Cosmological Weak Lensing and the Dark Universe Andy

Cosmological Weak Lensing and the Dark Universe Andy Taylor Institute for Astronomy, School of Physics, Royal Observatory, Blackford Hill, Edinburgh, UK 9/16/2021 Heidelberg 1

Edinburgh Weak Lensing Group • • • Andy Taylor David Bacon (PPARC PDRF, AF from Oct) Meghan Gray (PPARC PDRF, now at Nottingham) Michael Brown (PPARC PDRF) Tom Kitching (Ph. D student) 9/16/2021 Heidelberg 2

3 -D Gravitational Lensing • • • An Introduction to Gravitational Lensing 2 -D Dark Matter Mapping & Statistics 3 -D Dark Matter Mapping & Statistics Dark Energy from 3 -D Gravitational Lensing The Future of Gravitational Lensing 9/16/2021 Heidelberg 3

3 -D Gravitational Lensing • • • An Introduction to Gravitational Lensing 2 -D Dark Matter Mapping & Statistics 3 -D Dark Matter Mapping & Statistics Dark Energy from 3 -D Gravitational Lensing The Future of Gravitational Lensing 9/16/2021 Heidelberg 4

The “Standard Model” of Cosmology • WMAP, SNIa, 2 d. FGRS, Sloan Digital Sky Survey: – – 70% Dark Energy 25% Dark Matter 5% Baryonic Matter Spatially flat • Four outstanding problems: – – Dark Matter Dark Energy Inflation Galaxy formation 9/16/2021 Heidelberg (VIRGO Consortium) 5

The “Standard Model” of Cosmology • WMAP, SNIa, 2 d. FGRS, Sloan Digital Sky Survey: – – 70% Dark Energy 25% Dark Matter 5% Baryonic Matter Spatially flat • Four outstanding problems: – – Dark Matter Dark Energy Inflation Galaxy formation 9/16/2021 Heidelberg (VIRGO Consortium) 6

Gravitational Lensing • HST deep field of a galaxy cluster gravitational lens. 9/16/2021 Heidelberg 7

Gravitational Lensing • HST deep field of a gravitational lens, galaxy cluster Cl 2244. 9/16/2021 Heidelberg 8

Gravitational Lensing • HST deep field of a galaxy cluster; gravitational lens, Abell 2218. 9/16/2021 Heidelberg 9

Gravitational Lensing • Simulation of a gravitational lens. 9/16/2021 Heidelberg 10 Courtesy E. van Kampen

Gravitational Lensing • A simple scattering experiment: Observer 9/16/2021 Galaxy cluster/lens Heidelberg Background source 11

Gravitational Lens Distortions • Measure galaxy ellipticities, e: • Lensing effect: Shear matrix e’ = e + 2 g • Measure shear, g, by averaging galaxies, <e> = 0. • Shear matrix: 9/16/2021 g = g 1 Heidelberg + g 2 12

Weak Lensing • An observable is the shear (2 -d tidal) matrix: (Take derivatives on sky. ) • The 2 -d lensing scalar potential, f, is projected Newtonian potential, F: 9/16/2021 Heidelberg a 13

Mapping the Dark Matter • From shear to projected density (Kaiser & Squires, 1993): Surface potential Surface density 9/16/2021 Heidelberg (Courtesy A. Refregier)14

Mapping the Dark Matter • From shear to projected density (Kaiser & Squires, 1993): Surface potential Surface density 9/16/2021 = S/Sc Heidelberg (Courtesy A. Refregier)15

3 -D Gravitational Lensing • • • An Introduction to Gravitational Lensing 2 -D Dark Matter Mapping & Statistics 3 -D Dark Matter Mapping & Statistics Dark Energy from 3 -D Gravitational Lensing The Future of Gravitational Lensing 9/16/2021 Heidelberg 16

The COMBO-17 dataset Classifying Objects by Medium-Band Observations PIs: Chris Wolf (Oxford), Klaus Meisenheimer (MPIA, Heidelberg). + Heidelberg, Edinburgh, Bonn, Oxford 9/16/2021 Heidelberg (http: //www. mpia-hd. mpg. de/COMBO/combo_index. html) 17

The COMBO-17 data-set • With Chris Wolf (Oxford), Klaus Meisenheimer (Heidelberg) & Simon Dye (Imperial College). • • • ESO’s Wide Field Imager (WFI): 2 x 4 array of 2 kx 4 k pixel CCD on 2. 2 m at La Silla, Chile. ½ degree field of view over 5 fields (1. 25 sqdeg). 17 filters for ~2% accurate photometric redshifts. Uniform selection to z=1. Best seeing used for shear analysis (<0. 7’’). (http: //www. mpia-hd. mpg. de/COMBO/combo_index. html) 9/16/2021 Heidelberg 18

