# Presentation: 085519

## Weak Gravitational Lensingby Large-Scale Structure

**    **Alexandre Refregier (Cambridge)
- Collaborators:
- Richard Ellis (Caltech)
- David Bacon (Cambridge)
- Richard Massey (Cambridge)
- Snowmass 2001 - July 2001

## Weak Lensing by Large-Scale Structure

-      Distortion Matrix:
-  Direct measure of  the distribution of mass in the universe,
-      as opposed to the distribution of light, as in other methods
-      (eg. Galaxy surveys)

- Theory

## Scientific Promise of Weak Lensing

- Mapping of the distribution of Dark Matter on various scales
- Measurement of cosmological parameters, breaking degeneracies present in other methods (SNe, CMB)
- Measurement of the evolution of structures
- Test of gravitational instability paradigm
- Test of General Relativity in the weak field regime
- a mass-selected cluster catalog

- From the statistics of the shear field, weak lensing provides:

- Jain et al. 1997, 1x1 deg

## Deep Optical Images

- William Herschel Telescope
- La Palma, Canaries

- 16’x8’
- R<25.5
- 30 (15) gals/sq. arcmin

## Procedure

- Quadrupole moments:

- Ellipticity:

- Shear:

- Relation:

## Instrumental Distortion

- *

- Dithered fields

## PSF anisotropy

-  3-10% rms reduced to 0.1%

## Correction Method

- KSB Method:     (Kaiser, Squires & Broadhurst 1995)

- PSF Anisotropy:

- PSF Smear & Shear Calibration:

- Other Methods:  Kuijken (1999), Kaiser (1999), Rhodes, Refregier & Groth (2000),
-                                 Refregier & Bacon (2001)

## Current Observational Status

-  Different measurements are consistent
-  In agreement with cluster-normalised CDM model
-  measure of the amplitude of mass fluctuations:
-  8(m/0.3)0.5=1.07 ± 0.23

- Cluster counts (Viana & Liddle, Eke et al.): 8(m/0.3)0.5 =1.02± 0.11
-  In agreement, test of primordial non-gaussianity

- HST

- Shear variance in circular
- cells:

- HST

- 

- 2()=<2>

## Weak Lensing Power Spectrum

- CDM

- CDM
- (linear)

- OCDM

- SNAP WF survey [300 deg2 ; 100 g arcmin-2; HST image quality**]**

- Future surveys:
- Megacam, Subaru, VISTA, LSST, WHFRI, SNAP, etc
-  Measure cosmological parameters (8, m, , , etc)
-  very sensitive to
- non-linear evolution of
- structures

## Mapping the Dark Matter

- LCDM
- 0.5x0.5 deg
- Jain et al. 1998

## Skewness

- Variance:

- Skewness:

-   Skewness breaks degeneracies (e.g. M and 8 )

- Cf. Bernardeau et al. 1997

## Dark Energy

- Effect of Dark Energy on Weak Lensing Statistics:
-  Modifies the Angular-Diameter Distance                         +
-  Modifies the rate of growth of structures                          +
-  Modifes the shape of the linear matter power spectrum    -

- Cf. Benabed & Bernardeau 2001
-       Huteterer 2001
-       Refregier et al. 2001 (in preparation)

## Power Spectrum with Dark Energy

- Use the non-linear power spectrum for quintessence models of  Ma, Caldwell, Bode & Wang (1999)
-  The Dark Energy equation of state (w=p/****) can be measured from the lensing power spectrum
-  But, there is some degeneracy between w, M and 8

## Complementarity of Weak Lensing and Supernovae

**Weak Lensing + CMB**
**(approximate)**

- Weak Lensing breaks degeneracies in ***w-************  ***plane

## Good News and Bad News

-  Very sensitive to Non-linear Power spectrum: need very accurate fitting formulae from N-body simulations
-  Requires knowledge of the redshift distribution of the galaxies
-  requires tight control of systematic effects
- Additional information:
-  Power spectrum for different redshift bins (tomography)
-  High-order moments (skweness or bispectrum, etc)
-  Mass-selected cluster catalogues

## Conclusions

- Weak Lensing is emerging as a powerful technique to measure large-scale structure
- It is based on clean physics and directly measures the mass (as opposed to light)
- It will provide precise measurements of cosmological parameters, complementing other techniques (Sne, CMB, etc)
- Weak Lensing can set tight constraints on the Dark Energy
- Require tight control of systematics
- Wide prospects with upcoming and future surveys (Megacam, Subaru, VISTA, LSST, WHFRI, SNAP, etc)