Cosmological parameters from SNIa :

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Cosmological parameters from SNIa
Constraints and Bias from Analysis

• Jean-Marc Virey
• (Centre de Physique Theorique / Provence
  University)

In collaboration with CPT
P. Taxil CPPM A. Ealet, A.
Tilquin, C. Tao, D. Fouchez, A. Bonissent
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Summary

• Concordance Model and modelisation of Dark Energy

Constraints from SNIa
Analysis Bias w(z) cste Prior on
OM linear q(z)
J.-M. Virey et al., PRD70, 063514 (2004)
J.-M. Virey et al., PRD70, 121301R (2004)
J.-M. Virey et al., PRD72, 061302 (2005)
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Main Goal Constraints from SNIa with minimal
assumptions or priors
Concordance model is OK with high precision ???
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Homogeneity, Isotropy, comoving coordinates

• 1) kinematics

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2) Dynamics
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3) Modelisation of Dark Energy
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• Modelisation of the equation of state w(z)

w(z)cste
Approach with weff relatively general
weffgt-1
eg Linder 0402503
Parametrisations

• Taylor w(z)w0w1 z valid at small z since
  ?X(z)e3w1z
• Linder/Polarski w(z)w0wa (1-a) w0waz/(1z)
  
• Gerke/Efsthatiou w(z)w0a ln(1z)
• large number of possibilities several don t
  use w(z)

wa2w1
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4) Summary and cosmological parameters
Links with observations
OT1
Cosmological parameters

?X(z)/?X(0)
Ms OM (OX1-OM) para characterizing
wX(z)

q(z)
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Constraints from SNIa
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Conclusions from Riess et al.
Type Ia SN discoveries at zgt1 from the HST
Evidence for past deceleration and constraints on
Dark Energy evolution Riess et al.
astro-ph/0402512

• Acceleration is probed at 99 CL (zT0.460.13)
• A 3-fit dynamical (w10,OT1) with a strong
  prior OM 0.270.04 -1.46ltw0 lt-0.76 at
  95CL (ie very good agreement with
  Concordance model, rejection of grey dust models)
• OM 0.290.04 is obtained with w0-1 and OT1
• w1 can not have strong variations , errors
  divided by 8 and the quadrant w0gt -1 and w1lt0 is
  rejected

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Results for various fits (test ?2)
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Bias from Analysis
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• 1) Origin (theoretical)

Maor, Steinhardt et al., PRL 2002, PRD

• Fonctionnal form fondamental role (w(z), q(z),
  ?(z))
• Degeneracies among parameters (strong
  correlations)
• Number of parameters to fit

eg choice of a dynamical fitting function
Fitting parameters MS , WM , WR , WX , w0 , w1
.
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• 2) Bias due to the temporal evolution of wX

Virey et al., PRD70, 043514 (2004)
SNAP stat.
Illustration OMF0.3 w0F-0.7 w1F0.8 give
WM0.620.013 and
w0-1.550.19
Visualisation Fiducial plane (w0F, w1F)
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no/weak prior
SNAP stat.
Results
OM
Ms

• OM biased very quickly
• w0 biased if strong variations or if
  w0 is closed to 0

• With a strong prior, the bias is reported on w0
  which is now biased quickly if we are not on the
  w1F0 line

w0
strong prior (1)
full
Conclusions
ZV
w0
Neglecting w1 in the fitting procedure gives
erroneous results on OM and w0
ZB
ZNC
Re assuming w0-1 (DE?) is even more
restrictive !
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• 3) Bias from the strong prior on OM

J.-M. Virey et al., PRD70, 123501R (2004)
Remark fitted values (central errors)
strongly dependent on OMprior and
s(OMprior)
Fits on SNIa Gold sample

• np/weak prior OMgt0.3
• OMprior play a fundamental role on rôle w0 and
  s(w0)
• Riess choice OM 0.270.04 gt ?CDM small s

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Simulations and interpretation
OM 0.270.04
Illustration accelerating (best fit)
OMF0.5 w0F-2.2 w1F1.6 decelerating (q0Fgt0)
OMF0.5 w0F-0.6 w1F-10 but fitted with the
false prior OM 0.270.04
OM 0.50.04
68.3CL

• Results
• correct prior w0w0F and w1w1F but large s
• (false) prior OM 0.270.04 w0 and w1
  erroneous but close to ?CDM Indetectable
  with ?2 ! (s(w0) and s(w1) small)
• Gold data dont have enough stat. to distinguish
  both models but the false prior may induce
  wrong conclusions on the w0 and w1 values and
  their errors !!!

