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Advances in Weak Lensing Tomography: 3D and 2D Comparisons in Dark Energy Research

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This overview discusses recent developments in weak lensing tomography, particularly comparing two-dimensional (2D) and three-dimensional (3D) approaches. Key topics include the significance of photometric redshifts and their uncertainties, intrinsic alignments, shear calibration, and the impact of cosmological parameters on weak lensing power spectra. The work draws on foundational principles outlined by Hu (1999) and explores recent studies addressing the complexities of dark energy and structure growth at low redshifts.

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Advances in Weak Lensing Tomography: 3D and 2D Comparisons in Dark Energy Research

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  1. Weak Lensing Tomography Sarah Bridle University College London

  2. versus • 3d vs 2d (tomography) • Non-Gaussian -> higher order statistics • Low redshift -> dark energy

  3. Weak Lensing Tomography • In principle (perfect zs) Hu 1999 astro-ph/9904153 • Photometric redshifts Csabai et al. astro-ph/0211080 • Effect of photometric redshift uncertainties Ma, Hu & Huterer astro-ph/0506614 • Intrinsic alignments • Shear calibration

  4. 1. In principle (perfect zs) • Qualitative overview • Lensing efficiency and power spectrum • Dependence on cosmology • Power spectrum uncertainties • Cosmological parameter constraints

  5. 1. In principle (perfect zs) Core reference • Hu 1999 astro-ph/9904153 See also • Refregier et al astro-ph/0304419 • Takada & Jain astro-ph/0310125

  6. Cosmic shear two point tomography  

  7. Cosmic shear two point tomography  

  8. Cosmic shear two point tomography q  

  9. Cosmic shear two point tomography q

  10. (Hu 1999)

  11. (Hu 1999)

  12. (Hu 1999) Lensing efficiency Equivalently: gi(zl) = ∫zl ni(zs) Dl Dls / Ds dzs i.e. g is just the weighted Dl Dls / Ds

  13. (Hu 1999) Can you sketch g1(z) and g2(z)? gi(z) = ∫ zs ni(zs) Dl Dls / Ds dzs

  14. Lensing efficiency for source plane?

  15. (Hu 1999)

  16. Sensitivity in each z bin

  17. NOT

  18. (Hu 1999) Why is g for bin 2 higher? • More structure along line of sight • Distances are larger gi(zd) = ∫ zs1 ni(zs) Dd Dds / Ds dzs

  19. * *

  20. (Hu 1999) Lensing power spectrum

  21. (Hu 1999) Lensing power spectrum Equivalently: Pii(l) = ∫ gi(zl)2 P(l/Dl,z) dDl/Dl2 i.e. matter power spectrum at each z, weighted by square of lensing efficiency

  22. (Hu 1999)

  23. (Hu 1999) Measurement uncertainties • <2int>1/2 = rms shear (intrinsic + photon noise) • ni = number of galaxies per steradian in bin i Cosmic Variance Observational noise

  24. (Hu 1999)

  25. Sensitivity in each z bin

  26. NOT

  27. (Hu 1999)

  28. Dependence on cosmology Refregier et al SNAP3 A. m = 0.35 w=-1 B. m = 0.30 w=-0.7 ? ?

  29. Approximate dependence • Increase 8→A. P↓ B. P↑ • Increase zs →A. P↓ B. P↑ • Increase m →A. P↓ B. P↑ • Increase DE (K=0) →A. P↓ B. P↑ • Increase w →A. P↓ B. P↑ Huterer et al

  30. Effect of increasing w on P • Distance to z • A. Decreases B. Increases

  31. Fainter Accelerating m =1, no DE Decelerating (m =1, DE=0) == (m = 0.3, DE = 0.7, wDE=0) Perlmutter et al.1998 Further away

  32. w=-1 Fainter, further EdS OR w=0 Brighter, closer Perlmutter et al.1998

  33. Effect of increasing w on P • Distance to z • A. Decreases B. Increases • When decrease distance, lensing effect decreases • Dark energy dominates • A. Earlier B. Later

  34. Effect of increasing w on P • Distance to z • A. Decreases B. Increases • When decrease distance, lensing decreases • Dark energy dominates • A. Earlier B. Later • Growth of structure • A. Suppressed B. Increased • Lensing A. Increases B. Decreases • Net effects: • Partial cancellation <-> decreased sensitivity • Distance wins

  35. Approximate dependence • Increase 8→A. P↓ B. P↑ • Increase zs →A. P↓ B. P↑ • Increase m →A. P↓ B. P↑ • Increase DE (K=0) →A. P↓ B. P↑ • Increase w →A. P↓ B. P↑ Huterer et al

  36. Approximate dependence • Increase 8→A. P↓ B. P↑ • Increase zs →A. P↓ B. P↑ • Increase m →A. P↓ B. P↑ • Increase DE (K=0) →A. P↓ B. P↑ • Increase w →A. P↓ B. P↑ Huterer et al Note modulus

  37. Which is more important?Distance or growth? Simpson & Bridle

  38. Dependence on cosmology Refregier et al SNAP3 A. m = 0.35 w=-1 B. m = 0.30 w=-0.7 ? ?

  39. (Hu 1999)

  40. (Hu 1999) See Heavens astro-ph/0304151 for full 3D treatment (~infinite # bins)

  41. (Hu 1999)

  42. (Hu 1999) Parameter estimation for z~2

  43. Predict the direction of degeneracy in w versus m plane

  44. Refregier et al SNAP3

  45. (Hu 1999)

  46. Takada & Jain

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