]  Weak Lensing with Sloan Digital Sky Survey Commissioning Data: The Galaxy-Mass Correlation Function to 1 [CLC][ITAL]h[/ITAL][/CLC][TSUP]−1[/TSUP] M[CLC]pc[/CLC] , 2000 .

[39]  Wayne Hu.  � 2001. The American Astronomical Society. All rights reserved. Printed in U.S.A. MAPPING THE DARK MATTER THROUGH THE COSMIC MICROWAVE BACKGROUND DAMPING TAIL , 2001 .

[40]  H. Hoekstra.  Astronomy and Astrophysics the Effect of Distant Large Scale Structure on Weak Lensing Mass Estimates , 2022 .

[41]  M. Meneghetti,et al.  Giant cluster arcs as a constraint on the scattering cross-section of dark matter , 2000, astro-ph/0011405.

[42]  M. White,et al.  The Effect of the Cosmic Web on Cluster Weak Lensing Mass Estimates , 2000, astro-ph/0005442.

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

[44]  Gravitational lensing in modified Newtonian dynamics , 2001, astro-ph/0106100.

[45]  S. Borgani,et al.  THE EVOLUTION OF X-RAY CLUSTERS OF GALAXIES , 2002, astro-ph/0209035.

[46]  M. White,et al.  Future Galaxy Cluster Surveys: The Effect of Theory Uncertainty on Constraining Cosmological Parameters , 2002, astro-ph/0204273.

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

[48]  SEARCHING FOR DARK MATTER HALOS IN THE SUPRIME-CAM 2 SQUARE DEGREE FIELD , 2002, astro-ph/0210441.

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

[50]  Jeremiah P. Ostriker,et al.  The Cluster Mass Function from Early Sloan Digital Sky Survey Data: Cosmological Implications , 2002, astro-ph/0205490.

[51]  P. Schneider,et al.  B-modes in cosmic shear from source redshift clustering , 2002 .

[52]  M. White,et al.  Completeness in Weak-Lensing Searches for Clusters , 2001, astro-ph/0111490.

[53]  S. Maddox,et al.  Weak Gravitational Lensing by a Sample of X-Ray Luminous Clusters of Galaxies. I. The Data Set , 2002 .

[54]  T. Treu,et al.  The Internal Structure and Formation of Early-Type Galaxies: The Gravitational Lens System MG 2016+112 at z = 1.004 , 2002, astro-ph/0202342.

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

[56]  A. Réfrégier.  Shapelets: I. a method for image analysis , 2001, astro-ph/0105178.

[57]  Masahiro Takada,et al.  Cosmological parameters from lensing power spectrum and bispectrum tomography , 2003, astro-ph/0310125.

[58]  Edinburgh,et al.  Joint cosmic shear measurements with the Keck and William Herschel Telescopes , 2002, astro-ph/0203134.

[59]  A. Connolly,et al.  The Galaxy-Mass Correlation Function Measured from Weak Lensing in the Sloan Digital Sky Survey , 2003, astro-ph/0312036.

[60]  Submitted to ApJ Preprint typeset using L ATEX style emulateapj v. 11/12/01 THE HUBBLE CONSTANT FROM THE GRAVITATIONAL LENS B1608+656 1 , 2003 .

[61]  3D weak lensing , 2003, astro-ph/0304151.

[62]  Alexandre Refregier,et al.  Shapelets — II. A method for weak lensing measurements , 2003 .

[63]  Bhuvnesh Jain,et al.  Cross-correlation tomography: measuring dark energy evolution with weak lensing. , 2003, Physical review letters.

[64]  U. Washington,et al.  The inner structure of ΛCDM haloes – III. Universality and asymptotic slopes , 2003, astro-ph/0311231.

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

[66]  The Dark Matter Distribution in the Central Regions of Galaxy Clusters , 2003, astro-ph/0309465.

[67]  Simulations of weak gravitational lensing , 2003, astro-ph/0312133.

[68]  Henk Hoekstra.  The effect of imperfect models of point spread function anisotropy on cosmic shear measurements , 2004 .

