Cosmology with Gravitaional Lensing

Bhuvnesh Jain

University of Pennsylvania

• Current measurements in weak lensing

• New techniques for probing dark energy

• Dark matter/dark energy with cluster arcs

• What advances are needed?

Collaborators

Gary Bernstein

Mike Jarvis

Masahiro Takada

Andy Taylor (Edinburgh)

Wayne Hu (Chicago)

Galaxy Redshift Survey

Gravitational Lensing

CMB

Measure correlation statistics Constraints on cosmological models

Cosmological Surveys

Cosmology: Length and time scales

• CMB: z ~ 1100 d > 50 Mpc

• Galaxy Surveys: z < 0.3 d < 200 Mpc

• Lyman-alpha: z ~ 2 d < 40 Mpc

• Galaxy clusters: z < 1 d ~ 10 Mpc

• Weak lensing: z < 0.4 d < 20 Mpc

Lensing 2006: z < 0.6 d < 100 Mpc Lensing 2013: z < 1 0.02 < d < 500 Mpc

Convergence & Shear due to Lensing

• Image distortion can be linearly decomposed into convergence and shear .

• and are given by the projected gravitational potential:

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≡12 ∂1

2 + ∂22

( )ϕ 2−d = Ωm dz W (z,zs)δ∫ (z)

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1 ≡ 12 ∂1

2 −∂22

( )ϕ 2−d ,

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2 ≡ ∂1∂2ϕ 2−d

• 1 and 2 give the ellipticity induced on a galaxy image.

• , ～ O (1%) for typical line of sight!

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W (z,zs)∝dLS(z,zs)dL(z)

dS(zs)is the geometric factor

Simulated Lensing Maps

Field size: 3 x 3 deg, RMS amplitude: 2%

Jain, Seljak & White 2000

ShearConvergence

2-Point Correlation Function

x

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x + r

Lensing correlations given by projection of the mass power spectrum:€

ξ(r) = f (x) f (x + r) ⇔F .T .

P(k)

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(θ) = dz W 2(z)∫ dk∫ P(k,z) F(k,θ,z)

Measurement of cosmic shear

Intrinsic ellipticity of source galaxies > 10 x lensing signal (). Smooth over patches of sky to measure mean shear.

θ

Same argument applies to shear 2-point correlations.

Noise contribution to is plus sample variance.

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obs

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jasdkf

Average its square over

patches shear variance

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σ2

Npair

Lensing measurements

• Weak lensing in “blank fields” detected in 2000

• Shear correlations measured over 1 arcmin - 1 deg

• Constrain mass power spectrum and mean mass density

• Errors on measured parameters: ~10% currently.

• Prospects: effective survey size will increase 10-fold in 3 years, and about 1000-fold in 10 years.

• Goal: Better than 1% accuracy in lensing measurements.

Shear Variance Measurements

Aperture Mass Shear Variance

Jarvis et al 2002

Reanalysis of psf fitting (M. Jarvis): lower B-mode. New result: σ8=0.85 +/- 0.1. Other groups have new analyses as well.

E/B mode decomposition

E mode B mode

Gravitational lensing due to scalar potential field: no B-mode

Cosmological Mass Power Spectrum

“Vanilla” Lambda-CDM model (Tegmark & Zaldarriaga 2002)

Wide field lensing surveys

• Deep Lens Survey, s=30 deg2, ng=50 arcmin-2, 4 filters

• CFH Legacy Surveys=200 deg2, ng=30 arcmin-2, 5 filters

• LSST (Large Synoptic Survey Telescope)– 8.2 m, Field of view: 7 deg2

– s=4000 deg2, ng=50 arcmin-2, 5 filters

• SNAP (Supernova/Acceleration Probe)– 2m, Field of view: 1 deg2

s=1000 ? deg2, ng=100 arcmin-2, 9 filters

• PANSTARRS, VST…

Future surveys

Ongoing surveys

Tomography, cosmography, power, bispectra..

Mean tangential shear inside aperture compared for source galaxies at different z.

measured at different z.

