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Scalar field quintessence by cosmic shearScalar field quintessence by cosmic shear
constraints from VIRMOS-Descart and CFHTLS constraints from VIRMOS-Descart and CFHTLS and future prospectsand future prospects
July 2006, Barcelona IRGAC 2006
In collaboration with: I.Tereno, J.-P.Uzan, Y.Mellier, (IAP), L.vanWaerbeke (British Columbia U.), ...
Carlo SchimdCarlo Schimd
DAPNIA / CEA Saclay DAPNIA / CEA Saclay @ @ DUNE TeamDUNE Team
& Institut d’Astrophysique de Paris& Institut d’Astrophysique de Paris
Based on: astro-ph/0603158astro-ph/0603158
Dark energy:Dark energy: parametrization .vs. “physics” inspired parametrization .vs. “physics” inspired
{baryons,{baryons,,,}} + DM + GR + DM + GR alone cannot account for the cosmological dynamics seen by CMB + LSS + SNe + ...
GR : not valid anymore? scalar-tensor theories, braneworld, etc.
Other “matter” fields? cosmological constant, quintessence, K-essence, etc.
Dark energyDark energy H(z)-Hr+m+GR(z)
1/0 approach:1/0 approach: parameterization of w(z) departures from CDM
limitation in redshift ?pivot redshift zp : observable/dataset dependent
Not adapted for combining low-z and high-z observables and/or several datasets
parameters physics# p.: limitation to likelihood computation
perturbations: how ? Fitted T(k)
Physics-inspired approach:Physics-inspired approach: classes experimental/observational tests
high-energy physics ?!
w : full redshift range small # p.perturbations: consistently accounted for
Validity of Copernican principle? effect of inhomogeneities?
geodesic deviation equation
Quintessence by cosmic shear. IQuintessence by cosmic shear. I
convergence shear
2 4
( )
( ) ( ) ( ) ,K
k S
P P d q k P k
N-pts 2-pts correlation functions in real space:(0) ( )
Remark: just geometry, valid also for ST gravity
i i ji ijB v E v v
2 2 2( ) (1 2 ) ((1 2 ) 2 )i ii i j
ij jds a d d dx x dxB dE
C.S., J.-P.Uzan, A.Riazuelo (2004)
( ) ( )Pd W
obs
gal
1 22 2 2 21 2 1 2 1 2 2 1
LSS:
Map
2
v i
angular distanceangular distance q(z); 3D2D projectiongrowth factor growth factor amplitude of 3D L/NL power spectrum
amplitude + shape of 2D spectra
with respect to , quintessence modifies
Quintessence by cosmic shear. IIQuintessence by cosmic shear. II
2( ) ( ) ,( )
m
K
P dz q z P k zS z
( ) ( ), [ ( )]Kq z n z S z
NON-LINEAR regime:NON-LINEAR regime: N-body:N-body: ... mappings:mappings: stable clustering, halo model, etc.:
NLPm(k,z) = f[LPm(k,z)] e.g. Peacock & Dodds (1996) Smith et al. (2003)calibrated with CDM N-body sim, 5-10% agreementHuterer & Takada (2005)
QCDM QCDM GR GR
Poisson eq.
2
2
( )( , ) ( , )
( )
LIN LINm m lss
lss
D zP k z P k z
D z
...normalization to high-z (CMB):normalization to high-z (CMB):
the modes k enter in non-linear regime ( (k)1 ) at different time 3D non-linear power spectrum is modified 2D shear power spectrum is modified by k = / SK (z)
Ansatz:Ansatz: c, bias, c, etc. not so much dependent on cosmology at every z we can use them, provided we use the correct linear growth factor (defining the onset of the NL regime)...
