 Acceleration of Universe  Background level  Evolution of expansion: H(a), w(a)  degeneracy: DE & MG  Perturbation level  Evolution of inhomogeneity: G(a), G(a, k), Phi, Psi…  Smoothing energy component or modified gravity?  Scalar field  F(R), DGP, TeVeS,

 Growth of LSS  Expansion: H(a)  consistency relation: H_growth vs. H_expansion  Metric perturbation:

 Modified Gravity  H(a)  Modified Poisson equation.  G_eff  Parametrization  Growth index (scale-independent)

 convergence power (cross) spectrum  rich information (power spectrum, cross-spectrum) ‏  photo-z error

 standard ruler  Spectroscopic survey  δ field  Growth factor G(z)  v field  (redshift distortion)  β~ dlnG/dlna

2009 XuGuangqi-Galieo conference 7 A sensitive measure of gravity Guzzo et al Acquaviva et al Spectroscopic redshift surveys Measure beta from the anisotropy Measure galaxy bias Obtain f Current measurements

 Standard Candle  variation of SN peak L (after the standardization) ‏  photo-z error (without spectrum) ‏  z-dependent peak L (e.g. SN evolution, extinction) ‏

 mass of clusters are not measured directly (except for WL) ‏  complex baryon physics (hydrodynamics, galaxies formation) ‏  SZ flux decrement, X-ray temperature, gas mass  mass selection function

 number distribution  angular density

 BAO  Spectroscopic survey  Photometric survey

 Supernovae  200 SNIa/year/deg^2 available for z<1.2 (limit for ground experiment) ‏  SN1: 50 /y/deg^2  SN2: 100 /y/deg^2  photo-z error  N_c: # of spectra for calibration  Systematics (Nuisance parameters) :  absolute magnitude  quadratic offset

 Weak Lensing (same as Sun lei & Zhao Gongbo) ‏

 Clusters Count

 Genus  Gaussian fluctuation:  3D (δ)  2D (weak lensing, κ)

 Resistant against:  Bias, redshift distortion, weak nonliearity.  In GR  Invariant amplitude.  Standard ruler  In MG  Introduce new scale-dependence  time-varying  Complementary to growth rate of matter fluctuation.  Sensitive to scale-dependent modification at sub-horizon scale.

 Fisher calculation:

Testing the (generalized) Poisson Equation 2009 XuGuangqi-Galieo conference 19 = Gravitational lensing from peculiar velocity ? Galaxy redshifts to recover redshift information (2D ->3D)

2009 XuGuangqi-Galieo conference 20 LCDM f(R) DGP MOND/TeVeS ZPJ et al E G will be measured to 1% level accuracy within two decades Promising to detect one percent level deviation from general relativity+canonical dark energy model (if systematics can be controlled)!

2009 XuGuangqi-Galieo conference 21 ZPJ et al eta can be measured to 10% accuracy. Errors in eta is larger than errors in E_G Even so, eta can have stronger discriminating power, in some cases. η of DGP differs significantly from that of LCDM. (E G of DGP is very close to that of LCDM.) eta and E_G are complementary DGP with high Omega_m SKA forecast DGP MOND TeVeS dark energy with anisotropic stress One can further construct an estimator of Lensing: Φ-Ψ; Peculiar velocity: Ψ

Thanks