1. The Feasibility of Constraining Dark Energy Using LAMOST Redshift Survey L.Sun

2. Outline  Introduction  Methodology  Results and discussion  summary

3. Introduction : multiple evidence * Supernovae * CMB + galaxies, clusters or an h 0 prior * Late-time integrated Sachs- Wolfe(ISW) effect Concordance model : dark energy dominates !

4. 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) …… *......

5. 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 cluster B. Structure formation and evolution * Cluster of galaxies count * Weak lensing * ISW effect * Galaxy clustering

6. Introduction : motivation 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.

7. Introduction : SDSS vs LAMOST SDSS LAMOST 0 0.2 0 0.5 (L.Feng et al.,Ch.A&A,24(2000),413) Number density

8. 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?

9. 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)

10. 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┴X┴  z zz

11. AP effect in correlation function Correlation function  (z 1,z 2,  ) in redshift space Z1Z1 Z 2 cos  Z 2 sin 

12. Formulism Equation of state parameterization (linder 2003) Hubble parameter Linear growth factor Diameter distance

13. 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,  )

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

15. Results : two cases Case I : with a distant-observer approximation Case II : general case

16. 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 !

17. Results : the distant-observer approximation case Survey area is fixed Survey volume is fixed

18. Results : the dominant effect D(z) H(z)d A (z) Idealized case I The growth factor dominates !

19. Results : the distant-observer approximation case Low redshift samplesHigh 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,normalizati on is fixed !

20. Results : parameters for general case Consider: a realistic LRG sample for LAMOST in redshift range z~0.2-0.4 Set a sub-region Area: 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 A cone geometry!

21. 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

22. 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.

23. Results : limitation strong priors systematic errors

24. 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.

25. Thank you!