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 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

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

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

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

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

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 PART I : IMPROVING ESTIMATES OF LINEAR MATTER POWER SPECTRUM

The city light traces the human population

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

“Red State” Tegmark et al. 2006

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

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

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

Tegmark et al. 2006

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

Berlind et al 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

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

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

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

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

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

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

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

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

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

Luminous Red Galaxies SDSS Main SDSS LRG Tegmark

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

Q-model prescription for LRG? Tegmark et al. (2006) marginally inconsistent LRG Bias Shapes PART I : IMPROVING ESTIMATES OF 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 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 CONSTRAINING THE DARK SIDE OF THE UNIVERSE PART I: Improving Estimates of the Linear Matter Power Spectrum

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

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

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

 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!

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

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

 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!

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

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

Predictions PART II : ESTIMATING THE DENSITY AND CLUSTERING OF DARK MATTER = = Separation Lensing signals are different

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

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

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

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

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

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

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

“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

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

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

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

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

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

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

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

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

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

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

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!

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

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

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

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

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

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

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