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Simulations this type of distorsions is very
general

• OMF0.5, Fit with OM 0.270.04
• -5ltw0Flt0 but -1.8ltw0lt0
• -8ltw1Flt8 but 0ltw1lt3

Very strong correlations among OM, w0 and w1
Zone obtained by Riess et al. ...
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Results

• The values for w0 and w1 are brought artificially
  in the quadrant w0gt -1.8 and w1 gt0 by the strong
  prior OM 0.270.04.
• In this quadrant the errors are always small
• Q Can we believe blindly this prior ? What is
  the best strategy to extract correctly the
  cosmological parameters ?

• Re Where is OM 0.270.04 ? From combined
  analysis of CMBLSS data, which assume DE? .
  Relaxing some assumptions allows 0.1ltOMlt0.5

Briddle et al., Conversi et al.
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Constraints on Gold data with minimum bias

• w(z) non constant
• no/weak prior on OM

Necessity to analyze with

• w1gtgt0 forbidden since ?X(z)e3w1z
• Quintessence models (w0gt-1, 1gtw1gt0) strongly
  constrained eg SUGRA excluded at 80CL (??2 3.5)
• w0gt-1, w1lt0 (k-essence/Big Crunch) still
  allowed
• w0lt-1 (phantom/modif. Friedm.-R.G.) almost no
  constraints on w1 (and certainly not w1gt0 )
• models q0gt0 allowed if OM0.5 and w1ltlt0

95CL
Contradiction with the kinematical test of Riess
et al. ??? NO ...
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4) Bias for q0 and transition redshift zT
J.-M. Virey et al., PRD72, 061302 (2005)
Constraints on
Linear form
and
Pure kinematics model independent approach ??
(No !!!)
Riess q0 - 0.740.18 q11.590.63
q0 lt 0 at 99 C.L
NB avec LCDM
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Linear assumption for q(z) too strong results
are biased e.g. previous dynamical models are
not compatible with this assumption
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Constraints on Gold data with minimum bias
Strategy Fit Gold data using dynamical approach
(Ms,?M,w0,wa). q0 is a derived parameter,
obtained from
q0
wa
w0
?M
?M prior
0.270.04
0.270.2
For a weak prior, q0lt0 at 95 C.L. but at 2
sigma from ?CDM (q0-0.6) Without any prior on ?M
(minimum bias), q0lt0 at 80
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Conclusions

• The bias of analysis may have very important
  effects that may be misleadind when interpreting
  the results
• Due to these bias, the data analysis are NOT
  model independent
• Others fitting functions (e.g. Linder/Polarski,
  G/E, Corasaniti ... ?X(z), statefinder, principal
  componants ) have their own bias/limitations !
  (i.e. no miracle solution)
• Trying to answer any physical question need
  reflexions on the best fitting procedures and on
  the coherence of the various results
• Combined analysis (SNIaWeak LensingCMBLSS)
  interesting to lift the degeneracies among the
  cosmological parameters

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95CL
95CL
3 contours no prior, OM 0.270.04 and OM
0.50.04

• OMprior fundamental role (contours are
  disconnected)
• OMlt0.6 (assuming OT1 and w(z)w0 w1 z or
  w(z)w0waz/(1z) )
• OMprior0.270.04 gt ?CDM data or prior
  property ???????

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Confusion contours A large number of models
may be confused with ?CDM at 1 and 2 s
Error propagation The smallest errors are
obtained around ?CDM ...