1. The next decade of weak lensing science Rachel Mandelbaum, CMU

2. Cosmology A homogeneous and isotropic universe Spatially flat and expanding (accelerating!) General Relativity: 2 Function of the metric (defining space-time behavior) Stress-energy tensor describes matter/energy contents R. Mandelbaum

3. 3 Picture credits: NASA/WMAP science team Name for model:  CDM ????? ??

4. 4 Picture credits: NASA/WMAP science team Quantum fluctuations seed small (  /  ~10 -5 ) inhomogeneities… …which are imprinted in CMB... Matter domination: growth through gravitational instability R. Mandelbaum

5. Two classes of cosmological probes 5 Geometric: SN1A, BAOGrowth of structure Picture credits: ESA/ESO (left), MPE/V. Springel (right) R. Mandelbaum

6. Summary: current status in cosmology An observationally supported big picture BUT… many fundamental uncertainties nature of DM and DE, nature of inflationary era, GR confirmation on many scales. 6 ? R. Mandelbaum

7. A key problem: The universe is dominated by dark contents. But…we cannot directly observe those contents using a telescope. 7R. Mandelbaum

8. Gravitational lensing Lensing deflection of light: 8

9. R. Mandelbaum9 Sensitive to all matter along line of sight, including dark matter!

10. Weak lensing 10 UnlensedLensed R. Mandelbaum

11. Galaxies aren’t really round NASA, ESA, S. Beckwith (STScI) and the HUDF Team

13. 13 Cosmic shear Shape autocorrelation  statistical map of large-scale structure R. Mandelbaum

14. Galaxy-galaxy lensing Stacked lens galaxy position – source galaxy shape cross-correlation Reveals total average matter distribution around lens galaxies or cluster (galaxy-mass correlation) 14R. Mandelbaum

15. State of the field of weak lensing ~2020: 2 surveys will start to measure lensing with sub-% precision 2013: several large, ground-based surveys will start measuring lensing with unprecedented precision (~2%) 2002-2012: increasingly precise lensing measurements in a variety of datasets, down to ~5-10% errors 2000-2001: first cosmological weak lensing measurements (~20-30% errors) mid-1990s: first detections of weak lensing R. Mandelbaum15

16. Subaru telescope 8.2 meter primary mirror Mauna Kea Excellent imaging conditions 16R. Mandelbaum

17. Subaru telescope Many instruments for optical and spectroscopic observations, e.g. Suprime-Cam 17 Miyatake, Takada, RM, et al (2012) R. Mandelbaum

18. 18 Picture credit: S. Miyazaki R. Mandelbaum

19. HSC is on the telescope! R. Mandelbaum19 HSC blog at naoj.org

20. Looking good! R. Mandelbaum20

21. 3-layer HSC survey Wide: ~1400 deg 2, i<25.8 (grizy)  Weak lensing, z<1.5 galaxy populations Deep: ~26 deg 2, 1 mag deeper, 5 wide+3 NB filters  Ly-α emitters, quasars, deeper galaxy populations, lensing systematics, … Ultradeep: 3 deg 2, 1 mag deeper, 5 wide+6 NB filters  Supernovae, galaxies to z<7 Important synergies: CMB (ACT+ACTPol), redshifts (BOSS + assorted other), NIR, u band, … 21R. Mandelbaum

22. What has driven this development? ~8-10 years ago, people started to realize how very powerful cosmic shear is as a probe of dark energy! 22 (LSST science book) R. Mandelbaum

23. What has driven this development? ~8-10 years ago, people started to realize how very powerful cosmic shear is as a probe of dark energy! 23 Zhan et al. (2006, 2008) R. Mandelbaum

24. A reminder Cosmic shear measures the matter power spectrum This is easily predicted from theory (modulo small-scale effects) Contrast: the galaxy power spectrum from redshift surveys – galaxies are a biased tracer of matter 24R. Mandelbaum Position Galaxies Density Dark matter halo

25. BUT 25R. Mandelbaum

26. This is actually kind of difficult. 26 Cosmic shear is an auto-correlation of shapes: Multiplicative biases are an issue! Coherent additive biases become an additional term! R. Mandelbaum

27. That’s not the only problem, either. Intrinsic alignments Theoretical uncertainties on small scales (e.g. baryonic effects) Photometric redshift uncertainties 27R. Mandelbaum

28. Implications As datasets grow, our control of systematics must get increasingly better The past ~3 years have seen a change of perspective within the lensing community: We should measure cosmic shear But we should also identify combinations of lensing measurements with other measurements that allow us to calibrate out / marginalize over systematics directly Use ALL the information available Minimize the combination of statistical + systematic error! 28R. Mandelbaum

29. What data will we have? The lensing shear field: HSC The 2d galaxy density field: HSC (Sometimes) 3d galaxy density field and velocity field, with spectroscopy: BOSS X-ray (galaxy clusters): XMM SZ (galaxy clusters), CMB lensing: ACT Lensing magnification field? 29R. Mandelbaum (M. White)

30. 30 Summary of approach to future data: Cross-correlate everything with everything = more information = less sensitivity to observational uncertainties specific to one particular method R. Mandelbaum

31. What about galaxy-galaxy lensing? Typically undervalued for cosmology, because it measures gm correlations, not mm Observationally easier: Coherent additive shear errors do not contribute at all! (cross-correlation) Intrinsic alignments: Don’t enter at all, with robust lens-source separation If sources are not well behind lenses, they contribute, but in a different way from cosmic shear 31R. Mandelbaum