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(θ)

Lensing tomography

Shear at z1 and z2 given by integral of growth function &

distances over lensing mass distribution.

z1

z2

zl1

lensing mass

zl2

Sensitivity to dark energy

Lensing fields depend on: Distances affect W , sinceGrowth rate affects Both depend on integrals of expansion rate:

Lensing tomography probes dark energy equation of state. Empirical approach:

de = de/critical : dark energy density

P = w(a) de : equation of state

w(a) = w0 + wa(1-a)a = 1/(1+z) - expansion scale factor

w0 is constant term, wa the time evolution term

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=m dz W (z,zs)δ∫ (z)

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H ≡a.

a∝ ρ

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W ∝ d(z,zs)d(z) /d(zs)

1l

3l

1l2l

3l

Tomography: power spectrum and bispectrum

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( i)κ ( j ) ⇒ C(ij )(l) α W 2δ 2

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( i)κ ( j )κ (k ) ⇒ B(ijk )(l1,l2,l3) α W 3δ 4 : a function of triangles

: a function of separation l

2l€

l

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z1

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z2

Lensing power spectrum

The theorists version of a future lensing measurement

All triangle configurations, auto- and cross-spectra used. l < 3000 or > 5’.

Using CMB priors improves constraints on w0 and wa by over a factor of 2. (2-point: Hu 99,02; Huterer 02; Heavens 03; Linder,Jenkins 03; Song,Knox 03)

Parameter forecasts with tomography

Takada & Jain 03

Lensing tomography: Take II

What good are the foreground galaxies?

z1

z2

zl1

lensing mass

zl2

Cross-correlation cosmography

Galaxy-shear cross correlation, or mean tangential shear:

Ratio with 2 background redshift slices:

Relative shear amplitude is a pure geometric quantity!Stack groups and clusters: compare shear amplitudes in apertures ~ arcminute with varying background redshift. (Jain & Taylor 03) (Bernstein, Jain 03; Song, Knox 03; Zhang, Hui, Stebbins 03; Hu, Jain 03)

Shear in apertures

• Estimate geometric factor for each aperture• Combine estimates to probe dark energy evolution

Joint galaxy-lensing analysis

fsky =0.1; ng=70 survey

• Ongoing/future surveys: joint measurement of galaxy clustering and lensing

• 1st step: use all 2-point correlations and cross-correlations (Hu & Jain 03).

• Multiple probes of dark energy from single unified analysis

HST and weak lensing

- Dark energy with lensing: Small effects, sensitive to biases in

photo-z’s or PSF anisotropy

- Open questions: strategy for future space and ground surveys?

- HST: Deep multicolor images, with ~0.1 arcsec resolution

- Can make galaxy samples, as a function of type and z, up to z~2-3

Multi-color COSMOS would be great (for both ground and space plans)!

- ACS TNO deep field (Bernstein et al) valuable sample for SNAP planning

- Ongoing work on relating galaxy properties with ambient mass structures

- 3D mass mapping needs deep multicolor, high-res imaging!

- Using size magnification as an entirely independent lensing measure

Simulated cluster with arcs at z=1,2,3 (Meneghetti et al 2004) See: Soucail, Kneib, Golse 04 for observational attempt!

Cosmography with cluster arcs

Cosmography with cluster arcs

Critical curves for z=1,2 Average critical curve size vs. z

Sample of ~20 simulated lens clusters in 5 models. Results preliminary!

Constraints on w and Cluster Mass

With a Golden Lens can get mass and w from a single cluster.Helpful factors: Velocity Dispersions, SZ, X-ray, Luck…Statistical alternative: compare ~100 observed/simulated clusters

No external info. Arc zs=1,2 Vel. Dispersion + Arc zs=1,2,3

Gravitational Telescopes

Arcs at z~7 and z~10!Magnification: x20 to x50.

Cluster arcs and dark matter

• Radial and tangential arcs probe inner mass profiles

• With vel dispersions, attempt robust measurement of mass profile

• Compare to NFW predictions constrain dark matter properties

Sand et al 2002, 2003

• Sensitivity to ellipticity and substructure in the mass distribution?

Bartelmann & Meneghetti; Dalal & Keeton

• Gravitational telescopes: galaxy samples approaching z~10

• Arcs at multiple redshifts probe of dark energy

Questions about techniques remain, but real potential for discovery!

Observe tens of clusters at high resolution, with X-ray and spectroscopy

Summary

• Lensing tomography probes dark energy using the evolution of clustering and distances factors

• Lensing cosmography: a geometric probe of dark energy

• Arcs in galaxy clusters: dark matter/dark energy

• HST: cluster arcs, and planning weak lensing surveys.