1. Constraining the Dark Side of the Universe J AIYUL Y OO D EPARTMENT OF A STRONOMY, T HE O HIO S TATE U NIVERSITY Berkeley Cosmology Group, U. C. Berkeley, Nov, 14, 2006

2. COLLABORATORS David H. Weinberg (The Ohio State) Jeremy L. Tinker (KICP) Zheng Zheng (IAS)

3. CONTENTS Introduction Part I : Improving Estimates of Power Spectrum Part II : The Density and Clustering of Dark Matter Part III : Galaxy Clusters and Dark Energy Conclusion

4. In 1990s, models with a cosmological constant were gaining momentum (e.g. Efstathiou et al. 1990, Krauss and Turner 1995, Ostriker and Steinhardt 1995) In the late 1990s, the first direct evidence for acceleration (Riess et al. 1998, Perlmutter et al. 1999) In 2000s, numerous observations strengthen the argument for dark energy (CMB, galaxy power spectrum, Lya forest, BBN, and so on) Do we really understand the true nature of the dark side of the Universe? CONSTRAINING THE DARK SIDE OF THE UNIVERSE The Onset of the Dark

5. We develop analytic models Apply to the current and future surveys To constrain cosmological pameters Goals (I Can Achieve) CONSTRAINING THE DARK SIDE OF THE UNIVERSE

6. Refining the Power Spectrum Shape with HOD Modeling PART I : IMPROVING ESTIMATES OF LINEAR MATTER POWER SPECTRUM

7. Dark Matter Clustering Easy to predict given a cosmological model Correlation function, power spectrum Millennium Simulation

8. Linear Matter Power Spectrum

11. Galaxy Clustering We see galaxies, not dark matter Galaxy formation is difficult to model Dark matter halos are the habitat of galaxies Galaxy bias PART I : IMPROVING ESTIMATES OF LINEAR MATTER POWER SPECTRUM

12. The city light traces the human population

13. Linear Bias Approximation Linear bias factor (constant) Identical shape (just different normalization) How accurate on what scales? PART I : IMPROVING ESTIMATES OF LINEAR MATTER POWER SPECTRUM

14. “Red State” Tegmark et al. 2006

15. “Blue State”, in fact. “Red State” Tegmark et al. 2006

17. Scale-Dependent Bias PART I : IMPROVING ESTIMATES OF LINEAR MATTER POWER SPECTRUM Bias factor is changing at each k Different shape Bias Shapes

18. Q-Model Prescription Q-model prescription for scale-dependent bias (Cole et al. 2005) A is constant, Q is a free parameter Ad hoc functional form PART I : IMPROVING ESTIMATES OF LINEAR MATTER POWER SPECTRUM

19. Tegmark et al. 2006

20. Questions Is the Q-model an accurate description? Can the value of Q be predicted? PART I : IMPROVING ESTIMATES OF LINEAR MATTER POWER SPECTRUM

21. Our Approach Alternative, more robust approach Recovering the shape of power spectrum Based on the halo occupation distribution PART I : IMPROVING ESTIMATES OF LINEAR MATTER POWER SPECTRUM

22. Halo Occupation Distribution (HOD) Nonlinear relation between galaxies and matter Probability P(N|M) that a halo of mass M can contain N galaxies PART I : IMPROVING ESTIMATES OF LINEAR MATTER POWER SPECTRUM

23. Berlind et al. 2003 Probability Distribution P(N|M) Mean Occupation PART I : IMPROVING ESTIMATES OF LINEAR MATTER POWER SPECTRUM Halo Occupation Distribution (HOD) Mass Number of Galaxies Mean occupation SPH simulation

24. Halo Occupation Distribution (HOD) Halo population is independent of galaxy formation process It can be determined empirically PART I : IMPROVING ESTIMATES OF LINEAR MATTER POWER SPECTRUM

25. Can be determined from clustering measurements Zehavi et al. 2005 PART I : IMPROVING ESTIMATES OF LINEAR MATTER POWER SPECTRUM Halo Occupation Distribution (HOD) Number of Galaxies Projected correlation separation

26. Strategy Constrain HOD parameters Calculate scale-dependent bias shapes Based on complementary information Based on an adhoc functional form (Q-model) PART I : IMPROVING ESTIMATES OF LINEAR MATTER POWER SPECTRUM

27. Redshift-Space Distortion Deprojection (e.g., Padmanabhan et al. 2006, Blake et al. 2006) Angle-average (monopole) (e.g., Cole et al. 2005, Percival et al. 2006) Linear combination of monopole, quadrupole, hexadecapole (Pseudo real-space) (e.g., Tegmark et al. 2004, 2006) Investigate bias shapes for all of these PART I : IMPROVING ESTIMATES OF LINEAR MATTER POWER SPECTRUM