**
Ria
zuelo
& U
zan (
2002
)C
.S., U
z an &
Ria
zuelo
(2
004)
*
* CMB can be taken into account at no cost
Q models:Q models: self-interacting scalar fieldminimally/non-minimally couled to g
* *
*
pipelinepipeline
no fit for power spectrano fit for power spectra
(restricted) parameter space:(restricted) parameter space:Q, , ns, zsource; marginalization over zsource
4( ) /V M 4 212( ) / exp( )V M
0 1 2 3 4 50.0
0.5
1.0
z
n(z) VIRMOS
deep wide
wide surveywide survey :: Q - geometrical effects (IPL) Q - geometrical effects (IPL)inverse power law
Peacock & Dodds (1996)
CFHTLS wide/22deg2 (real datareal data)
CFHTLS wide/170deg2 (synthsynth)
CFHTLS wide/170deg2 (synthsynth)
top-hattop-hat variance
top-hattop-hat variance
aperture mass aperture mass variancevariance
only scales > 20 arcmin> 20 arcmin
CFHTLS wide/170deg2 (synthsynth)
top-hattop-hat variance
wide survey wide survey :: Q - geometrical effects (SUGRA) Q - geometrical effects (SUGRA)SUGRA
Peacock & Dodds (1996)
CFHTLS wide/22deg2 (real datareal data)
CFHTLS wide/170deg2 (synthsynth)
CFHTLS wide/170deg2 (synthsynth)
top-hattop-hat variance
top-hattop-hat variance
aperture mass aperture mass variancevariance
only scales > 20 arcmin> 20 arcmin
CFHTLS wide/170deg2 (synthsynth)
top-hattop-hat variance
cosmic shear + SNecosmic shear + SNe + CMB+ CMB : Q equation of state : Q equation of state
inverse power lawinverse power law SUGRASUGRA
(ns,zs): marginalized ; all other parameters: fixed
SNe: confirmed literature
TT-CMB: rejection from first peak (analytical (Doran et al. 2000) & numerical)
Mass scale M: indicative
Cosmic shearCosmic shear (real data only):
• IPL: IPL: strong degeneracy with SNe
• SUGRA:SUGRA:
1) beware of systematics! (wl: calibration when combining datasets)
2) limit case: prefectly known/excluded Q model (weakly -dependence)
Van Waerbeke et al. (2006)
VIRMOS-Descart + CFHTLS deep + CFHTLS wide/22deg2 + “goldset”@SNe
Q by cosmic shear Q by cosmic shear : Fisher matrix analysis: Fisher matrix analysis
CFHTLSCFHTLSwide/170wide/170
DUNEDUNE
= real data analysis += real data analysis + reion :: all but (,q,ns) fixed, (reion,zs) marginalized
inverse-power lawinverse-power law
SNeSNe“goldset”
CFHTLSCFHTLSwide/170wide/170
TT @ CMBTT @ CMBWMAP 1yr
•A = 170 deg2
•ngal = 20/arcmin2
SUGRASUGRA
DUNE (pi: A.Réfrégier):DUNE (pi: A.Réfrégier):
wide, shallow surveyoptimized for WL + SNe
• A= 20000 deg2
• ngal = 35/arcmin2
All but (,q) fixed
inverse-power lawinverse-power law
present setup:
conclusions & prospects conclusions & prospects
quintessence at low-zquintessence at low-z by SNe + cosmic shear, using high-z informations (TT-CMB/Cl normalization)
dynamical models of DE (not parameterization): CDMCDM
wide, shallow cosmic shear surveyswide, shallow cosmic shear surveys are suitable
for the first time cosmic shear datadata to this task
NL regime:NL regime: (two) L-NL mappings (caveatcaveat)
Q parameters (seem to) feel only geometry
consistent joint analysis of high-z (CMB) and low-z (cosmic shear, Sne,...) observables no stress between datasets; no pivot redshift
analysisanalysis of realistic (=dynamical) models of DE using severalseveral parametersparameters
other techniquesother techniques: cross-correlations (ISW), 3pts functions, tomography
Work in progress:Work in progress:
pipeline: pipeline: Boltzmann code + lensing code + data analysis by grid method:
in collaboration with: I.Tereno, Y.Mellier , J.-P. Uzan, R. Lehoucq, A. Réfrégier & DUNE team
1.1. + CMB data; 2.2. MCMC analysis (Tereno et al. 2005)
astro-ph/0603158astro-ph/0603158
Thank youThank you
CMB:CMB: TT anisotropy spectrum @ WMAP-1yr initial conditions/
SNe:SNe: “goldset”
cosmic shear:cosmic shear: VIRMOS-Descart VanWaerbeke, Mellier, Hoekstra (2004)Semboloni et al. (2005)
CFHTLS wide/22deg2 & 170deg2 (synth)
0 1 2 3 4 50.0
0.5
1.0
z
n(z) VIRMOS
deep wide
wl observables:wl observables: top-hat variance; aperture mass variance
Riess et al. (2004)
cosmic shear:cosmic shear: by wide-field imager/DUNE-like satellite mission
Hoekstra et al. (2005)
normalization
CFHTLS deep
Q models, datasets & likelihood analysisQ models, datasets & likelihood analysis
(restricted) parameter space:(restricted) parameter space:Q, , ns, zsource; marginalization over zsource
Q models:Q models:
2( ) ( ) ( , )U U d U
/
4( ) /V M 4 212( ) / exp( )V M ;;