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

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,, ...

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

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)

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)?

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=0.35-1.39 WFMOS: Spectrograph on Gemini (Subaru) telescope, limiting m=24, wide survey: 2000 deg2, z = 0.5-1.3; deep survey: 300 deg2, z = 2.3 - 3.3. DUNE: Satellite; Imaging survey, photo-z; z=0.1-1.1, 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

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

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

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

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 = 0.0053; 2 = 0.031)

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

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

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

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 ...