1. Tracking quintessence by cosmic shear constraints from VIRMOS-Descart and CFHTLS and future prospects May 2006 workshop PNC – IPNL Lyon In collaboration with: I.Tereno, J.-P.Uzan, Y.Mellier, (IAP), L.vanWaerbeke (British Columbia U.),... Carlo Schimd DAPNIA / CEA Saclay & IAP Based on: astro-ph/0603158

2. Dark energy: parametrization.vs. field theory inspired {baryons, , } + DM + GR {baryons, , } + DM + GR alone cannot account for the cosmological dynamics seen by CMB + LSS + SNe +...    GR : not valid anymore? Other “matter” fields? Cosmological constant? Dark energy Dark energy  H(z)-H r+m+GR (z) 1/0 approach: 1/0 approach: parameterization of w(z)  departures from  CDM limitation in redshift ? pivot redshift z p : 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) Which class ?  Physics-inspired approach:  high-energy physics ?!  w : full redshift range  small # p.  perturbations: consistently accounted for Uzan, Aghanim, Mellier (2004); Uzan, astro-ph/0605313

3. scalar field quintessence: models CMB SNe, WL, n(z) Inverse power law (Ratra-Peebles): » + SUGRA corr. :    1 p.  SUGRA by-product: w(z) and w’(z) at whatever pivot redshift (z p )  z p = 0z p = 0.5 w w’

4. quintessence by cosmic shear  angular distance   angular distance  q(z); 3D  2D projection  growth factor   growth factor  amplitude of 3D L/NL power spectrum   amplitude + shape of 2D spectra with respect to , quintessence modifies 2pts statistics z=1 10% 20% K = 0 cosmic shear = weak lensing by LSS weak lensing by LSS obs gal   statistics, e.g. 

5. non-linear regime  N-body:  N-body:...  mappings:  mappings: stable clustering, halo model, etc.: NL P m (k,z) = f [ L P m (k,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 = / S K (z) no more  ,but incertitude on TT-CMB Cl’s  e.g. Peacock & Dodds (1996) Smith et al. (2003)  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)... calibrated with  CDM N-body sim, 5-10% agreement Huterer & Takada (2005) Q: Q: dependence of 3D NL power spectrum on w Q ? McDonald, Trac, Contaldi (2005)

6. pipeline ** Riazuelo & Uzan (2002) C.S., Uzan & Riazuelo (2004) * They include larger framework: scalar-tensor theories of gravitation / extended Q models * CMB can be taken into account at no cost  Q models:  Q models: inverse power law with/without SUGRA corrections  (restricted) parameter space:  Q, , n s, z source  ; marginalization over z source ** * * *

7. dataset  CMB:  CMB: TT anisotropy spectrum @ WMAP-1yr  initial conditions/  SNe:  SNe: “goldset”  cosmic shear:  cosmic shear: VIRMOS-Descart + CFHTLS deep VanWaerbeke, Mellier, Hoekstra (2004) Semboloni et al. (2005) + CFHTLS wide/22deg2 & 170deg2 (synth)  0.92, 1.0, 0.76 n gal  15, 22, 20 /arcmin 2 area  8.5, 2.2, 22(170) deg 2 I AB  24.5, 26, 26 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

8. cosmic shear data*: effects of L-NL mapping Ratra-Peebles SUGRA * Joint VIRMOS-Descart + CFHTLS deep + CFHTLS wide/22deg2 analysis Peacock & Dodds (1996) Smith et al. (2003) Top-hat shear variance   Peacock & Dodds Smith et al.  

