1. 23 Sep.20051 The Feasibility of Constraining Dark Energy Using LAMOST Redshift Survey L.Sun Peking Univ./ CPPM

2. 23 Sep.20052 Outline  Introduction  Analysis of correlation function of galaxies  Results and discussion  Summary

3. 23 Sep.20053 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 ----

4. 23 Sep.20054 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 ----

5. 23 Sep.20055 Comparison : 2df, SDSS vs LAMOST Aperture (m) Field of View N. of Fibers N. of Spectra (Galaxies) 2dF 3.9 2°400 10 5 SDSS 2.5 3°640 10 6 LAMOST 4 5°4000 10 7

6. 23 Sep.20056 Comparison : SDSS vs LAMOST SDSS LAMOST 0 0.2 0 0.5 (L.Feng et al.,Ch.A&A,24(2000),413) Number density

7. 23 Sep.20057 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?

8. 23 Sep.20058 Analysis of correlation function * peculiar velocity (z 1,z 2,) z1z1 z2z2  Galaxy clustering in redshift space *AP effect linear growth factor D(z) Hubble parameter H(z) and diameter distance d A (z) Equation of state parmetrization : w(z)=w 0 +w a z/(1+z)

9. 23 Sep.20059 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┴X┴

10. 23 Sep.200510 AP effect in correlation function Correlation function  (z 1,z 2,  ) in redshift space (Matsubara 2004) Z1Z1 Z 2 cos  Z 2 sin 

11. 23 Sep.200511 Analysis of correlation matrix Place smoothing cells in redshift space Count the galaxy number n i of each cell Calculate the redshit-space correlation matrix C ij 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 n i in a survey sample. directly associated with  (z 1,z 2,  )

12. 23 Sep.200512 Results : samples York at el., (2000) LRGs Main galaxies Samples : (according to SDSS) main sample LRG sample

13. 23 Sep.200513 Results : two cases Case I : with a distant-observer approximation Case II : general case

14. 23 Sep.200514 Results : parameters for case I Survey area is divided into 5 redshift ranges central redshift : z m = 0.1,0.2,0.3,0.4,0.5 Redshift interval :  z=0.1 Set a cubic box in each range central redshift : z m box size : cell number : 1000 (10  10  10 grids) cell radius : R=L/20 (top-hat kernel is used) Fiducial models: bias : b=1,2 for main sample and LRG sample respectively power 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 Locally Euclidean coordinates !

15. 23 Sep.200515 Results : the distant-observer approximation case Survey area is fixed Survey volume is fixed

16. 23 Sep.200516 Results : the dominant effect D(z) H(z)d A ( z) Idealized case I In this case, growth factor dominates !

17. 23 Sep.200517 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 !

18. 23 Sep.200518 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 A cone geometry!

19. 23 Sep.200519 Results : general case z~0.2-0.4 The constraints on Wa is improved : mainly by the AP effect Rotation of the degeneracy direction : to combine the two observations

20. 23 Sep.200520 Results : general case A factor of 3 improvement

21. 23 Sep.200521 Results : general case A factor of 3 improvement caveats : strong priors systematic errors

22. 23 Sep.200522 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 w 0 and w a 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. 23 Sep.200523 Thank you!