28. Real-Space and Redshift-Space PART I : IMPROVING ESTIMATES OF LINEAR MATTER POWER SPECTRUM

29. Redshift-Space Distortion PART I : IMPROVING ESTIMATES OF LINEAR MATTER POWER SPECTRUM Hamilton 1997 Large scale Small scale Finger-of-God

30. PART I : IMPROVING ESTIMATES OF LINEAR MATTER POWER SPECTRUM SDSS galaxies Redshift distance

31. Analytic and Numerical Models N-body test shape comparison PART I : IMPROVING ESTIMATES OF LINEAR MATTER POWER SPECTRUM

32. Scale-dependent bias relations : where Q-model prescription is not an accurate description Recovering Linear Matter Power Spectrum PART I : IMPROVING ESTIMATES OF LINEAR MATTER POWER SPECTRUM

33. Luminous Red Galaxies SDSS Main SDSS LRG Tegmark

34. Test of Analytic Model PART I : IMPROVING ESTIMATES OF LINEAR MATTER POWER SPECTRUM N-body test

35. Q-model prescription for LRG? Tegmark et al. (2006) marginally inconsistent LRG Bias Shapes PART I : IMPROVING ESTIMATES OF LINEAR MATTER POWER SPECTRUM

36. Linear bias relation works on large scales, but Accuracy is challenged by measurement precision Accurate description of scale-dependent bias Based on complementary measurements CONSTRAINING THE DARK SIDE OF THE UNIVERSE PART I: Improving Estimates of the Linear Matter Power Spectrum

37. Smaller systematic errors, better statistical constraints than fitting linear theory or Q-model Can use data to k=0.4 before systematic uncertainties are too large It can be further refined with better constraints from more precise correlation measurements CONSTRAINING THE DARK SIDE OF THE UNIVERSE PART I: Improving Estimates of the Linear Matter Power Spectrum

38. From Galaxy-Galaxy Lensing to Cosmological Parameters PART II : ESTIMATING THE DENSITY AND CLUSTERING OF DARK MATTER

39. Statistically robust measurements of galaxy clustering Information on the galaxy formation process Can we do cosmology just with ? PART II : ESTIMATING THE DENSITY AND CLUSTERING OF DARK MATTER Galaxy Clustering

40. Can you tell the difference? PART II : ESTIMATING THE DENSITY AND CLUSTERING OF DARK MATTER The Universe can fool you! Separation

41.  m = 0.1,  8 = 0.95  m = 0.63,  8 = 0.6  m = 0.3,  8 = 0.80 Tinker et al. (2005) Light Galaxies! Heavy Galaxies!

43. Weak distortion of background galaxy shapes Higher S/N and more reliable than cosmic shear Information on the matter distribution around foreground lensing galaxies PART II : ESTIMATING THE DENSITY AND CLUSTERING OF DARK MATTER Galaxy-Galaxy Lensing

44. Linear Bias Approximation, For a given (fixed), Nonlinearity? and stochasticity? PART II : ESTIMATING THE DENSITY AND CLUSTERING OF DARK MATTER

45. Strategy Find the best-fit HOD parameters with observed galaxy clustering measurements Predict Comparison to lensing measurement determines and No need for an unknown coefficient PART II : ESTIMATING THE DENSITY AND CLUSTERING OF DARK MATTER

46.  m = 0.1,  8 = 0.95  m = 0.63,  8 = 0.6  m = 0.3,  8 = 0.80 Tinker et al. (2005) Light Galaxies! Heavy Galaxies!

47. Test of HOD Calculations Dependence of a halo’s large-scale environments: A flaw of the standard HOD? (e.g. Gao et al. 2005, Wechsler et al. 2005, Croton et al. 2005) PART II : ESTIMATING THE DENSITY AND CLUSTERING OF DARK MATTER Separation

48. Test of Analytic Model The analytic model provides accurate predictions for consistent with N-body results. PART II : ESTIMATING THE DENSITY AND CLUSTERING OF DARK MATTER Separation N-body test

49. Predictions PART II : ESTIMATING THE DENSITY AND CLUSTERING OF DARK MATTER =0.6 --- 1.0=0.2 --- 0.4 Separation Lensing signals are different

50. Is it linear? Accuracy of the linear bias approximation Test of Linear Bias Scaling PART II : ESTIMATING THE DENSITY AND CLUSTERING OF DARK MATTER

51. PART II: THE DENSITY AND CLUSTERING OF DARK MATTER Combination constrains Better exploitation of data on nonlinear scales Application to SDSS measurements CONSTRAINING THE DARK SIDE OF THE UNIVERSE

