Complementarity of Dark Energy Probes

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Complementarity of Future Dark Energy Probes

• Jiayu Tang, Filipe Abdalla and JW
• (DETFUCL)

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What would we like to learn from a Dark Energy
experiment?

• Possible explanations of observed accelerated
  expansion
• extra energy component in the Universe (see
  Copeland)
• modification of gravity on large scales (see
  Maartens)
• inhomogeneous Universe - acceleration effect of
  averaging procedure
• Key Question Different from cosmological
  constant?
• unique feature of ? energy density constant
• test if energy density varies with time
  (redshift, scale factor)
• effectively looking for wp/? of course not
  really physical meaning for 2. and 3.

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Parameterizations of Dark Energy

• Background evolution
• w w0
• w w0w1z
• w w0? ln(a) (Efstathiou 1999)
• w w0wa(1-a) (Chevalier 2001, Linder 2003)
• binned w(z) (parameter free)
• Perturbations cs2,?, ...

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Binning of w(z)

• use 50 (large number) bins
• zmax given by particular survey
• effectively parameter free
• continuous binning required for including CMB
  (Crittenden Pogosian 2005)
• Fiducial model w -0.9 constant

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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 of survey
• (Huterer and Starkman 2003 Crittenden Pogosian
  2005)
• Going beyond DETF figure of merit and pivot
  redshift

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Analysis with Principal Components

• Establish leading components via Fisher matrix
• 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)?

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Future Observations (very subjective)

• 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 z0-1 gt30,000 deg2 23.8
  mag griz and y filter and wide band (gri) 4
  cameras at PS4 on 1.8m mirror (1.4 billion
  pixels) (see Phleps talk).
• Dark Energy Survey Imaging Survey on 4m Blanco
  5,000 deg2 sky coverage 24mag in grizVISTA IR
  photo-z z0.35-1.39 (see Lahav talk)
• WFMOS Spectrograph on Gemini (Subaru) telescope,
  limiting m24, wide survey 2000 deg2, z
  0.5-1.3 deep survey 300 deg2, z 2.3 - 3.3
  (see Parkinson/Miyazaki talk)
• DUNE Satellite Imaging survey, photo-z
  z0.1-1.1, half sky, one wide (riz) band and
  NIR mag limit 24.5 ground based complement (see
  Refregier talk)
• SNAP Satellite 6 optical 3 NIR filters
  z0-1.7, 300 deg2 WL

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Supernovae Probes

• Measure of redshift - distance relation
• SNAP 3000 SNe
• Most weight at redshift z0.2 (DE domination)
• Modes above 3rd are very weakly constrained (??1
  0.14 ??2 0.30 ??3 0.55)

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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 and PanStarrs very similar

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Weak Lensing Probes

• Probing expansion and growth of structure
• DES zmax 2.0 ?? 0.34
• Leading Principal Components reflect redshift
  bins
• Strong constraints at z0.3 and z1.0
• ??1 0.25 ??2 2.95 ??3 3.93

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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)

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Baryon Acoustic Oscillations

• Measure of angular diameter distance
• Combination of wide and deep WFMOS survey.
• kmax 0.15 cut-off
• Peak constraint above z0.5!
• ??1 0.17 ??2 0.53 ??3 0.66

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Sunayev-Zeldovich Galaxy Cluster Counts

• Measure of growth and volume
• zmax 1.5
• Peak below z0.5
• ??1 0.39 ??2 0.96 ??3 1.55

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Effects of Other Cosmological Parameters

• Other cosmological parameters (?m, H0,M,...)
• Marginalize Fisher matrix over extra parameters
  and then calculate principal components
• sign of mode changes above z0.5
• peak of modes shifts to lower redshift
• so far no priors on w
• conservative (-1ltwlt-1/3)
• smoothness

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Comparing Different Surveys

• Clearly WL (from DUNE) is best constraint for
  zlt1, while BAO is most promising for larger
  redshifts, however these are Stage IV (DETF)
  missions
• Galaxy cluster number counts not as good as SNe
  (but are forthcoming data sets) and are at Stage
  II-III.
• More to come ... (ADEPT, PANSTARRS WL, ...)