23 Sep.2005 1

The Feasibility of Constraining Dark Energy Using LAMOST Redshift Survey

L.SunPeking Univ./ CPPM

23 Sep.2005 2

Outline

Introduction Analysis of correlation function o

f galaxies Results and discussion Summary

23 Sep.2005 3

Introduction : cosmological observables

A. the global geometry & expansion of the universe

* luminosity distance : type Ia supernavae (Riess et al.2004)

* angular diameter distance : x-ray cluster (Allen et al.2004)

x-ray + Sunyaev-Zeldovich effect (Reese et al.2004) B. dynamical evolution of LSS * evolution of cluster abundance (Haiman et al.2001) * gravitational lensing effects (Javis et al.2005)

* spatial clustering of galaxies

To constrain dark energy ----

23 Sep.2005 4

Introduction : cosmological observables

A. the global geometry & expansion of the universe

* luminosity distance : type Ia supernavae (Riess et al.2004)

* angular diameter distance : x-ray cluster (Allen et al.2004)

x-ray + Sunyaev-Zeldovich effect (Reese et al.2004) B. dynamical evolution of LSS * evolution of cluster abundance (Haiman et al.2001) * gravitational lensing effects (Javis et al.2005)

* spatial clustering of galaxies

Matsubara & Szalay (2003) : an application of the Alcock-Paczynski (AP) test to redshift-space correlation function of intermidiate-redshift galaxies in SDSS redshift survey can be a useful probe of dark energy.

To constrain dark energy ----

23 Sep.2005 5

Comparison : 2df, SDSS vs LAMOST

Aperture

(m)

Field of View

N. of Fibers

N. of Spectra

(Galaxies)

2dF 3.9 2° 400 105

SDSS 2.5 3° 640 106

LAMOST 4 5° 4000 107

23 Sep.2005 6

Comparison : SDSS vs LAMOST

SDSS

LAMOST

0

0.2

0

0.5

(L.Feng et al.,Ch .A&A,24(2000),413)

Number density

23 Sep.2005 7

Comparison : SDSS vs LAMOST

SDSS

LAMOST

0

0.2

0

0.5

(L.Feng et al.,Ch .A&A,24(2000),413)

Number density

Can LAMOST do a better job?

23 Sep.2005 8

Analysis of correlation function

* peculiar velocity

(z1,z2,)

z1z2

Galaxy clustering in redshift space

*AP effectlinear growth factor D(z)

Hubble parameter H(z) and diameter distance dA(z)

Equation of state parmetrization :w(z)=w0+waz/(1+z)

23 Sep.2005 9

What is AP effect ?

Consider a intrinsic spherical object centered at redshift z, the comoving distances through the center parallel and perpendicular to the line-of-sight direction are given by

AP effect factor

x||

X┴

23 Sep.2005 10

AP effect in correlation function

Correlation function (z1,z2,) in redshift space (Matsubara 2004)

Z1

Z2cosZ

2sin

23 Sep.2005 11

Analysis of correlation matrix

Place smoothing cells in redshift space

Count the galaxy number ni of each cell

Calculate the redshit-space correlation matrix Cij

We use a Fisher information matrix method to estimate the expected error bounds that LAMOST can give.

In real analysis, we deal with the pixelized galaxy counts ni in a survey sample.

directly associated

with (z1,z2,)

1 11( )

2

C CF Tr C C

23 Sep.2005 12

Results : samples

York at el., (2000)

LRGs

Main galaxies

Samples : (according to SDSS)

main sample

LRG sample

23 Sep.2005 13

Results : two cases

Case I : with a distant-observer approximation

Case II : general case

23 Sep.2005 14

Results : parameters for case I

Survey area is divided into 5 redshift rangescentral redshift : zm= 0.1,0.2,0.3,0.4,0.5Redshift interval : z=0.1Set a cubic box in each rangecentral redshift : zmbox size : cell number : 1000 (101010 grids)cell radius : R=L/20 (top-hat kernel is used)Fiducial models: bias : b=1,2 for main sample and LRG sample respectivelypower spectrum : a fitting formula by Eisenstein & Hu (1998)Rescale the Fisher matrix : normalized according to the ratio

of the volume of the box to the total volume

0 1 8( , , , , / , , , )M B M h n (0.3,0.7, 1,0,0.13,0.7,1,1)

1200 zL h Mpc

Locally Euclidean coordinates !

23 Sep.2005 15

Results : the distant-observer approximation case

Survey area is fixed

Survey volume is fixed

23 Sep.2005 16

Results : the dominant effect

D(z) H(z)dA(z)

Idealized case I

In this case, growth factor dominates !

23 Sep.2005 17

Results : the distant-observer approximation case

Low redshift samples

High redshift samples

If there is appropriate galaxy sample as tracers up to z~1.5, the equation of state of dark energy can be constrained surprisingly well only by means of the galaxy redshift survey !

23 Sep.2005 18

Results : parameters for general case

Consider: LRG sample for LAMOST in redshift ranges z~0.2-0.4 / z~0.4-0.5 / z~0.2-0.4 + z~0.4-0.5

Set a sub-region:Area: 300 square degree

Cell radius:

Filling way: a closed-packed structure

Cell number: ~1800/~1700/~3500

Fiducial model: the same as case I

Rescale the fisher matrix: the ratio of the sub-region to the total volume

115R h Mpc

A cone geometry!

23 Sep.2005 19

Results : general case z~0.2-

0.4The constraints on Wa is improved : mainly by the AP effect

Rotation of the degeneracy direction : to combine the two observations

23 Sep.2005 20

Results : general case

A factor of 3 improvement

23 Sep.2005 21

Results : general case

A factor of 3 improvement

caveats : strong priors systematic errors

23 Sep.2005 22

Summary

The method does have a validity in imposing relatively tight constraint on parameters, and yet the results are contaminated by degeneracy to some extent.

With the average redshift of the samples increasing, the degeneracy direction of parameter constraints involves in a rotatian.Thus, the degeneracy between w0 and wa can be broken in the combination of samples of different redshift ranges.

It is a most hopeful way to combine different cosmological observations to constrain dark energy parameters(+SNIa+weaking lensing…).

A careful study of the potential origins of systematics and the influence imposed on parameter estimate is main subject we expect to work on in future.

23 Sep.2005 23

Thank you!