Constraining Constraining dark energydark energy from from large scale structureslarge scale structures

Yipeng Jing

Shanghai Astronomical Observatory

Perlmutter et al. 1999, Riess et al. 1998

The “Hubble diagram” of Type Ia supernovae tells us that matter is not enough…

log(

Dis

tanc

e d L

)lo

g(D

ista

nce

d L)

dL (1 z)c dz'

H(z',m , )0

z

Redshift of spectral lines Redshift of spectral lines

H Ý a

a

a(t)

Luigi Guzzo

Cosmic ConcordanceCosmic Concordance

Large-Scale Structure/Clusters

•m =0.25-0.3

Cosmic Microwave Background

• Flat geometry (TOT=1)

• m ~0.25 > 0

Supernovae

Accelerating expansion

• ~ 1

Altogether (any two of them)

• m ~0.25 ~0.75

1990 Dec Nature, 348,20

Matter (m)

Dark energy (

Today

Size=2 Size=4Size=1/2Size=1/4

If w=-1 and the cosmological constant corresponds to some sort of “quantum zero-point”, then its value today is a factor ~10120 too small, plus it is suspiciously fine-tuned: anthropic argument?

time

Fine-tuning and Cosmic Fine-tuning and Cosmic CoincidenceCoincidence

Fine-tuning and Cosmic Fine-tuning and Cosmic CoincidenceCoincidence

Thus could we have w = w(z) ? --> e.g. quintessence, a cosmic scalar field slowly rolling to the minimum of its potential (e.g. Wetterich 1988), inducing an evolving -1 < w(z) < -1/3. Or more complex interactions between DM and DE (e.g. Amendola 2000; Liddle et al. 2008; He et al.) ?

redshift

z=3 z=1

Observational Probes

• Supernovae M(z)

• Baryonic Acoustic Oscillations (BAO)

• Abundance of rich clusters

• Weak Lensing

• Redshift distortion

SNe Future experiments: JDEM, DES,

PanSTARRS,LSST

BAO: SDSS/2dF, WiggleZ, FMOS, BOSS,Bigboss HETDEX, WFMOS,

PAU

Luminous Red Galaxies ， LRG) two-point CF

. J. Eisenstein et al., Astrophys. J. 619, 178 (2005).

But we need to look at both sides of the But we need to look at both sides of the story…story…

R 1

2g R

8G

c2 T

Add dark energyModify gravity theory [e.g. R f(R) ]

R 1

2g R

8G

c2 T g

“…the Force be with you”

So, the equation of state is not the end of the So, the equation of state is not the end of the story…story…

Cosmic acceleration can also be explained by modifying the theory of gravity [as e.g. in f(R) theories, Capozziello et al. 2005, or in multi-dimensional “braneworld” models, Dvali et al. (DGP) 2000].

The growth equation (and thus the growth rate) depends not only on the expansion history H(t) (and thus on w) but also on the gravitation theory (e.g. Lue et al. 2004)

which has a growing solution:

(x , t) ˆ (x )D(t)

Ý Ý 2H (t) Ý 4G

f d lnD

d lnafrom which we define a growth rate

How to distinguish between these two options, observationally?Growth of linear density fluctuations in the expanding Universe (in GR):

Observational Probes

• Supernovae M(z)

• Baryonic Acoustic Oscillations (BAO)

• Abundance of rich clusters

• Weak Lensing

• Redshift distortion

Clusters:SZA, SPT, DES, ACT, 400d, eROSITA

Weak Lensing: LSST, EUCLID, DES, PanSTARRS

1.1o1.1o simulated shear field by Hamana

()

(+)

Redshift distortion: Bigboss, Vipers, Euclid etc

4 个引力模型 : GR ，f(R) ， DGP ， TeVeS

张鹏杰等提出在宇宙学尺度上检验广义相对论与其

他引力论的新方法

通过通过 EEGG 方法，广义相对论方法，广义相对论在一亿光年尺度上得到了确认在一亿光年尺度上得到了确认

Reyes et al. (Nature,464, 256-258,11 March 2010) 应用我们的 EG 方法分析了 SDSS 星系巡天的数据。

右图即为其主要结果。测量到的一亿光年尺度上的 EG 与广义相对论的预言相符。

该结果基本排除了 TeVeS 修改引力，并有力限制对 f(R) 引力

We also consider the dependence on the information used: the full galaxy power spectrum P(k), P(k) marginalized over its shape, or just the Baryon Acoustic Oscillations (BAO). We find that the inclusion of growth rate information (extracted using redshift space distortion and galaxy clustering amplitude measurements) leads to a factor of 3 improvement in the FoM, assuming general relativity is not modified. This inclusion partially compensates for the loss of information when only the BAO are used to give geometrical constraints, rather than using the full P(k) as a standard ruler. We

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