Probing dark energy by a multi probe approach

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Probing dark energy by a multi probe approach
A.Ealet With Ch.Yèche (CEA/ SPP), A. Réfrégier
(CEA/SAP), C. Tao (CPPM), A. Tilquin (CPPM),
J.-M. Virey (CPT) and D. Yvon (CEA/SPP).
See Prospects for dark energy evolution a
frequentist multi-probe approach, AA, 448, 831
(2006).
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The dark energy question

• Beyong a precise measure of the standard
  cosmological parameters.. The question is
• Is acceleration due to the cosmological constant
  ?
• Can we discriminate alternatives?
• Cosmological constant
• Quintessence are any dynamical component ?
• A modification of gravity ?
• Some inhomogeneities in LSS
• What is the best strategy to probe the nature of
  the dark energy ?

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Classifying theoretical models
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Consistency and precision gt many probes

• Background evolution H(z) gt distances
  measurement
• Probing perturbations gdr/r/a

• 3D weak lensing (DA, and g)
• Baryon wiggles (DA)
• Supernova Hubble diagram (DL)
• Cluster abundance vs z (g)
• CMB (DA and g)

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• In many analyses,basic asumptions are LCDM flat
  universe,w- 1, no DE clustering etc

But many parameters are strongly correlated
Removing degeneracy without bias gt No
direct external prior Take into account all
correlations (with all cosmological and
astrophysical parameters)

• Test of consistencies
• gttake all correlation into account
• gt Introduce a systematic error treatment
• gt need at least 4 different probes

Blanchard,Douspis 2004
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Dark energyUsing w(z)
simulation Wm 0.3 w0 -0.7 wa 0.8

• it is fundamental to have at least
• 2 free parameters , w and dw/dz
• w(z) parametrisation..
• w(z) w0 (1-a) wa
• Effect of the parametrisation?
• Extraction of wa is difficult
• Example in supernovae
• wa is degenerated with Wm

Maor
Riess 2004 data
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The statistical approach

• Developp a flexible tool
• A maximum of free parameters
• Take all correlation into account
• Coherent assumption of models
• Can add or remove probes and parameters

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Frequentist or Bayesian ??

• Frequentist approach
• region of the parameters for which the data have
  at least a given probability (1-CL) of being
  described by the model.( Well known by HEP..)
• We assume a true value (here ? (optical depth))
  and we measure the agreement of the model for
  this given value.
• Bayesian approach
• calculate the probability distribution of the
  true parameters by assigning probability density
  functions to all unknown parameters.
• The method searches to predict a value

1-CL
WMAP Team Official paper
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impact of a prior

• a basic example
• Two parameters A and ?.
• A (?82) is measured with TT and TE spectra.
• ? depends only on the first point
• of the TE spectrum.
• Likelihood marginalized for different
• priors for ?.
• PDF(A) depends a lot on ? prior choice !

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Fitter with Frequentist approach

• Principle
• Minimize the ?2
• Fix one of the variables, for instance ?I
• Repeat the fit and determine the new minimum
• Confidence Level f parameter ?i is defined by
• Extension to 2-D contours with two fixed
  parameters ?i and ?j.

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The tools

• Minuit as Fitter
• Cmbeasy for CMB
• Kosmoshow (from A.Tilquin) for SNIa .
• Minimization after 200-300 call to Cmbeasy.
• One job per batch (1h) at CCIN2P3 (IN2P3
  computing Center)
• Flexible can easily add or remove parameter..

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A test of faisability ..

• Use SN and CMB data
• Use 1st year WMAP TT and TE spectrum
• Use SNIa 157 SNIa Riess et al. (2004).
• Fit with 9 parameters

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The parameters
9 free parameters

• ?b/?m density for baryon/matter
• h Hubble constant,
• ns spectral index,
• ? reionisation optical depth
• A(?82) normalization parameter for CMB (and
  WL).
• Ms0 normalization parameter for SNIa.
• ( NB neutrino masses neglected)
• Parameterization of Dark Energy
• Dark Energy perturbations for CMB
• 2 options
• No perturbation DE homogeneous and no
  clustering
• With perturbations APPLIED only for wgt-1

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fit results for w0 and wa

• Value of w0 smaller than -1.0 are favored
• Discrepancy in w0 / strategy for DE perturbation
  treatment.
• Errors significantly be degraded when DE
  perturbations added.