[69]  Wayne Hu,et al.  Joint galaxy - lensing observables and the dark energy , 2004 .

[70]  Do arcs require flat halo cusps , 2003, astro-ph/0312011.

[71]  G. M. Bernstein,et al.  Dark Energy Constraints from Weak-Lensing Cross-Correlation Cosmography , 2003, astro-ph/0309332.

[72]  Properties of Galaxy Dark Matter Halos from Weak Lensing , 2003, astro-ph/0306515.

[73]  T. Broadhurst,et al.  The Surprisingly Steep Mass Profile of A1689, from a Lensing Analysis of Subaru Images , 2004, astro-ph/0412192.

[74]  X-Ray Temperatures for the Extended Medium-Sensitivity Survey High-Redshift Cluster Sample: Constraints on Cosmology and the Dark Energy Equation of State , 2004, astro-ph/0404142.

[75]  Yong-Seon Song,et al.  Determination of cosmological parameters from cosmic shear data , 2004 .

[76]  Christopher M. Hirata,et al.  Intrinsic alignment-lensing interference as a contaminant of cosmic shear , 2004, astro-ph/0406275.

[77]  Uros Seljak,et al.  Gravitational lensing as a contaminant of the gravity wave signal in the CMB , 2004 .

[78]  D. Spergel,et al.  Shear-selected Cluster Cosmology: Tomography and Optimal Filtering , 2004, astro-ph/0404349.

[79]  J. Brinkmann,et al.  Galaxy halo masses and satellite fractions from galaxy–galaxy lensing in the Sloan Digital Sky Survey: stellar mass, luminosity, morphology and environment dependencies , 2005, astro-ph/0511164.

[80]  Detection of Cosmic Magnification with the Sloan Digital Sky Survey , 2005, astro-ph/0504510.

[81]  M. Zaldarriaga,et al.  Lensing Reconstruction Using Redshifted 21 Centimeter Fluctuations , 2005, astro-ph/0511547.

[82]  E. Deul,et al.  GaBoDS: The Garching-Bonn Deep Survey; IV. Methods for the Image reduction of multi-chip Cameras , 2005 .

[83]  Jun Zhang,et al.  Isolating Geometry in Weak-Lensing Measurements , 2003, astro-ph/0312348.

[84]  D. Bacon,et al.  Galaxy-Galaxy Flexion: Weak Lensing to Second Order , 2004, astro-ph/0406376.

[85]  SDSS galaxy bias from halo mass-bias relation and its cosmological implications , 2004, astro-ph/0406594.

[86]  Ellipticity of dark matter haloes with galaxy–galaxy weak lensing , 2005, astro-ph/0507108.

[87]  Dealing with systematics in cosmic shear studies: New results from the VIRMOS-Descart survey , 2004, astro-ph/0406468.

[88]  Mass Distributions of HST Galaxy Clusters from Gravitational Arcs , 2005, astro-ph/0511330.

[89]  Wayne Hu,et al.  Effects of Photometric Redshift Uncertainties on Weak-Lensing Tomography , 2005 .

[90]  A. Bolton,et al.  The Sloan Lens ACS Survey. III. The Structure and Formation of Early-Type Galaxies and Their Evolution since z ≈ 1 , 2006, astro-ph/0601628.

[91]  Edward J. Wollack,et al.  Wilkinson Microwave Anisotropy Probe (WMAP) Three Year Results: Implications for Cosmology , 2006, astro-ph/0603449.

[92]  L. Knox,et al.  Distance-redshift and growth-redshift relations as two windows on acceleration and gravitation: Dark energy or new gravity? , 2006 .

[93]  Constraint on the post-Newtonian parameter γ on galactic size scales , 2006, astro-ph/0607657.

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

[95]  Tucson,et al.  A Direct Empirical Proof of the Existence of Dark Matter , 2006, astro-ph/0608407.

[96]  Rachel Mandelbaum,et al.  Detection of large-scale intrinsic ellipticity—density correlation from the Sloan Digital Sky Survey and implications for weak lensing surveys , 2006 .

