The Feasibility of Constraining Dark Energy Using LAMOST Redshift Survey

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 h0 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 Number density 0.2 SDSS 0 0.5 LAMOST 0 (L.Feng et al.,Ch .A&A,24(2000),413)

8. Introduction : SDSS vs LAMOST Number density 0.2 SDSS 0 Can LAMOST do a better job? 0.5 LAMOST 0 (L.Feng et al.,Ch .A&A,24(2000),413)

9. Analysis of correlation function z1 z2 * peculiar velocity  (z1,z2,) Galaxy clustering in redshift space linear growth factor D(z) Hubble parameter H(z) and diameter distance dA(z) *AP effect

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 x|| z z X┴ AP effect factor 

11. AP effect in correlation function Z1 Z2sin Z2cos Correlation function (z1,z2,) in redshift space

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

13. Analysis of correlation matrix In real analysis, we deal with the pixelized galaxy counts ni in a survey sample. Place smoothing cells in redshift space Count the galaxy number ni of each cell directly associated with (z1,z2,) Calculate the redshit-space correlation matrix Cij We use a Fisher information matrix method to estimate the expected error bounds that LAMOST can give.

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

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 : zm= 0.1,0.2,0.3,0.4,0.5 Redshift interval :z=0.1 Set a cubic box in each range central redshift : zm 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)dA(z) The growth factor dominates ! Idealized case I

19. Results :the distant-observer approximation case Low redshift samples High redshift samples Note,normalization is fixed ! 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 !

20. Results :parameters forgeneral 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 The constraints on 1 is improved : mainly by the AP effect Rotation of the degeneracy direction : to combine the two observations (Linder 2003) 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!