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The Feasibility of Constraining Dark Energy Using LAMOST Redshift SurveyL.Sun
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Outline
Introduction Methodology Results and discussion summary
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Introduction : multiple evidence
* Supernovae* CMB + galaxies, clusters or an h0 prior* Late-time integrated Sachs-Wolfe(ISW) effect
Concordance model : dark energy dominates !
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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) ……*... ...
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Introduction : cosmological probesA. 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
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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.
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Introduction : SDSS vs LAMOST
SDSS
LAMOST
00.2
00.5
(L.Feng et al.,Ch .A&A,24(2000),413)
Number density
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Introduction : SDSS vs LAMOST
SDSS
LAMOST
00.2
00.5
(L.Feng et al.,Ch .A&A,24(2000),413)
Number density
Can LAMOST do a better job?
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Analysis of correlation function
* peculiar velocity
(z1,z2,)
z1 z2
Galaxy clustering in redshift space
*AP effectlinear growth factor D(z)Hubble parameter H(z) and diameter distance dA(z)
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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
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AP effect in correlation function
Correlation function (z1,z2,) in redshift space
Z1
Z2cos
Z2sin
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Formulism
123 2
0 0 0 00
1 ( )( ) 1 1 exp 31
z
M K QzH z H z z dzz
lnln
d D fd a
2 1 3 3(1 )ln 2 2 2
MQ M
df wf fd a
Equation of state parameterization(linder 2003)
Hubble parameter
Linear growth factor
Diameter distance1/ 2 1/ 2
1/ 2 1/ 2
( ) sinh ( ) ( ) 0
( ) ( ) 0
( ) sin ( ) ( ) 0A
k k x z K
d z x z K
k k x z K
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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
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Results : samples
York at el., (2000)
LRGs
Main galaxies
Samples : (according to SDSS) main sample LRG sample
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Results : two cases
Case I : with a distant-observer approximationCase II : general case
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Results : parameters for case ISurvey 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 !
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Results : the distant-observer approximation case
Survey area is fixed
Survey volume is fixed
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Results : the dominant effect
D(z) H(z)dA(z)
Idealized case I
The growth factor dominates !
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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 !
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Results : parameters for general case
Consider: a realistic LRG sample for LAMOST in redshift range z~0.2-0.4Set a sub-regionArea: 300 square degreeCell radius:Filling way: a cubic closed-packed structureCell number: ~1800Fiducial model: the same as case IRescale the fisher matrix: the ratio of the sub-region to the total volume
115R h Mpc
A cone geometry!
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Results : general case
(Linder 2003)
The constraints on 1 is improved : mainly by the AP effectRotation 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
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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.
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Results : limitation
strong priors systematic errors
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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.
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Thank you!