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

[98]  B. Garilli,et al.  Accurate photometric redshifts for the CFHT legacy survey calibrated using the VIMOS VLT deep survey , 2006, astro-ph/0603217.

[99]  On the proof of dark matter, the law of gravity, and the mass of neutrinos , 2006, astro-ph/0609125.

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

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

[102]  First Results on Shear-selected Clusters from the Deep Lens Survey: Optical Imaging, Spectroscopy, and X-Ray Follow-up , 2005, astro-ph/0507606.

[103]  T. Schrabback,et al.  GaBoDS: The Garching-Bonn Deep Survey: VI. Cosmic shear analysis , 2006, astro-ph/0606571.

[104]  Gary Bernstein,et al.  Dark Energy Constraints from the CTIO Lensing Survey , 2006 .

[105]  Yannick Mellier,et al.  ESA-ESO Working Group on "Fundamental Cosmology" , 2006 .

[106]  Density profiles of galaxy groups and clusters from SDSS galaxy–galaxy weak lensing , 2006, astro-ph/0605476.

[107]  G. Bernstein,et al.  Shear Recovery Accuracy in Weak-Lensing Analysis with the Elliptical Gauss-Laguerre Method , 2006, astro-ph/0607062.

[108]  A. Heavens,et al.  Potential sources of contamination to weak lensing measurements: constraints from N-body simulations , 2006, astro-ph/0604001.

[109]  Precision measurement of cosmic magnification from 21 cm emitting galaxies , 2005, astro-ph/0504551.

[110]  G. Bernstein,et al.  PSF anisotropy and systematic errors in weak lensing surveys , 2005, astro-ph/0510231.

[111]  Masahiro Takada,et al.  Systematic errors in future weak-lensing surveys: requirements and prospects for self-calibration , 2006 .

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

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

[114]  The effects of ellipticity and substructure on estimates of cluster density profiles based on lensing and kinematics , 2005, astro-ph/0509323.

[115]  D. Nagai,et al.  Testing X-Ray Measurements of Galaxy Clusters with Cosmological Simulations , 2006, astro-ph/0609247.

[116]  R. Metcalf,et al.  High-resolution imaging of the cosmic mass distribution from gravitational lensing of pre-galactic H i , 2006, astro-ph/0611862.

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

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

[119]  R. Massey,et al.  A Subaru Weak-Lensing Survey. I. Cluster Candidates and Spectroscopic Verification , 2007, 0707.2249.

[120]  L. Verde,et al.  On model selection forecasting, Dark Energy and modified gravity , 2007 .

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

[122]  The observed concentration–mass relation for galaxy clusters , 2007, astro-ph/0703126.

[123]  H. Hoekstra.  A comparison of weak-lensing masses and X-ray properties of galaxy clusters , 2007, 0705.0358.

[124]  Y. Mellier,et al.  Cosmic variance of weak lensing surveys in the non‐Gaussian regime , 2006, astro-ph/0606648.

[125]  Henk Hoekstra,et al.  The Masses and Shapes of Dark Matter Halos from Galaxy-Galaxy Lensing in the CFHT Legacy Survey , 2007, 0707.1698.

[126]  R. Bouwens,et al.  Discovery of a Ringlike Dark Matter Structure in the Core of the Galaxy Cluster Cl 0024+17 , 2007, 0705.2171.

[127]  H. Hoekstra,et al.  A Dark Core in Abell 520 , 2007, 0706.3048.

[128]  Separating Dark Physics from Physical Darkness: Minimalist Modified Gravity vs. Dark Energy , 2006, astro-ph/0608681.

[129]  G. Lewis,et al.  Dark Matter Power Spectra to 1% Accuracy Between Dynamical Dark Energy Cosmologies , 2007, 0704.0312.

[130]  Rachel Mandelbaum,et al.  Intrinsic galaxy alignments from the 2SLAQ and SDSS surveys: luminosity and redshift scalings and implications for weak lensing surveys , 2007 .

[131]  H. Hoekstra,et al.  Evidence for non-hydrostatic gas from the cluster X-ray to lensing mass ratio , 2007, 0710.4132.