Supercluster Abell 901/2 • z=0. 17 • R=25 • B=25 A 901 a A 901 b 1/2 deg 3 Mpc/h A 902 9/16/2021 19 (Gray &Heidelberg Taylor, et al. , 2002, Ap. J, 568, 141)

Mass and light in Supercluster A 901/2 Dark Matter (contours) Elliptical galaxy starlight (purple-scale) Cosmic filament ? 9/16/2021 20 (Gray &Heidelberg Taylor, et al. , 2002, Ap. J, 568, 141)

Cosmic Shear • Lensing by the large-scale dark matter distribution: 9/16/2021 Heidelberg 21

4 COMBO-17 fields (maps by Meghan Gray) • 2 -D Dark Matter Maps: Chandra Deep Field South Galactic Pole S 11 FDF • Area = 1 sq deg. 9/16/2021 Heidelberg 22

E/B mode decomposition • Shear can be decomposed into an even-parity (E) lens convergence, k: E E B B and odd-parity (B) b-field: • E-modes are due to mass, B-modes are a test of noise, systematic and intrinsic alignment effects. 9/16/2021 Heidelberg 23

Angular Power Spectra • Shear can be expanded in a 2 -D Fourier series on a flat sky: • 2 -point statistics: power spectrum • With B-modes, can measure 3 power spectra; 9/16/2021 Heidelberg 24

Cosmic Shear Power Spectrum • Maximum Likelihood Analysis of Cosmic Shear. Measured over 4 random COMBO-17 fields. zm = 0. 85+/-0. 05 from photometric redshifts Shear Amplitude 50 R(Mpc/h) 5 0. 5 LCDM Multipoles 9/16/2021 Heidelberg Brown, Taylor, et al, 2003, MNRAS, 341, 100 25

Results from Cosmic Shear • The density and clustering of Dark Matter Amplitude of matter clustering s 8=(0. 72+/-0. 08) (Wm/0. 3)-0. 5 s 8 (Redshift errors included) Correlation function fit 9/16/2021 Shear power Wm Mass-density Brown, Taylor, et al, Heidelberg 2003, MNRAS, 341, 100 26

Results from Cosmic Shear • Combine with 2 d. F Galaxy Redshift Survey & pre-WMAP CMB Percival et al (2002) CMB 2 d. F s 8 Lewis & Bridle (2002) s 8 = 0. 73+/-0. 05 WMAP Wm = 0. 27+/-0. 02 GL (t=0. 1) Wm 9/16/2021 Heidelberg Brown, Taylor, et al, 2003, MNRAS, 341, 100 27

Results from Cosmic Shear • For effects of galaxy alignment on cosmic shear see; Catherine Heymans et al, 2003, MNRAS, 347, 895 9/16/2021 Heidelberg 28

3 -D Gravitational Lensing • • • An Introduction to Gravitational Lensing 2 -D Dark Matter Mapping & Statistics 3 -D Dark Matter Mapping & Statistics Dark Energy from 3 -D Gravitational Lensing The Future of Gravitational Lensing 9/16/2021 Heidelberg 29

3 -D Mapping of Dark Matter • Why map the 3 -D Dark Matter distribution with Gravitational Lensing ? • • • Image the Dark Matter distribution on cosmic scales. See the cosmic growth of Dark Matter structures. Measure evolution of parameters. Break parameter degeneracies. Remove projection & intrinsic correlation effects. 3 -D mass selected cluster catalogues. 9/16/2021 Heidelberg 30

Mapping the Dark Matter in 3 -D • Lensing is a line integral through the 3 -D Newtonian potential: (Taylor, 2001) • Inverting we get: Observer 9/16/2021 Galaxy cluster/lens Heidelberg Background source 31

Simulating 3 -D mass mapping • Calculate the shear pattern due to two clusters on a 3 D grid: (Slice through one cluster) 9/16/2021 Heidelberg 32 (with David Bacon)

Simulating 3 -D mass mapping • Input Newtonian potential: F (Taylor, 2001) 1 z 9/16/2021 Heidelberg 0 x 8 Mpc 33 (with David Bacon)

Simulating 3 -D mass mapping • Estimate Newtonian potential: F (Taylor, 2001) 1 z 9/16/2021 Heidelberg 0 x 8 Mpc 34 (with David Bacon)

