JeanMarc Virey Centre de Physique Thorique

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Dark Energy Models and Constraints

• Jean-Marc Virey Centre de Physique
  Théorique
• 
  Université de Provence, Marseille

Workshop Probing the Universe with Weak Lensing
Surveys
Marseille, 24-25 April 2007
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Dark Energy and Concordance Model
The Universe is accelerating
SN data q0lt0, w0lt-0.5, OXgt0.4
SN CMB LSS data (DE ?)
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Is ?CDM a nice candidate ?
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In fact, ?vac has multiple contributions
(fluct.pot. from all the fields ? ??) all
are larger than what is measured Need for a
microscopic theory valid at very high energy to
get a relevant estimation of ?vac
Very high energy Physics (early universe physics)
play a fundamental role in cosmology !!!!
However This Physics is unknown (eg
Supergravity, String/Branes Theories
(extradimensions) .

Loop
Quantum Gravity .) Coïncidence problem is
unsolved ...
From all these motivations, numerous physicists
consider several alternatives for the Dark Energy
origin of the dynamical DE models
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Dark Energy Models and Alternatives
Present framework G.R. Homo./Iso. Expansion
Distinguishing these various interpretations is
very ambitious !!
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DE indispensable ? Models without DE
modify Friedmann Eq. - backreactions
from inhomogeneities (acceleration
structure formation) (Ellis, Wetterich, Kolb,
Matarese, Alimi, Buchert ) -
Polytropic/Cardassian models (Freese, Wang,
Linder ) (eg string, DM self
interactions, k-essence) (? Chaplygin
gas,  Unified DM ) pb in general, no
prediction for the growth of structures
modify GR - Scalar-Tensor theories -
modify Einstein/Hilbert action (Carroll )
- String theories/extradimensio
ns (cosmosubmm) (Dvali, Deffayet )
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Remarks

• Some alternatives are degenerate
• Scalar-Tensor theories Theories with
  additional curvature terms  back-reactions 
  models quintessence models ...
• One can define weff for these alternatives
  (Linder03)
• see Linder 0601052 for the correspondance between
  weff and the GR alternatives

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Dark Energy Models

• Scalar Field(s) Models f

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Quintom (Zhang) 2 scalar fields
QuintessencePhantom Avoid the  phantom
divide  problem (Zhang, Hu, Caldwell )

• Models with f-Matter couplings
• (Zhang, Peccei, Nelson, Kaplan )

quintom/mass varying particles/...
In general, many new parameters are introduced Re
A very interesting models f-? couplings
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Are we able to distinguish the various DE
interpretations ?
Question ? a common approach to all these
models ?
Re Some models are degenerate (ie same weff)
but an important selection can be done
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Quintessence
BraneWorld
Phantom
Polytropic
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Problem 1 w(z) and w(z) are not constrained
directly by observations
One need to define a parameterization for w(z)
(or perform a non-parametric test)
Problem 2 ad hoc choice, introduce bias and
degeneracies ! Are we
able to do something else ???????

• Parameterization examples
• Taylor w(z)w0w1 z valid at small z
  ?X(z)e3w1z
• Linder/Polarski w(z)w0wa (1-a) w0waz/(1z)
  
• Gerke/Efsthatiou w(z)w0w lna w0-w ln(1z)

Linder-Huterer 0505330
? many other param., but 2 parameters only may be
constrained !!
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LyaSN-gold SDSSWMAP at 95CL
Barger et al. 06

• Some models are disconnected in this plane
  distinction is possible !!!!

• ? is the crossing point of all the classes of
  models Fid?? ? ???????

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Are the (w0,wa) constraints easy to obtain ?
Unfortunately the answer is NO ! Cosmological
parameters are highly degenerate and too numerous
!! We need also to introduce some unknown
functional form
Consequences

• Reduce the number of parameters gt
  source of bias
• Perform analysis combining several cosmological
  probes but

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An example of the power of combined analysis
C. Yèche et al. 0507170

• Mid-term scenario
• 2007-2008 (before Planck)
• CMB WMAP Olimpo (balloon experiment with good
  resolution and a small field)
• SNIa SNLSSNFactoryHST
• WL CFHT-LS.

• No assumption on OM
• and dynamical w(z)

• reduce prior assumptions
• reduce degeneracies
• but coherence test necessary
• many open questions

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Is it possible to define other analysis
procedures ?
? other model independent approaches (with own
pbs) other parameterizations
(w(z)w0w1z , w(z).) other basic
observables (H(z), q(z) (kinematic), ?X(z)/?X(0)
(dynamic)) or non-parametric tests
(binning with window functions, smoothderive
data)

• Whatever the method is
• Need to perform combined analysis
• And find that
• the Universe is accelerating
• ? is OK at 68CL (at the boundary)

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Combined analysis present data relaxed priors
constraints on
curvature and DE EoS
Based on Gong-Bo Zhao et al. astro-ph/0612728

• EoS parameterization
• Perturbation included
• Method MCMC
• Data CMB(WMAP3)LSS(SDSS2dF)SN(SNLS,Gold)
• Cosmological parameters

We use priors
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Ok free, compare SN data sets
Compare for SNLS the cases Ok free Ok 0
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Impact of relaxing the prior on h (with gold
set, smaller effects with SNLS data) 95CL
constraints corresponds roughly to the  reduce 
plane -2ltw0lt-0.5 -3ltwalt3 Present CMBLSSSN data
give almost no constraints on DE EoS when priors
are relaxed
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Knowledge of (w0,wa) is suficient to distinguish
the various DE models ?
Unfortunately the answer is NO ! Separation of
some classes, but models of very different nature
stay degenerate eg back-reactions
Quintessence
First tentative of solution compare
constraints on (w0,wa) from different tests
Geometrical tests (distances, background)
vs Tests of the growth of structures
(perturbations)
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Manifestation of the DGP model (extra-dimensions)
when General Relativity is assumed ( classical
assumptions on primordial fluctuations)
Ishak et al. astro-ph/0507184
Problem other sources of bias (analysis,
astrophysical and theoretical) may produce
similar inconsistencies ...
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Other interesting approaches parameterize the
growth function Linder-Cahn 07 mix various
tests Uzan 04, Bean-Carroll-Trodden 06
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Conclusions and Perspectives

• ? is a very good candidate to describe DE
• ? many other possible interpretations
• Distinguishing these various models is not
  simple (theoretical physical quantities ?
  observables, eg Model (w(z),w(z))
  (w0,wa)
• Many problems have been hidden !!!

modif GR modif Friedmann champ scalaire

• Need for combinaisons to get fiable w0 and wa !
• Need for combinaisons to go beyond (w0,wa)
• Choice of the statistical method (Bayes/freq.,
  param./non param.)
• Choice of the basic observable in respect of the
  physical question
• Comparison of the various fitting procedures
• Treatment of the DE perturbations