52. New Results! HOD parameters from clustering measurements Predictions PART II : ESTIMATING THE DENSITY AND CLUSTERING OF DARK MATTER

53. New Results! HOD parameters from clustering measurements Predictions PART II : ESTIMATING THE DENSITY AND CLUSTERING OF DARK MATTER

54. New Results! PART II : ESTIMATING THE DENSITY AND CLUSTERING OF DARK MATTER HOD parameters from clustering measurements Predictions (this is not a fit)

55. New Results! PART II : ESTIMATING THE DENSITY AND CLUSTERING OF DARK MATTER HOD parameters from clustering measurements Predictions (this is not a fit)

56. Probing Dark Energy with Cluster-Galaxy Weak Lensing PART III : GALAXY CLUSTERS AND DARK ENERGY Work in progress

57. “Is it a cosmological constant?” Dark energy observable: the expansion history of the Universe the growth rate of structure PART III : GALAXY CLUSTERS AND DARK ENERGY Probing Dark Energy with Cluster-Galaxy Weak Lensing

58. Angular diameter distance is closer Volume of survey area is smaller Expansion History PART III : GALAXY CLUSTERS AND DARK ENERGY Fiducial model vs Comparison model with w=-0.8

59. Larger structure in the past Massive halos are more abundant Growth Rate of Structure PART III : GALAXY CLUSTERS AND DARK ENERGY Fiducial model vs Comparison model with w=-0.8

60. Number of massive clusters from halo mass function from physical volume of survey area Accurate mass measurement is crucial Galaxy-Cluster Method PART III : GALAXY CLUSTERS AND DARK ENERGY

61. X-rays + Optical Sunyaev-Zel'dovich effect Weak Lensing SZA image of A1914 Temperature map + strong lensing Andrey Kravtsov

62. nearby clusters Alexey Vikhlinin distant clusters (z ~ 0.6) Chandra X-ray images of clusters

63. Alternative method, robust to the scatter Cluster-galaxy weak lensing Monotonic relation of mass-observables Stacked sample of the most rich clusters Our Method PART III : GALAXY CLUSTERS AND DARK ENERGY

64. Scatter in mass-observable relation Cluster Mass-Observable Relation Robust to the scatter Stacked sample very close to most massive clusters PART III : GALAXY CLUSTERS AND DARK ENERGY

65. Advantages : No irregularity of individual halos Higher S/N ratio of lensing measurements Lensing measurements at multiple radii Upside and Downside PART III : GALAXY CLUSTERS AND DARK ENERGY

66. Disadvantages : Small but nonzero impact of the scatter Weak lensing systematic errors Statistical uncertainties in galaxy shape Upside and Downside PART III : GALAXY CLUSTERS AND DARK ENERGY

67. 50 most rich clusters at z=0.3 from SDSS catalog Stacked samples are different! Sensitivity PART III : GALAXY CLUSTERS AND DARK ENERGY Changing only one parameter

68. Sensitivity PART III : GALAXY CLUSTERS AND DARK ENERGY Changing only one parameter 50 most rich clusters at z=0.3 from SDSS catalog Stacked samples are different!

69. Sensitivity with Priors Flat universe & LSS Distance cosmological parameters are not independent Dark energy density is lower PART III : GALAXY CLUSTERS AND DARK ENERGY

70. Sensitivity with Priors Flat universe & LSS Distance cosmological parameters are not independent Dark energy density is lower “20% scatter” in the mass-observable relation

71. PART III: GALAXY CLUSTERS AND DARK ENERGY CONSTRAINING THE DARK SIDE OF THE UNIVERSE Cluster-galaxy lensing best constrains Constrain w with combination of others Robust to the scatter For an observational program It can be applied to future imaging surveys at no extra observational cost

72. Analytic models To improve estimates of power spectrum To estimate the density and clustering of DM To predict the dependence of cluster-galaxy lensing signals CONSTRAINING THE DARK SIDE OF THE UNIVERSE Conclusion

73. New, multi-band, wide-field imaging surveys (PanSTARRS, DES, LSST, SNAP) Power spectrum recovery from LRG (SDSS-II, SDSS-III BAO, WFMOS, ADEPT) Joint analysis of galaxy and shear Constraing dark energy with galaxy clusters CONSTRAINING THE DARK SIDE OF THE UNIVERSE Conclusion

74. Complementary measurements Comprehensive analysis will provide a unique opportunity to understand the true nature of the dark side of the Universe CONSTRAINING THE DARK SIDE OF THE UNIVERSE Conclusion

75. Constraining the Dark Side of the Universe J AIYUL Y OO D EPARTMENT OF A STRONOMY, T HE O HIO S TATE U NIVERSITY Berkeley Cosmology Group, U. C. Berkeley, Nov, 14, 2006