Realistic 3 -D mass mapping • But shot-noise (for groundbased data) large for 3 -D fields: DF = 10 -7 (z/0. 1)2 • So Wiener filter: (Bacon & Taylor, MN, 2003; Hu & Keeton, Phy. Rev. D, 2003) T -1 F’ = S(S+N) F (S = <FF >) • …but distorts amplitude of fields. 9/16/2021 Heidelberg 35

3 -D Matter potential in COMBO-17 • Potential Field: z • Galaxy density: 9/16/2021 Heidelberg 36 Taylor, Bacon, Gray, et al, 2004 MN

3 D Lensing with COMBO-17 • Potential Field: • Galaxy density: 9/16/2021 Heidelberg 37 Taylor, Bacon, Gray, et al, 2004 MN

Imaging the 3 -D Dark Matter • The Dark Matter potential and galaxy number density. Galaxy number density Dark Matter potential 9/16/2021 Heidelberg 38 Taylor, Bacon, Gray, et al, 2004 MN

. 2 -cluster fit to A 902 & CBI Fit 2 colinear isothermal spheres for (sv 902, z 902, sv. CBI, z. CBI): Observer Galaxy cluster/lens A 902 Source CBI Shear 9/16/2021 Source Redshift Heidelberg 39 Taylor, Bacon, Gray, et al, 2004 MN

2 -cluster fit to A 902 & CBI redshift Fit shear to: c 2(sv 902, z 902, sv. CBI, z. CBI) Redshifts from number density 9/16/2021 Heidelberg A 902 redshift 40 Taylor, Bacon, Gray, et al, 2004 MN

2 -cluster fit to A 902 & CBI velocity dispersion Fit shear to: c 2(sv 902, z 902, sv. CBI, z. CBI) 9/16/2021 Weak Constraint: z 2<1 Heidelberg A 902 velocity dispersion 41 Taylor, Bacon, Gray, et al, 2004 MN

Marginalised cluster velocity dispersions: P(velocity dispersion) . 2 -cluster fit to A 902 & CBI A 902 Fix redshifts: z 1=0. 16 z 2=0. 48 CBI velocity dispersion 9/16/2021 Heidelberg 42 Taylor, Bacon, Gray, et al, 2004 MN

A 901/2 + CBI Cluster parameters Cluster redshift M (<0. 5 Mpc) (10^13 Mo) A 901 a 0. 17 10. 8+-3 A 901 b 0. 17 16. 4+-4 A 902 0. 17 5. 6+-3 CBI 0. 48 9. 2+-5 L(<0. 5 Mpc) (10^11 Lo) 13. 4 6. 7 8. 5 6. 6 M/L (M 0/L 0) 81 254 66 140 • No clear relation between mass and light. • This is a typical, dynamically unstable system. • Planning 100 times larger 3 -D survey for VST. 9/16/2021 Heidelberg 43 Taylor, Bacon, Gray, et al, 2004 MN

3 -D Cosmic Shear • Can probe the density field at different redshifts: z. L 2 Observer 9/16/2021 Galaxy cluster/lens z. L 1 Heidelberg z 2 z 1 44

3 -D Cosmic Shear • Can probe the density field at different redshifts: Shear-shear cross-power Observer Redshift 9/16/2021 Heidelberg 45

The Growth of Dark Matter Clustering • The evolution of the matter power spectrum: 1 -sigma Pm(k, z) c 2 -fit to data. 2 -sigma Dark matter clustering does evolve. Fundamental prediction of cosmology. 9/16/2021 LCDM Heidelberg Redshift 46 (Bacon & Taylor, et al 2004, MN)

3 -D Gravitational Lensing • • • An Introduction to Gravitational Lensing 2 -D Dark Matter Mapping & Statistics 3 -D Dark Matter Mapping & Statistics Dark Energy from 3 -D Gravitational Lensing The Future of Gravitational Lensing 9/16/2021 Heidelberg 47

Dark Energy • 70% of energy-density of universe in form of a negativepressure `Dark Energy’. 9/16/2021 z Heidelberg 48

Dark Energy from Lensing (work with Bhuvnesh Jain (U. Penn) & Tom Kitching) • • For acceleration require; p < -r/3. Characterize by equation of state: • • If w = -1 could be Einstein’s Cosmological Constant. But if dynamical, with w = w(z), could be due to vacuum energy. Dark Energy affects growth of structure and global geometry of universe, so detectable via lensing. • 9/16/2021 Heidelberg 49

