XXIII Colloquium IAP July 2007 Extended quintessence by cosmic shear Carlo Schimd DAPNIA/SPP, CEA Saclay  LAM Marseille

Beyond  CDM Beyond  CDM: do we need it? Copernican principle + GR/Friedmann eqs + {baryons, , } + DM ok w.r.t. CMB + SnIa + LSS + gravitational clustering + Ly-alpha... Dark energy  H(z) - H r+m+GR (z)    GR : not valid anymore? f(R) /scalar-tensor theories, higher dimensions (DGP-like,...), TeVeS,... ? backreaction of inhomogeneities, local Hubble bubble, LTB,...  Other (effective) “matter” fields violating SEC? quintessence, K-essence, Chaplygin gas / Dirac-Born-Infeld action, naturalness pb:      cr,0  GeV 4   EW – QCD - Planck 2. coincidence pb:    m,0 ( 10 6 GeV 4 ) EW or ( GeV 4 ) QCD or ( GeV 4 ) Planck Alternative :  Cosmological constant ...but dufficult to explain on these basis in any case:  has to be replaced by an additional degree of freedom  1  JP Uzan’s talk

Scalar-tensor theories – Extended Quintessence 2 Standard Model~ quintessence hyp: dynamically equivalent to f(R) theories, provided f ’’ (  )  0 F(  ) = const F(  ) = const : GR F(  )  const F(  )  const : scalar-tensor anisotropy stress-energy tensor:   modified background evolution: F (  )  const distances, linear growth factor: e.g. Wands 1994   G cav  const  space-time variation of G and post-Newtonian parameters  PPN and  PPN :

Aim 3  Three runaway models: Gcav,  _PPN, cosmology  Weak-lensing/cosmic-shear: geometric approach, non-linear regime  2pt statistics: which survey ? very prelilminary results  Concluding remarks Local (= Solar-System + Galactic) – cosmic-shear joint analysis deviations from LCDM by Outline:  Sanders’s & Jain’s talks

Three EQ benchmark models 1.exp coupling in Jordan/string frame : 2.generalization of quadratic coupling in JF : 3.exp coupling in Einstein frame: Non-minimal couplings: + inverse power-law potential: Gasperini, Piazza & Veneziano 2001 Bartolo & Pietroni 2001 (runaway dilaton) idea: models assuring the attraction mechanism toward GR (Damour & Nordvedt 1993) and stronger deviation from GR in the past (...dilaton)   + 2 parameters well-defined theory 4

Local constraints: G cav and  PPN ok Range of structure formation cosmic-shear Cassini :  PPN -1=(2.1  2.3)10 -4 G cav  PPN  = 10 -4,  = 0.1  = 10,  = 1 B=0.008

Cosmology: D A & D + deviation w.r.t. concordance LCDM  = b = 5   = 0.1 b = 5   = 0.1 b =  = b = 0.1  = 0.1 b = 0.1  = 0.1 b = 0.2  = 0.5  = 5   = 1.0  = 5   = 1.0  =  D A /D A  D + /D +  = 10 The interesting redshift range is around , where structure formation occurs and cosmic shear is mostly sensitive  Remarks: For the linear growth factor, only the differential variation matters, because of normalization  Pick and for tomography-like exploitation?  6

Weak lensing: geometrical approach      geodesic deviation equation Solution: g  =  g   + h   order-by-order C.S. & Tereno, th 1st Sachs, 1962 Hyp: K = 0 7

8 hor...gauge pb hor  :  EQ  GR  modified Poisson eq. allowing for  fluctuations extended Newtonian limit (N-body): Perrotta, Matarrese, Pietroni, C.S matter perturbations:...  matter fluctuations grow non-linearly, while EQ fluctuations grow linearly (Klein-Gordon equation) C.S., Uzan & Riazuelo 2004  Non-linear regime no vector & tensor ptbs

Onset of the non-linear regime Let use a Linear-NonLinear mapping... NL P m (k,z) = f [ L P m (k,z)] e.g. Peacock & Dodds 1996 Smith et al  Ansatz:  Ansatz:  c, bias, c, etc. not so much dependent on cosmology  at every z we can use it, but......normalized to high-z (CMB):...and using the correct linear growth factor : the modes k enter in non-linear regime (  (k)  1 ) at different time  different effective spectral index 3 + n_eff = - d ln   (R) / d ln R different effective curvature C_eff = - d 2 ln   (R) / d ln R 2     Q =  m -1 late growth  LCDM 9

 Map 2  : which survey? deviation from LCDM Remark: exp  2  exp  JFEF  = 0.5  = 5   = 1.0  = 5   = 1.0  = z_mean = 0.8, z_max = 0.6 z_mean = 1.0, z_max = 0.6 z_mean = 1.2, z_max = 1.1  =  = 5   = 0.1  = 5   = 0.1  = To exploit the differential deviation, a wide range of scales should be covered For a given model, a deep survey globally enhances the relative deviation   10 work in progress

 = 10 “Focused” tomography: deviation from LCDM work in progress 2%  D A /D A  D + /D + >20% top-hat n > (z): z_mean = 1.2, z_max = 1.1 top-hat n < (z): z_mean = 0.8, z_max = 0.6 R = R / R_ LCDM

NL regime: adapted L-NL mapping (caveat), but N-body / some perturbation theory / analytic model (e.g. Halo model) are required  consistent pipeline allowing for joint analysis of high-z (CMB) and low-z (cosmic shear, Sne, PPN,...) observables  no stress between datasets  geometric approach to weak-lensing / cosmic shear allows to deal with generic metric theories of gravity (e.g. GR, scalar-tensor) three classes of Extended Quintessence theories showing attraction toward GR  no parameterization, but well-defined theories   Concluding remarks To e done: 1.Fisher matrix analysis (parameters)  Bayes factor Heavens, Kitching & Verde (2007) (models) 2.“Focused” tomography: error estimation 3.Look at CMB,...  astro-ph/0611xxx Thank you including vector and tensor perturbations (GWs) in non-flat RW spacetime  Measuring deviation from LCDM: it seems to be viable if looking over a wide range of scales, from arcmin to > 2deg ( + mildly non-linear / linear regime)  “Focused” tomography: it seems (too?!) promising 