9. wide survey : Q - geometrical effects (RP) Ratra-Peebles Peacock & Dodds (1996) real data CFHTLS wide/22deg2 (real data) synth CFHTLS wide/170deg2 (synth)   top-hat top-hat variance aperture mass variance > 20 arcmin only scales > 20 arcmin synth CFHTLS wide/170deg2 (synth) top-hat top-hat variance

10. wide survey : Q - geometrical effects (SUGRA) SUGRA Peacock & Dodds (1996) real data CFHTLS wide/22deg2 (real data) synth CFHTLS wide/170deg2 (synth)   top-hat top-hat variance aperture mass variance > 20 arcmin only scales > 20 arcmin synth CFHTLS wide/170deg2 (synth) top-hat top-hat variance

11. cosmic shear alone : summary  Two classes of cosmological parameters: other parameters: other parameters: sensible to L-NL mapping Q parameters: Q parameters: not sensible to linear-to-nonlinear mapping  This conclusions holds for both Ratra-Peebles and SUGRA models real data (VIRMOS-Descart + CFHTLS deep + CFHTLS wide/22deg2)  synthetic data (CFHTLS wide/170deg2)   Confirmation of results based on real data joint analysis  Based on top-hat shear variance measurements  Agreement top-hat shear variance – aperture mass variance Compatible with  CDM (  =0), towards n s =0.95 (like WMAP3!)   Analysis of wide scale  reducing the non-linear contamination  confirming Simpson & Bridle (2005)

12. cosmic shear + SNe + CMB: Q equation of state Ratra-PeeblesSUGRA (n s,z s ): 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 shear Cosmic shear (real data only): RP: RP: strong degeneracy with SNe SUGRA: SUGRA: 1) beware of systematics! (wl: calibration when combining datasets) 2) limit case: prefectly known/excluded Q model (weakly  -dependece) Van Waerbeke et al. (2006)

13. cosmic shear & CMB: variance on 8h -1 Mpc ( 8 ) contours follow  8 degeneracy WMAP3 – weak lensing: WMAP3 – weak lensing: stress {h,  reion,normalization,  q } Ratra-Peebles SUGRA Spergel et al. 2006  Check normalization procedure  Check calibration of datasets  Deviations from  CDM ?

14. a remark on constant w z de z acc  de /  m = 0.6/0.4 Spergel et al. 2006 Hoekstra et al. 2006 Astier et al. 2005  w = const

15. Q by cosmic shear: Fisher matrix analysis CFHTLSwide/170  SNAP Like previous data analysis: Like previous data analysis: all but ( ,  q,n s ) fixed, z s marginalized   SNAP  DUNE CFHTLSwide/170 Adding a parameter: Adding a parameter: Like upper plots but  reion marginalized  size, orientation 

16. conclusions & prospects  quintessence at low-z  quintessence at low-z by SNe + cosmic shear, using high-z informations (TT-CMB/Cl normalization)   CDM dynamical models of DE (not parameterization):  CDM wide field surveys  wide field surveys are needed  DUNE, LSST data for the first time cosmic shear data to this task  improvement: improvement: bigger parameter space  1.  1. combining also CMB data (high-z effects of DE) +... ; 2. 2. MCMC analysis; 3. 3. deviation from GR, e.g. EQ  w Q < -1  NL regime:caveat  NL regime: L-NL mappings (caveat) Martin, C.S., Uzan (2005) some parameters (n S ) are sensible to L-NL mappings (  integrated effect ?), Q parameters feel only geometry  Tereno et al. (2005) deep surveys  deep surveys help to exploit the linear regime  SKA Schneider (1999); Chang, Réfrégier, Helfand (2004)  consistent joint analysis of high-z (CMB) and low-z (cosmic shear, Sne,...) observables  no stress between datasets; no pivot redshift analysisseveralparameters analysis of realistic (=dynamical) models of DE using several parameters other techniques other techniques: cross-correlations (ISW), 3pts functions, tomography  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    

17. Thank you

18. Q by cosmic shear: Fisher matrix analysis All but ( ,  q ) parameters: fixed  SNe “goldset” CFHTLS wide: TT @ CMB WMAP 1yr A = 170 deg 2 Ratra-PeeblesSUGRA n gal = 20/arcmin 2 DUNE-like: A= 20000 deg 2 n gal = 35/arcmin 2