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)

~

1

~

~ ~

( ) gravity:

DGP gravity: 1

TeVeS: ( ,other fields)

R

Geff f

eff

eff eff uv

f R G

G

G G g

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 conference7

A sensitive measure of gravity

Guzzo et al. 2008

Acquaviva et al. 2008

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

)d 2s＝ （ － ）W( ,

2 ( ) 8 G

2009 XuGuangqi-Galieo conference 19

=

Gravitational lensing

v H

f

fH

/

from peculiar velocity

?

Galaxy redshifts to recover redshift information (2D ->3D)

2009 XuGuangqi-Galieo conference 20

LCDMf(R)DGPMOND/TeVeS

ZPJ et al. 2007

• EG 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 conference21

ZPJ et al. 2008

•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. (EG of DGP is very close to that of LCDM.)

•eta and E_G are complementary

•DGP with high Omega_m

SKA forecast

DGP

MONDTeVeS

dark energy with anisotropic stress

One can further construct an estimator ofLensing: Φ-Ψ; Peculiar velocity: Ψ

Thanks