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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. Outline. Dark Energy, Dark Matter Weak lensing

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Dark Energy with 3D Cosmic Shear

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  1. 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 (DL) • Baryon wiggles (DA) • Cluster abundance vs z (g) • 3D weak lensing (r(z), and g) • Probing bothr(z) andg 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 θ β 2 Van Waerbeke & Mellier 2004 1 Complex shear  =1 + i 2 e.g. Gunn 1967 (Feynman 1964); Kristian & Sachs 1966

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

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

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

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

  11. 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 lensinge = eI +   ee* = eIe*I + *

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

  13. Efstathiou & Jones 1979 • 1000 particle simulations

  14. SDSS: Mandelbaum et al 2005 Theory: Heymans, AFH et al 2006 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

  15. 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 DL DLS/DS Heymans, AFH et al 2006 Aid to removal King 2005 - template fitting

  16. 3D Lensing Why project at all? With distance information, we have a 3D SHEAR FIELD, sampled at various points. + z

  17. 2½D lensing in slices Dividing the source distribution improves parameter estimation Hu 1999

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

  19. Transform of the shear field Include photo-z errors Integral nature of lensing Transform of density field z and r 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)

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

  21. Planck + 3D WL

  22. Combining 3D lensing, CMB, BAO, SNe DARK ENERGY: Assume w(a)=w0+wa(1-a) 3.5% accuracy on w at z=0 ~1% on w(z) at z~0.4

  23. Observer Galaxy cluster/lens z1 zL z2 Geometric Dark Energy Test g1 g2 • Depends only on global geometry of Universe: ΩV, Ωm and w. • Independent of structure. (Jain & Taylor, 2003, Taylor, Kitching, Bacon, AFH astroph last week)

  24. Kim et al 2004; Taylor et al 2006; Heavens et al 2006 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 F=Generalised Fisher matrix

  25. 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)

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