Dark Energy from shear n Pressure affects the evolution of density fields: Hence affects evolution of the Universe: and radial distances: 9/16/2021 Heidelberg 50

Dark Energy from shear n Pressure also affects evolution of density perturbations, d=dr/r, via Hubble rate: Acceleration suppresses growth of structure. Both radial distances and growth of structure are probed by cosmological weak lensing. 9/16/2021 Heidelberg 51

Dark Energy from Lensing • Shear-shear correlations (e. g. Hu 2000, Heavens 2004, Bacon & Taylor, et al 2004) 9/16/2021 Heidelberg 52

Dark Energy from shear • Dark Energy from shear-shear correlations in two COMBO fields: 2 D shear constraint Dark Energy density WV WMAP Priors: WV +Wm =1 s 8 9/16/2021 Heidelberg Amplitude of matter clustering 53 (Bacon & Taylor, et al 2004, MN)

Geometric effect from Clusters n n Jain & Taylor, Phys Rev Lett, 2004 Dependent only on WV, w (and WK). Observer 9/16/2021 Galaxy cluster/lens z. L Heidelberg z 1 z 2 54

Dark Energy from Weak Lensing • • Geometric effect of WV and w on R(WV, w). Default WV=0. 7 and w=-1. No response from WV until beyond z=1. Main effect from w at z=0. 5! 9/16/2021 Heidelberg 55

Geometric effect from Clusters n Estimate parameters by minimising c 2 -fit over all plane configurations. Observer 9/16/2021 Galaxy cluster/lens z. L Heidelberg z 1 z 2 56

Dark Energy from Weak Lensing • Combined constraints on WV and w from shear-shear correlations and geometric test. Data from COMBO-17. Shear-shear from 2 fields. Geometric test from A 901/2 w Heidelberg (with 9/16/2021 Tom Kitching and David Bacon) WV 57

Dark Energy from Weak Lensing • Combined constraints on WV and w from geometric test and WMAP constraint on WV. Data from COMBO-17. Geometric test from A 901/2. Dw~0. 35 from 1 cluster. w Heidelberg (with 9/16/2021 Tom Kitching and David Bacon) WV 58

Dark Energy Estimate error on dark energy parameters Numbers for LSST/SNAP. 10% of sky 68% confidence s(w)=1% w’=0 Marginalised over w’ & Wm with 1%, 3% prior. w 0 z. Lens = 0. 3 zmedian= 1. 5 WV 9/16/2021 Heidelberg Jain & Taylor, Phys. Rev. Lett, 59 2004

Evolution of Dark Energy Estimate error on dark energy parameters w=w 0+wa(1 -a) Numbers for 10% of sky LSST/SNAP. 68% confidence s(w)=1% Marginalised over w s(wa)=6% & Wm with 0%, 1%, 3% wa~2 w’ prior. z. Lens = 0. 3 zmedian= 1. 5 w 0 9/16/2021 Heidelberg Jain & Taylor, Phys. Rev. Lett, 60 2004

3 -D Gravitational Lensing • • • An Introduction to Gravitational Lensing 2 -D Dark Matter Mapping & Statistics 3 -D Dark Matter Mapping & Statistics Dark Energy from 3 -D Gravitational Lensing The Future of Gravitational Lensing 9/16/2021 Heidelberg 61

The Future of Cosmic Shear • Cosmic shear: – – Dark Matter: 3 D mapping/evolution Dark Energy: WV, w(z) Galaxy formation CMB: Lensing + B-mode contamination. • Lensing Surveys: – CFHT Legacy Survey (Canada/France: 2004) – VST Lensing Survey (ESO: 2005) • 2007 and beyond: – – – 9/16/2021 Ground: dark. CAM on VISTA (2009? ), Pan-STARRS (Hawaii: 2009? ) Dark Energy Camera on CTIO (2010? ) Large Synoptic Survey Telescope (2013? ). Space: NGST, SNAP, Dark Energy Probe/DUNE? . Heidelberg 62

dark. CAM on VISTA • Comparison of lensing telescopes grasp (area x fov) and timescales. 9/16/2021 Heidelberg 63

Summary • 2 -D Weak Lensing is revealing the Cosmic Web of Dark Matter and probing Galaxy Formation. • Measuring cosmological parameters to ~10%. • With redshifts can now measure the 3 -D Dark Matter potential. • Detection of the growth of Dark Matter clustering. Heidelberg • Equation of state & evolution of dark energy. 9/16/2021 64