The Feasibility of Constraining Dark Energy Using LAMOST

Redshift Survey

L.Sun

Outline

Introduction Methodology Results and discussion summary

Introduction : multiple evidence

* Supernovae* CMB + galaxies, clusters or an h0

prior* Late-time integrated Sachs-Wol

fe(ISW) effect

Concordance model : dark energy dominates !

Introduction : dark energy candidates

* Cosmological constant = -1* Dynamical field models

Quintessence model -1 1 Phantom model -1 Quintom model across -1 (Li,Feng&

Zhang,hep-ph/0503268) ……

*... ...

Introduction : cosmological probes

A. Distance measures * Standard candles a. Type Ia supernavae

b. Gamma ray burst * Standard rules a. Baryon oscillation b.SZE+X-ray the scale of clusterB. Structure formation and evolution * Cluster of galaxies count * Weak lensing * ISW effect * Galaxy clustering

Introduction : motivation

Matsubara & szalay (2003) : an application of the Alcock-Paczynski (AP) test to re

dshift-space correlation function of intermidiate-redshift galaxies in SDSS redshift survey can be a useful probe of dark energy.

Introduction : SDSS vs LAMOST

SDSS

LAMOST

0

0.2

0

0.5

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

Number density

Introduction : 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?

Analysis of correlation function

* peculiar velocity

(z1,z2,)

z1 z2

Galaxy clustering in redshift space

*AP effect

linear growth factor D(z)

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

What is AP effect ?

Consider a intrinsic spherical object made up of comoving points 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┴

z z

AP effect in correlation function

Correlation function (z1,z2,) in redshift space

Z1

Z2cos

Z2sin

Formulism

1

23 2

0 0 0 00

1 ( )( ) 1 1 exp 3

1

z

M K Q

zH z H z z dz

z

ln

ln

d Df

d a

2 1 3 3(1 )

ln 2 2 2M

Q M

df wf f

d a

Equation of state parameterization(linder 2003)

Hubble parameter

Linear growth factor

Diameter distance

1/ 2 1/ 2

1/ 2 1/ 2

( ) sinh ( ) ( ) 0

( ) ( ) 0

( ) sin ( ) ( ) 0

A

k k x z K

d z x z K

k k x z K

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

Results : samples

York at el., (2000)

LRGs

Main galaxies

Samples : (according to SDSS)

main sample

LRG sample

Results : two cases

Case I : with a distant-observer approximation

Case II : general case

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 th

e 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 !

Results : the distant-observer approximation case

Survey area is fixed

Survey volume is fixed

Results : the dominant effect

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

Idealized case I

The growth factor dominates !

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 !

Note,normalization is fixed !

Results : parameters for general case

Consider: a realistic LRG sample for LAMOST in redshift range z~0.2-0.4

Set a sub-regionArea: 300 square degree

Cell radius:

Filling way: a cubic closed-packed structure

Cell number: ~1800

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!

Results : general case

(Linder 2003)

The constraints on 1 is improved : mainly by the AP effect

Rotation of the degeneracy direction : to combine the two observations

The expected error bounds of the two parameters 0 and 1 ,1 uncertainty level of one-parameter and joint probability distribution

Results : general case

A promising LRG sample in redshift range z~0.2-0.5 is also considered for LAMOST survey, which with a sub-region filled with ~3500 cells.

Results : limitation

strong priors systematic errors

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 rotation.Thus, the degeneracy between 0 and 1 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.

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.

Thank you!