1. Dark Energy with 3D Cosmic Shear Dark Energy with 3D Cosmic Shear Alan Heavens Institute for Astronomy University of Edinburgh UK with Tom Kitching, Patricia Castro, Andy Taylor, Catherine Heymans et al Bernard Jones. Valencia 30/06/06

2. Outline  Dark Energy, Dark Matter  Weak lensing  3D weak lensing Statistical and systematics control  First 3D results from COMBO-17  Future

3. Bernard and lensing

4. Major questions  What is the Dark Matter?  What is the Dark Energy/Λ? Scalar field? Quintessence:

5. Detection of w(z)  Effects of w: distance-redshift relation r(z), and growth rate g  Various methods  Supernova Hubble diagram (D L )  Baryon wiggles (D A )  Cluster abundance vs z (g)  3D weak lensing (r(z), and g)  Probing both r(z) and g may allow lifting of degeneracy between dark energy and modified gravity law  3D weak lensing: physics well understood; needs excellent optical quality

6. Gravitational Lensing  Coherent distortion of background images  Shear, Magnification, Amplification 11 22 e.g. Gunn 1967 (Feynman 1964); Kristian & Sachs 1966 Complex shear  =  1 + i  2 β θ Van Waerbeke & Mellier 2004

7. Shear, Dark Matter and Cosmology  Lensing potential φ Lensing potential related to peculiar gravitational potential by (Flat Universe)

8.  Ellipticity of galaxy e = e(intrinsic) +   Cosmic shear: ~1% distortions  Estimate  by averaging over many galaxies Estimating shear

10.  E.g. Shear-shear correlations on the sky  Theoretically related to nonlinear matter power spectrum  Need to know redshift distribution of sources – photo-zs 2D weak lensing 3D nonlinear matter power spectrum Number density of sources (photo-zs) Peacock, Dodds 96; Smith et al 2003 Simulated: Jain et al 2000

11. Recent results: CFHTLS Hoekstra et al 2005; see also Semboloni et al 2005 22 sq deg; median z=0.8

12. What are the fundamental limitations?  Intrinsic alignments ? Lensing signal: coherent distortion of background images Lensing analysis assumes orientations of source galaxies are uncorrelated Intrinsic correlations destroy this Weak lensing e = e I +    ee*  =  e I e* I  +  * 

13. Intrinsic alignments Heavens, Refregier & Heymans 2000, Croft & Metzler 2000, Crittenden et al 2001 etc Observations (SuperCOSMOS) Brown et al 2001 Theory: Tidal torques   e I e I *  : Theory: Tidal torques Downweight/discard pairs with similar photometric redshifts (Heymans & Heavens 2002; King & Schneider 2002a,b) REMOVES EFFECT ~COMPLETELY  ee*  =  *  +  e I e I *  + 2  e I  * 

14. Efstathiou & Jones 1979  1000 particle simulations

15. Shear-intrinsic alignments ‹eγ*›  Tidal field contributes to weak shear (of background)  Tidal field could also orient galaxies (locally) (Hirata & Seljak 2004; Mandelbaum et al 2005, Trujillo et al 2006, Yang et al 2006) Expect 5-10% contamination Theory: Heymans, AFH et al 2006SDSS: Mandelbaum et al 2005

16. Removing contamination  Intrinsic-intrinsic removal is easy (with zs)  Shear-intrinsic is harder. However:  massive galaxies largely responsible  If present, it gives a B-mode signature  Redshift-dependence is as expected: Contamination signal proportional to D L D LS /D S Heymans, AFH et al 2006 Aid to removal King 2005 - template fitting

17. Why project at all? With distance information, we have a 3D SHEAR FIELD, sampled at various points. 3D Lensing + z

18. 2½D lensing in slices Hu 1999 Dividing the source distribution improves parameter estimation

19. 3D cosmic shear Shear is a spin-weight 2 field Spin weight is s: under rotation of coordinate axes by ψ, A → Aexp(is ψ ) Spin weight is s: under rotation of coordinate axes by ψ, A → Aexp(is ψ ) In general, a spin-weight 2 field can be written as  =½ðð (  E +i  B )  =½ðð (  E +i  B ) Castro, AFH, Kitching Phys Rev D 2005 Real  1 imag i  2  =  1 +i  2

20. Relationship to dark matter field: Natural expansion of shear is spherical Bessel functions and spin-weight 2 spherical harmonics. For small-angle surveys (Heavens, Kitching & Taylor astroph Monday) Transform of the shear field Integral nature of lensing Include photo-z errors Transform of density field z and r

21.  CMB: Planck  BAO: WFMOS 2000 sq deg to z=1  SNe: 2000 to z=1.5 Combination with other experiments

22. Planck + 3D WL

23. Combining 3D lensing, CMB, BAO, SNe DARK ENERGY: Assume w(a)=w 0 +w a (1-a) 3.5% accuracy on w at z=0 ~1% on w(z) at z~0.4

24. Geometric Dark Energy Test Depends only on global geometry of Universe: Ω V, Ω m and w. Depends only on global geometry of Universe: Ω V, Ω m and w. Independent of structure. Independent of structure. (Jain & Taylor, 2003, Taylor, Kitching, Bacon, AFH astroph last week) Observer Galaxy cluster/lens z2z2 z1z1 zLzL    

25. Systematics  Can marginalise over ‘nuisance’ parameters, such as a bias in the photo-zs  Quick check on such errors from expected shift of maximum likelihood point:  Shift in estimate of w ~ 1.2 x mean error in photo-zs (Shear ratio is more affected: 9 x)  3D shear power seems less sensitive to this error than tomography (Huterer et al 2005, Ma et al 2005)  May require fewer calibrating spectroscopic redshifts Kim et al 2004; Taylor et al 2006; Heavens et al 2006 F=Generalised Fisher matrix

26. Conclusions  Dark Energy and Dark Matter are now key scientific goals of cosmology  Lensing in 3D is very powerful: accuracies of ~1-3% on w potentially possible  Physical systematics can be controlled  Large-scale photometric redshift survey with extremely good image quality is needed ~10000 sq deg, median z~0.7  Space (imaging) + ground (photozs)