32. Observational quantities  gg from galaxy clustering  gg from galaxy clustering  gm from g-g weak lensing  gm from g-g weak lensing Infer matter clustering (schematically) : Infer matter clustering (schematically) : 32 Constrain nonlinear matter power spectrum on large scales R. Mandelbaum

33. Let’s include cosmic shear Use cosmic shear (mm), galaxy-galaxy lensing (gm), and galaxy clustering (gg) Dependence on intrinsic alignments, shear systematics: Different for the two lensing measurements  Joachimi & Bridle 2011, Kirk et al. (2011), Laszlo et al. (2011) showed that the cosmological power is = that of cosmic shear, even when marginalizing over extensive models for systematics! 33R. Mandelbaum

34. A concrete example: Lensing + clustering in SDSS DR7 (RM, Anze Slosar, Tobias Baldauf, Uros Seljak, Christopher Hirata, Reiko Nakajima, Reinabelle Reyes, 2012) 34R. Mandelbaum

35. Observational quantities  gg from galaxy clustering  gg from galaxy clustering  gm from g-g weak lensing  gm from g-g weak lensing Infer matter clustering (schematically) : Infer matter clustering (schematically) : 35 Constrain nonlinear matter power spectrum Cross-correlation coefficient between galaxies, matter R. Mandelbaum

36. Problem: small scales Theoretical uncertainties in Σ (surface density): Baryonic effects Cross-correlation ≠ 1 Cannot remove by avoiding small scale ΔΣ 36 Integration lower limit is the problem R. Mandelbaum

37. Solution to small-scale issues Define “ Annular differential surface density” (ADSD): NO dependence on signal below R 0 ! 37 →0 at R 0 →ΔΣ at R>>R 0 T. Baldauf, R. E. Smith, U. Seljak, RM, 2010, Phys. Rev. D, 81, 3531 RM, U. Seljak, T. Baldauf, R. E. Smith, 2010, MNRAS, 405, 2078 R. Mandelbaum

38. Example from simulations 38 Cross-correlation coeff (r cc ) Using ΔΣ Using ϒ, R 0 =3 Mpc/h Reconstruction ϒ mm R. Mandelbaum

39. Sensitivity to cosmology 39 Fiducial cosmology: Ω m =0.25 σ 8 =0.8 n s =1.0 R. Mandelbaum

40. R Results Lenses: SDSS-I spectroscopic samples: LRGs, z~0.3, typically 3L *, ~10 5 Main, z~0.1, typically L *, 6 × 10 5 Sources: 6 × 10 7 fainter galaxies Treat samples separately, for sanity checks Updated treatment of lensing systematics (RM et al. 2011, Reyes et al. 2011) 40R. Mandelbaum

41. Example of current data 41 Stacked data: ~10 5 LRGs (lenses), 70M sources Lensing signal Transverse separation R (Mpc/h) R. Mandelbaum

42. Lensing data R. Mandelbaum42

43. Clustering data R. Mandelbaum43

44. Actual procedure Direct fitting: Nonlinear power spectrum PT-motivated parametrization of non- linear bias With these data alone, fitting for σ 8, Ω m, and bias, marginalizing over bias and lensing calibration: σ 8 (Ω m /0.25) 0.57 = 0.80±0.05 44R. Mandelbaum

45. 45 Non-flat, free w de

46. Comparison to cosmic shear results COSMOS (Schrabback et al. 2010), 11% σ 8 constraint CFHTLenS (Kilbinger et al. 2012), 4% σ 8 constraint Typical z~1, 0.8 vs. 0.25 for SDSS SDSS gives better control of redshift systematics 46 Results shown here establish SDSS among the most competitive extant surveys for weak lensing cosmology! R. Mandelbaum

47. Near future improvements R. Mandelbaum47 BOSS + HSC: Less dominated by lensing statistical errors

48. But that’s not all… Small-scale lensing profiles reveal galaxy DM halos 48 Transverse separation R (Mpc/h) R. Mandelbaum

49. Example of how we can use this: FoG R. Mandelbaum49 Small-scale effect due to velocity dispersion within halos Cannot simply eliminate by using only individual halos, unless chosen “center” is really at center White et al. (2011): contours of 3d correlation function

50. Idea for how to calibrate out FoG Hikage, Takada, Spergel (2011) Rely on spectroscopic / photometric survey synergy Select halos, then compare several measurements for different choices of halo centers: Redshift-space power spectra Galaxy-galaxy lensing (matter distribution) Photometric galaxy cross-correlation R. Mandelbaum50

51. Modeling Need HOD model for how galaxies populate halos Include variable fraction that are offset within halos, their spatial and velocity distributions R. Mandelbaum51 Hikage, RM, Takada, Spergel (2012)

52. The punch line 40% (70%) of bright (faint) LRGs are actually off-centered satellites Typical off-centering radius of 400 kpc/h Typical velocity dispersion: 500 km/s R. Mandelbaum52

53. Conclusions Current g-g lensing measurements: Test theory predictions for galaxy-DM relationship Constrain cosmological parameters at various redshifts Lensing is the ONLY technique that directly probes the total matter distribution! Future datasets: better S/N  cosmologically interesting powerful constraints on growth of structure, done optimally via combination of multiple observables 53R. Mandelbaum