# Presentation: 041587

## 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?

-     (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

- 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

## Linear Matter Power Spectrum

## 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”

- “Red State”

- Tegmark et al. 2006

## “Blue State”, in fact.

- “Blue State”, in fact.

- “Red State”

- Tegmark et al. 2006

## 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**

## Halo Occupation Distribution (HOD)

- Berlind et al. 2003

- Probability Distribution P(N|M)

- Mean Occupation

**PART I : IMPROVING ESTIMATES OF LINEAR MATTER POWER SPECTRUM**

- 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**

## Halo Occupation Distribution (HOD)

-    _*Can be determined from clustering measurements*_

- Zehavi et al. 2005

**PART I : IMPROVING ESTIMATES OF LINEAR MATTER POWER SPECTRUM**

- 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

## 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**

## Recovering Linear Matter Power Spectrum

-     where
_*Q-model prescription is not an accurate description*_

**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

## LRG Bias Shapes

_*Tegmark et al. (2006) marginally inconsistent*_

**PART I : IMPROVING ESTIMATES OF LINEAR MATTER POWER SPECTRUM**

## PART I: Improving Estimates of the Linear Matter Power Spectrum

_*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

## PART I: Improving Estimates of the Linear Matter Power Spectrum

- 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      ?

- Information on the galaxy formation process
_*Can we do cosmology just with      ?*_

**PART II : ESTIMATING THE DENSITY AND CLUSTERING OF DARK MATTER**

- Galaxy Clustering

## The Universe can fool you!

**PART II : ESTIMATING THE DENSITY AND CLUSTERING OF DARK MATTER**

- Separation

## Light Galaxies!

-    m = 0.1, 8 = 0.95

- m = 0.63, 8 = 0.6

-    m = 0.3, 8 = 0.80

- Tinker et al. (2005)

- Heavy Galaxies!

## Slide 42

## Weak distortion of background galaxy shapes

Higher S/N and more reliable than cosmic shear

Information on the matter distribution around foreground lensing galaxies

- 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**

## Light Galaxies!

-    m = 0.1, 8 = 0.95

- m = 0.63, 8 = 0.6

-    m = 0.3, 8 = 0.80

- Tinker et al. (2005)

- 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**

- =0.6 --- 1.0

- =0.2 --- 0.4

- Separation

- Separation

_*Lensing signals are different*_

## Test of Linear Bias Scaling

- Accuracy of the linear bias approximation

**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

- Dark energy observable:
-          _*the expansion history of the Universe*_
-          _*the growth rate of structure*_

**PART III : GALAXY CLUSTERS AND DARK ENERGY**

- Probing Dark Energywith Cluster-Galaxy Weak Lensing

## Expansion History

-  Volume of survey area is smaller

**PART III : GALAXY CLUSTERS AND DARK ENERGY**

- Fiducial model vs Comparison model with w=-0.8

## Growth Rate of Structure

-  Larger structure in the past
-  Massive halos are more abundant

**PART III : GALAXY CLUSTERS AND DARK ENERGY**

- Fiducial model vs Comparison model with w=-0.8

## Galaxy-Cluster Method

-  from halo mass function
-  from physical volume of survey area
_* *__*Accurate mass measurement is crucial*_

**PART III : GALAXY CLUSTERS AND DARK ENERGY**

## Andrey Kravtsov

***X-rays ******+****** ******Optical***

***Sunyaev-Zel'dovich effect***

***Weak Lensing***

***SZA image of A1914***

***Temperature map ******+***

***strong lensing***

## Chandra X-ray images of clusters

- nearby clusters_ _

*Alexey Vikhlinin*

- distant clusters (z ~ 0.6)_ _

## Our Method

-  Cluster-galaxy weak lensing
-  Monotonic relation of mass-observables
-  Stacked sample of the most rich clusters

**PART III : GALAXY CLUSTERS AND DARK ENERGY**

## Cluster Mass-Observable Relation

_* *__*Scatter in mass-observable relation*_

-  Robust to the scatter
-  Stacked sample
-   _*very close to*_
-   most massive clusters

**PART III : GALAXY CLUSTERS AND DARK ENERGY**

## Upside and Downside

-  No irregularity of individual halos
-  Higher S/N ratio of lensing measurements
-  Lensing measurements at multiple radii

**PART III : GALAXY CLUSTERS AND DARK ENERGY**

## Upside and Downside

-  Small but nonzero impact of the scatter
-  Weak lensing systematic errors
-  Statistical uncertainties in galaxy shape

**PART III : GALAXY CLUSTERS AND DARK ENERGY**

## Sensitivity

_* *__*Stacked samples are different!*_

**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

**PART III : GALAXY CLUSTERS AND DARK ENERGY**

-   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

- 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

-     (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

- 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