peculiar velocity: a window to the dark universe

KIAS cosmology 2008 1

Peculiar velocity: a window to the dark universe张鹏杰（ Zhang, Pengjie)

中国科学院上海天文台Shanghai Astronomical Observatory

Chinese Academy of Science

Based onZPJ, Michele Liguori, Rachel Bean & Scott Dodelson, 2007, PRLZPJ & Xuelei Chen, 2008, PRDBhuvnesh Jain & ZPJ, 2008, PRDZPJ, Hume Feldman, Roman Juszkiewicz, Albert Stebbins, 2008, MNRASZPJ, 2008, arxiv: 0802.ZPJ, Rachel Bean, Michele Liguori, & Scott Dodelson, 2008, arxiv:0809.


The dark universe

The visible world

Dark matter?

Dark energy?

Modified gravity?


Windows to the dark universe

z ~ 1000 z ~ 30 z ~ 6 z ~ 0z ~ 1000 z ~ 30 z ~ 6 z ~ 0z ~ 1000 z ~ 30 z ~ 6 z ~ 0

21cmSoon to detect


lensing

SNe Ia

BAOcluster abundance

peculiar velocity

CMBWe are able to put everything together to reconstruct the elephant!

the dark universe


The dark energy task force recommends fourprobes of the expansion: SN and BAOprobes of structure growth: weak lensing and cluster abundance

Figure of merit for stage IV space projects

Peculiar velocity as the fifth!!


• Matter distribution in our universe is inhomogeneous

• Gravitational attraction arising from inhomogeneity perturbs galaxies and causes deviation from the Hubble flow

v

r

v

r

peculiarvelocity

v=Hr v=Hr


What makes peculiar velocity special and important to probe the dark universe?

At scales larger than galaxy clusters, only respond to gravity

In linear regime, honest tracer of matter distribution

Necessary for the complete phase-space description of the universe

dt

vd

dt

av)d（

01

vadt

d


GREAT attractor(s), with far more mass than expected, must exist in order to pull the Milky way at ～ 600 km/s with respect to CMBSuch gigantic structures should be no coincidence, if we believe in the cosmological principle

Great attractor

Shapely concentration

Early applications of peculiar velocity: (1) A brave new world with gigantic structures


Early applications of peculiar velocity: (2) road to the standard LCDM cosmology

• Largely based on peculiar velocity measurements of local and nearby galaxies, some cosmologists (e.g. Jim Peebles) argued that the the cosmological constant may exist and account for ~80% of the energy budget of the universe, in early 80s.


How to measure peculiar velocity?Traditional method

v

r

Subtract the Hubble flow to obtain the peculiar velocity

v=Hr

Measure the recession velocity from the redshift

Measure the distance through FP,TF,FJ,SN, etc.

Error increases linearly with distance.Can not apply to cosmological distances


New probes of large scale peculiar velocity which do not rely on distance indicators

These new probes of large scale peculiar velocity do not rely on subtracting the Hubble flow, so are applicable to z~1

• Redshift distortion (bonus of BAO surveys)

• The kinetic Sunyaev Zel'dovich effect of galaxy clusters

• Type Ia supernovae at z<~0.5


)()1)(()( 22

H

kuFukPkP g

sg

)(ln

ln ; z

ad

Ddf

b

fm

g

Redshift distortion and cosmology

Peacock et al. 2001

Kaiser effectinduced by large scale coherent infall

Finger of Godinduced by small scale random motion


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


BAO surveys (Refer to the WiggleZ talk) are reshaping the field of redshift distortion measurement!(1) the expansion from BAO and(2) the growth rate from redshift distortion

Amendola, Quercellini &Giallongo 2004

BAO

BAO+RD

RD helps to improve dark energy constraints

However, the improvementis not significant for future big surveysBecause if smooth dark energy, BAO and RD basically probes the same H(z)


Strong tests on gravity

Yun Wang 2007See also Eric Linder 2007

DE and MG can have nearly degenerate H(z)

But their structure growthrate can be very different


Testing the consistency relation through spectroscopic redshift surveys

Acquaviva et al. 2008

=0 in GR+smooth dark energy

BAO+CMB

Redshift distortion


Physics behind the consistency relation

02

33/32

200

22

2

aH

H

aaH

dadH

da

d

da

d

2 ( ) 8 G

= / 1

18

2visible

uv uv uv uvR g R g GT CDMuvT


~

1

~

~ ~

( ) gravity:

DGP gravity: 1

TeVeS: ( ,other fields)

R

Geff f

eff

eff eff uv

f R G

G

G G g

/ 1 2DE: ( ) 12 (1 )

DGP: = (z) 1

k G w

2 ( ) 8 G

=effG

)10(1 5 O

ZPJ et al. 2007; Amendola et al. 2007Caldwell et al. 2007; Bertschinger& Zukin. 2008

Also Uzan 2006Hu & Sawicki 2007


Testing the (generalized) Poisson Equation

)d 2s＝（－）W( ,

2 ( ) 8 G

=

Gravitational lensing

v H

f

fH

/

from peculiar velocity

?

