XXIII Colloquium IAP July 2007

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

2.  in any case: L has to be replaced by an additional degree of freedom Beyond LCDM: do we need it?  JP Uzan’s talk  Dark energy  H(z) - Hr+m+GR(z) Cosmological constant  Copernican principle + GR/Friedmann eqs + {baryons, g, n} + DM ok w.r.t. CMB + SnIa + LSS + gravitational clustering + Ly-alpha ... ( 106 GeV4 )EWor ( 10-3 GeV4 )QCDor ( 1076 GeV4 )Planck ...but dufficult to explain on these basis 1. naturalness pb: rL = WL rcr,0  10-47 GeV4  rvac @ EW – QCD - Planck 2. coincidence pb: WL  Wm,0  Alternative : Other (effective) “matter” fields violating SEC? quintessence, K-essence, Chaplygin gas / Dirac-Born-Infeld action, ...  GR : not valid anymore? f(R) /scalar-tensor theories, higher dimensions (DGP-like,...), TeVeS, ...  ? backreaction of inhomogeneities, local Hubble bubble, LTB, ...  Beyond LCDM 1

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

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

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

6. Local constraints: Gcav and gPPN Cassini : gPPN-1=(2.12.3)10-4 Gcav gPPN ok • = 10, a = 1 B=0.008 ok x = 10-4,a = 0.1 Range of structure formation cosmic-shear x = 10-4,a = 0.1

7. Cosmology: DA & D+ deviation w.r.t. concordance LCDM DDA/DA DD+/D+ b = 10 • = 10-3 b = 510-4 • = 0.1 b = 510-4 • = 0.1 b = 10-3 • = 0.5 B = 510-3 • = 1.0 B = 510-3 • = 1.0 B = 10-2 • = 10-3 b = 0.1 • = 0.1 b = 0.1 • = 0.1 b = 0.2 Remarks:  The interesting redshift range is around 0.1-10, where structure formation occurs and cosmic shear is mostly sensitive  For the linear growth factor, only the differential variation matters, because of normalization  Pick and for tomography-like exploitation? 6

8. 0th 1st C.S. & Tereno, 2006 Weak lensing: geometrical approach k(l), g1(l), g2(l): geodesic deviation equation Sachs, 1962 Solution: gmn= gmn+ hmn order-by-order Hyp: K = 0 7

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

10. ...normalized to high-z (CMB): late growth a  LCDM ...and using the correct linear growth factor : the modes k enter in non-linear regime ( s(k)1 ) at different time   different effective spectral index 3 + n_eff = - d ln s2(R) / d ln R WQ = Wm -1 different effective curvature C_eff = - d2 ln s2(R) / d ln R2  Onset of the non-linear regime Let use a Linear-NonLinear mapping... e.g. Peacock & Dodds 1996 Smith et al. 2003 NLPm(k,z) = f[LPm(k,z)] • Ansatz:dc, bias, c, etc. not so much dependent on cosmology  at every z we can use it, but... 9

11. Map2 : which survey? deviation from LCDM work in progress JF EF z_mean = 0.8, z_max = 0.6 z_mean = 1.0, z_max = 0.6 z_mean = 1.2, z_max = 1.1 • = 10-3x = 510-4 • = 0.1 x = 510-4 • = 0.1 x = 10-3 • = 0.5 B = 510-3 • = 1.0 B = 510-3 • = 1.0 B = 10-2  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  Remark: exp(x j2)  exp(x j) 10

12. b = 10 DDA/DA DD+/D+ “Focused” tomography: deviation from LCDM work in progress top-hat var. @ n>(z): z_mean = 1.2, z_max = 1.1 top-hat var. @ n<(z): z_mean = 0.8, z_max = 0.6 R = R / R_LCDM >20% 2%

13. Concluding remarks 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  astro-ph/0611xxx including vector and tensor perturbations (GWs) in non-flat RW spacetime  consistent pipeline allowing for joint analysis of high-z (CMB) and low-z (cosmic shear, Sne, PPN, ...) observables  no stress between datasets  NL regime: adapted L-NL mapping (caveat), but N-body / some perturbation theory / analytic model (e.g. Halo model) are required  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  To e done: Fisher matrix analysis (parameters)  Bayes factor analysis @ Heavens, Kitching & Verde (2007) (models) “Focused” tomography: error estimation Look at CMB, ...  Thank you