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Comparison with other combinations

• Seljak et al. (2004)
• w0 -1 and wa0.
• 2) Upadhye et al. (2004)
• w0 -1.3 and wa1.2

the 2s discrepancy may be due to a different
treatment of DE perturbation in CMB. 1) No DE
perturbations 2) DE perturbations for wgt-1.
Upadhye et al., astro-ph/0411803
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can be use for prospectives 3 scenarii

• Today Reference point
• WMAP 1 year
• 157 SNIa (Riess 2004).
• Mid-term 2007-2008
• CMB WMAP Olimpo (balloon with good
  resolution and a small field).
• SNIa SNLS (700) SNFactory (200) HST (50)
• WL CFHT-LS. (170 deg2)
• Long-term 2012-2015
• CMB Planck
• SNIa SNAP/JDEM (2000 300) 2 of systematic
• WL SNAP/JDEM 1000 deg2

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Some prospectives adding WL on wa

• Fisher approach on (w0,wa)
• Add WL information
• (Icosmo program (A.Refregier))

Simulation of a mid term data WMAP 1 year
Olympo CFHTLS WL SNLS SNIA
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Expected sensitivity

• With ground observations (mid-term), good
  precision on w0 alone, but not on wa.
• Satellite observations (Planck and SNAP) are
  required to achieve the 0.1 precision on w.
• Very impressive sensitivity on other parameters,
  in particular ns (test of inflationary models).

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Some helpful degeneracies for wa
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Expected sensitivity for Long Term Scenario
SUGRA
?-CDM
Phantom

• precision of the long-term scenario, needed to
  discriminate models ( here Phantom - ?CDM
  SUGRA).
• Sensitivity depends on the position in the w0-wa
  plane.

• In the Long-term scenario, WL gives very
  promising results (as good as SNCMB).
• However, systematics effects not studied for WL.

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FUTURE

• Optimizing the tool
• we plan to have a software package allowing
  contour plots in a few minutes for more than 10
  cosmological parameters.
• Provide a graphical interface

• Preparing a frame
• add new probes (BA0, clusters, SZ..)
• Work on experimental and theoretical systematic
  modelization
• define benchmark of models for test hypothesis

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Conclusion

• We have used a frequentist approach to test DE
  with a combination
• We test the methode on current data (WMAP1 year
  SNIa),
• For the DE evolution, we get
• We have observed a strong effect on (w0, wa)
  related to the treatment of DE perturbations,
  which may explain the discrepancies observed in
  the literature.
• Our prospect study demonstrates that we need
  satellite observations and many probes to
  achieve a 0.1 sensitivity on wa.

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Stronger constraints thanks to correlations

• For ?m-w0 and for w0-wa, we observe
• orthogonal correlations between (CMB-WL)
• and SNIa
• It allows to break the degeneracies.

• Actually we have 9-dim correlations,
• we gain more than the simple 2-dim
• overlap!
• We use the full correlation matrix.

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Stronger constraints thanks to correlations

• For ?m-w0 and for w0-wa, we observe
• orthogonal correlations between (CMB-WL)
• and SNIa
• It allows to break the degeneracies.

• Actually we have 9-dim correlations,
• we gain more than the simple 2-dim
• overlap!
• We use the full correlation matrix.

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Error on Cl with Olimpo
Cosmic variance
Detector performances
Cosmic variance
Resolution effect

• Nominal configurations
• Observed Sky S300 deg2
• Detector sensitivity s150 ?Ks1/2
• Number of bolometers Nbolo 20
• Observation time Tobs 10 days
• Resolution ?fwhm 4 arcmin

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Error on Cl with Planck

• Nominal configurations
• Full Sky, 12 months
• 3 Frequencies 100 / 143 / 217 (GHz)
• Sensitivity R 2.0 / 2.2 / 4.8 (?K/K)
• Resolution ?fwhm 9.2 / 7.1 / 5.0 arcmin
• (Figures extracted from The Planck mission J.A.
  Tauber
• JASR 6394 (2004) )

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Examples of 1D Confidence Level Plot
WMAP ?bh2 Scan
?bh2 0.0215, 0.0239_at_68 0.0209,
0.0247_at_90 ?mh2 0.130, 0.162_at_68
0.121, 0.174_at_90 h 0.66, 0.75_at_68
0.63, 0.78_at_90 A 0.75, 0.93_at_68 0.70,
1.00_at_90 ns 0.958, 1.013_at_68 0.943,
1.034_at_90 ? 0.091, 0.0173_at_68 0.068,
0.204_at_90
WMAP h Scan
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