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


Weak lensingCosmic shear

DES, LSST, SNAP, Euclid, SKA, etc.Cosmic magnification

SKACosmic microwave and 21cm backgrounds

Large scale peculiar velocities (bulk flows)Galaxy redshift distortion from spectroscopic redshi

ft surveysStage III: LAMOST, BOSS, WFMOS, etc.Stage IV: ADEPT, Euclid, HSHS, SKA, etc.

Other methods (KSZ, SNe Ia.... )


A discriminating probe of gravity

•No dependence on galaxy bias

•No dependence on the shape and amplitude of the matter power spectrum, in the linear regime

•Scale independent in LCDM and QCDM, whose amplitude is completely fixed by the expansion rate

•Contains smoking guns of modifications in gravity and particle physics•Changes in the amplitude•Violation of the scale independence

22

( ) ( ) 1gG

g

PE

P

Poisson equation!

Linear density growth rate

galaxy-galaxy lensing

redshift distortion

f


LCDMf(R)DGPMOND

ZPJ, Liguori, Bean & Dodelson2007, PRL

• 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)!


One can further construct an estimator of η≡-Φ/ΨLensing: Φ-Ψ; Peculiar velocity: Ψ

ZPJ et al. 2008b

Velocity measurement forecasted for SKA

?


ZPJ et al. 2008b

•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 Omeag_m

SKA forecast

DGP

MONDTeVeS

dark energy with anisotropic stress


Layers of assumptions/approximations

2 412( , ) ( 2 ..) ( )s

g g gv vP k u P u P u P F ku

2 412( , ) ( 2 ) ( )s

g g gv vP k u P u P u P F ku

e.g. Matsubara 2007

e.g. Tegmark et al. 2002,2004Scoccimarro 2004ZPJ et al. 2007, ZPJ 2008

deterministic bias

e.g. Peacock et al. 2001;Guzzo et al. 2008;Amendola et al. 2004Linder 2007;Wang 2007More uncertainties:

•Linear evolution•Light cone•distant observer assumption•.....

F: Lorentz or Gaussian

2 212( , ) (1 ) ( ) ( )s

g gP k u u P k F ku

scale independent galaxy bias

e.g. Acquaviva et al. 2008


On real data

• Tegmark et al. 2002 on 2dF

• Tegmark et al. 2004, on SDSS

One can measure the gg,gv,vv power spectra simultaneously.

errors (vv)>errors(gv)>errors(gg)


Forecast for future surveys the Square Kilometer Array (SKA) as an example

Future surveys can detect (1) stochasticity in galaxy bias (2) scale dependence in galaxy bias

We are no longer able to use the usual Kaiser formula.

At such stage, more detailed check against current RD model and/or more accurate RD modeling are required

Other velocity probes?

ZPJ 2008

SKA, ADEPT, HSHS, Euclid


CMB photonfree electron

scattered CMB photon

pgksz vMS

vp: bulk velocityscattering probability

The kinetic Sunyaev Zel'dovich effect of galaxy clusters

Recently, the South Pole Telescope (SPT) has for the first time discovered clusters, through the thermal SZ effect!


Measuring velocity from KSZ

Allows statistical measurement of vp (vp power spectrum)

Measure vp of individual clusters

• Requires other measurements to infer Mg

– Thermal SZ to have MgT– X-ray to have T

ZPJ et al. 2008, MNRAS

pgksz vMS

Haehnelt & Tegmark 1996;Kashlinsky & Atrio-Barandela 2000; Aghanim et al.2001; Atrio-Barandela et al. 2004; Holder 2004

Statistical errors>systematical errors


SNe Ia as cosmic speed censors at intermediate redshift ~0.5

ZPJ & Chen, 2008, PRD

Peculiar velocity causes fluctuations in SNe Ia flux

Already allow velocity measurement at z<0.1

At z>0.1, lensing dominates over velocity

Measure the 3D power spectrum ofSNe Ia flux, in which noise can be significantly suppressed

signal (velocity)

Noise (lensing)

z=0.5


If 3 or more independent LSS variables can be measured, modified gravity models can be unambiguously discriminated from DE/DM

Weak lensingPeculiar velocity......

Bhuvnesh Jain & ZPJ, 2008, PRD

Peculiar velocity is indispensable for ultimate discrimination between dark energy and modified gravity

One necessary condition for DE to mimic MG

peculiar velocity: a window to the dark universe

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