1. 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?

2. Collaborators Gary Bernstein Masahiro Takada Mike Jarvis
Andy Taylor (Edinburgh)
Wayne Hu (Chicago)

3. Cosmological Surveys CMB Gravitational Lensing Galaxy Redshift Survey
Measure correlation statistics  Constraints on cosmological models

4. Cosmology: Length and time scales
CMB: z ~ 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 < < d < 500 Mpc

6. Convergence & Shear due to Lensing
Image distortion can be linearly decomposed into convergence  and shear .
 and  are given by the projected gravitational potential:
is the geometric factor
1 and 2 give the ellipticity induced on a galaxy image.
,  ～ O (1%) for typical line of sight!

7. Simulated Lensing Maps
Convergence
Shear
Field size: 3 x 3 deg, RMS amplitude: 2%
Jain, Seljak & White 2000

8. 2-Point Correlation Function
Lensing correlations given by projection of the mass power spectrum:

9. Measurement of cosmic shear
Intrinsic ellipticity of source galaxies  > 10 x lensing signal ().
 Smooth over patches of sky to measure mean shear. θ
Average its square over patches  shear variance
Same argument applies to shear 2-point correlations.
Noise contribution to is plus sample variance.

10. 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.

11. Shear Variance Measurements
Aperture Mass
Shear Variance
Jarvis et al 2002
Reanalysis of psf fitting (M. Jarvis): lower B-mode.
New result: 8=0.85 +/ Other groups have new analyses as well.

12. E/B mode decomposition
E mode
B mode
Gravitational lensing due to scalar potential field: no B-mode

13. Cosmological Mass Power Spectrum
“Vanilla” Lambda-CDM model (Tegmark & Zaldarriaga 2002)

14. Wide field lensing surveys
Ongoing surveys
Deep Lens Survey, s=30 deg2, ng=50 arcmin-2, 4 filters
CFH Legacy Survey s=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

15. Tomography, cosmography, power, bispectra..
Mean tangential shear inside aperture compared for source galaxies at different z.
measured at different z.

16. Lensing tomography zl1 zl2 z1 lensing mass z2
Shear at z1 and z2 given by integral of growth function & distances over lensing mass distribution.

17. Sensitivity to dark energy
Lensing fields depend on:
Distances affect W , since
Growth 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

18. Tomography: power spectrum and bispectrum
: a function of separation l
: a function of triangles

19. Lensing power spectrum
The theorists version of a future lensing measurement

20. Parameter forecasts with tomography
Takada & Jain 03
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)

21. Lensing tomography: Take II
zl1
zl2 z1
lensing mass z2
What good are the foreground galaxies?

22. 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)

23. Shear in apertures Estimate geometric factor for each aperture
Combine estimates to probe dark energy evolution

24. Joint galaxy-lensing analysis
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
fsky =0.1; ng=70 survey

25. 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

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

27. 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!

28. Constraints on w and Cluster Mass
No external info. Arc zs=1,2
Vel. Dispersion + Arc zs=1,2,3
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

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

31. 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

32. 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.