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Constraining the Dark Side of the Universe

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

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Constraining the Dark Side of the Universe

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  1. Constraining the Dark Side of the Universe JAIYUL YOO DEPARTMENTOF ASTRONOMY, THE OHIO STATE UNIVERSITY 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. CONSTRAINING THE DARK SIDE OF THE UNIVERSE The Onset of the Dark • 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?

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

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

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

  8. Linear Matter Power Spectrum

  9. Linear Matter Power Spectrum

  10. Linear Matter Power Spectrum

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

  12. The city light traces the human population

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

  14. Tegmark et al. 2006 “Red State”

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

  16. Tegmark et al. 2006

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

  18. PART I : IMPROVING ESTIMATES OF LINEAR MATTER POWER SPECTRUM 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

  19. Tegmark et al. 2006

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

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

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

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

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

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

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

  27. PART I : IMPROVING ESTIMATES OF LINEAR MATTER POWER SPECTRUM 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

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

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

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

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

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

  33. Luminous Red Galaxies SDSS Main SDSS LRG Tegmark

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

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

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

  37. CONSTRAINING THE DARK SIDE OF THE UNIVERSE PART I: Improving Estimates of the Linear Matter Power Spectrum • 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

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

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

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

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

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

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

  44. PART II : ESTIMATING THE DENSITY AND CLUSTERING OF DARK MATTER 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

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

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

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

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

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

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