1. Complementarity of Dark Energy Probes
Jiayu Tang, Filipe Abdalla and JW

2. Parameterizations of Dark Energy
Background evolution
w = w0
w = w0+w1z
w = w0+ ln(a) (Efstathiou 1999)
w = w0+wa(1-a) (Chevalier 2001, Linder 2003)
binned w(z) (‘parameter free’)
Perturbations: cs2,, ...

3. Binning of w(z) use 50 bins zmax given by particular survey
effectively parameter free
continuous binning required for including CMB (Crittenden & Pogosian 2005)
Fiducial model: w = -0.9 constant

4. Principal Component Analysis
Calculate Fisher matrix for leading order approximation of Likelihood
Diagonalize Fisher matrix do establish independent modes
Decompose w(z) in Eigenmodes
Inverse of eigenvalue is measure of uncertainty in Eigenmode (j = j-1/2), Eigenmode reflects redshift sensitivity
(Huterer and Starkman 2003; Crittenden & Pogosian 2005)

5. Analysis with Principal Components
Establish leading components via Fisher matrix (fixed vs. non-fixed cosmological parameters, below)
Estimate coefficients with MCMC or full likelihood (may need to iterate fiducial model)(Huterer and Peiris, 2007)
How about priors on Eigenmodes?
How to establish number of modes to take along (risk, likelihood ratio, F-test, evidence)?

6. Future Observations
South Pole Telescope: 1000 element Bolometer Array; 4,000 deg2; 150,250 and 270 GHz; 10m telescope; 1’ beam; deployed begining of 2007.
PanStarrs: photo-z; z=0-1; >30,000 deg2; 23.8 mag; griz and y filter and wide band (g+r+i); 4 cameras at PS4 on 1.8m mirror (1.4 billion pixels).
Dark Energy Survey: Imaging Survey on 4m Blanco; 5,000 deg2 sky coverage; 24mag in griz+VISTA IR; photo-z; z=
WFMOS: Spectrograph on Gemini (Subaru) telescope, limiting m=24, wide survey: 2000 deg2, z = ; deep survey: 300 deg2, z =
DUNE: Satellite; Imaging survey, photo-z; z= , half sky, one wide (r+i+z) band and NIR; mag limit 24.5; ground based complement
SNAP: Satellite; 6 optical + 3 NIR filters; z=0-1.7, 300 deg2 WL
For WFMOS take VVDS DEEP as distribution
DUNE in conjunction with ground based observation
Get more from DUNE webpage
about SNAP from Refregier paper

7. Supernovae Probes Measure of redshift - distance relation
SNAP: 3000 SNe
Most weight at redshift z=0.2 (DE domination)
Modes above 3rd are very weakly constrained (1 = 0.14; 2 = 0.30; 3 = 0.55)
Mode becomes negative here
Is statement about DE domination correct

8. Comparison of SNe probes
DES: 1,900 SNe (1 = 1.26; 2 = 3.46)
PanStarrs: 6,000 SNe (1 = 0.13; 1 = 0.28)
SNAP, DUNE and PanStarrs very similar

9. Weak Lensing Probes Probing expansion and growth of structure
DES: zmax = 2.0; = 0.34
Leading Principal Components reflect redshift bins
Strong constraints at z=0.3 and z=1.0
1 = 0.25; 2 = 2.95; 3= 3.93

10. Comparison of WL probes
Use simulated galaxy redshift distributions (DES: Huan Lin, DUNE: Peter Capak)
SNAP 2-bins: zmax = 3.0; =0.31 (1 = 1.67; 2 = 5.91)
SNAP 3-bins: (1 = 0.39; 2 = 2.37)
DES 1-bin: (1 = 50.0; 2 = 78.0)
DES 3-bins: (1 = 0.25; 2 = 2.95)
DUNE 1-bin: zmax = 3.0; =0.40 (1 = 24.9; 2 = 33.7)
DUNE 5-bins: (1 = ; 2 = 0.031)

11. Baryon Acoustic Oscillations
Measure of angular diameter distance
Combination of wide and deep WFMOS survey.
kmax = 0.15 cut-off
Peak constraint above z=0.5!
1 = 0.17; 2 = 0.53; 3= 0.66
used bias b=1, probably an underestimate

12. Sunayev-Zel’dovich Galaxy Cluster Counts
Measure of growth and volume
zmax = 1.5
Peak below z=0.5
1 = 0.39; 2 = 0.96; 3= 1.55

13. Effects of Other Cosmological Parameters
Include other cosmological parameters (m, H0,M,...)
Marginalize Fisher matrix over extra parameters and then calculate principal components
sign of mode changes above z=0.5
peak of modes shifts to lower redshift

14. Comparing Different Surveys
We compare the best example of each type of surveys.
Clearly WL from DUNE is best constraint for z<1, while BAO is most promising for larger redshifts, however these are Stage IV (DETF) missions
Galaxy cluster number counts almost as good as SNe and deliver information to higher redshift (these are forthcoming data sets) and are at Stage II-III.
More to come ...