Constraints on primordial non-Gaussianity from LSS-CMB

cross-correlations

Yoshitaka Takeuchi (Nagoya Univ.)

Collaboration with T.Matsubara and K.Ichiki

6-8, Jun. 2011 @ 竹原理論物理学研究会

Based on arXiv:1005.3492

Outline• Introduction

• Scale-dependent bias

(from primordial non-Gaussianity)

• Cross-Correlation power spectrum

• Constraints on primordial non-Gaussianity

• Summary

Introduction

13.7 Gyr©NASA WMAP TEAM

CMB LSS (Large Scale Structure)

WMAP

Inflation

Quantumfluctuations

Introduction• N-body simulation

– NG significantly influences the structure formation.– Rare objects are even more affected.

Dalal+08

fNL = -5000

fNL = +5000

fNL = +500

fNL = -500

fNL = 0

Large-Scale StructurePrimordial fluctuations

?particles: 5123

box size: 800 h-1 Mpcmass: mp = 2.52x1011 h-1Msun 375h-1 Mpc

80h

-1 M

pc

Φ(x) = ΦG(x) + fNL(ΦG2 (x) - <ΦG(x)2>)

Introduction• Current constraints on NG (local type)

– with scale-dependent bias from ….

NVSS:• fNL = 74 ± 40

SDSS (QSO):• fNL = 59 ± 21

SDSS (LRG):• fNL = 153 ± 95

– CMB bispectrum from WMAP-7yr Komatsu+10• fNL = 32 ± 21

– Planck will measure fNL with error level ΔfNL 〜 1-3.

scale-dependent bias: bNG = bG + Δb

combined result: fNL = 48 ± 20Xia+11

Dalal+08, Slosar+08, Afshordi+08

Motivation• To constrain on primordial non-Gaussianity (NG)

from Large-Scale Structure (LSS):– △ small-scale: non-linearity dominant.– ◎ large-scale: scale-dependent bias for local type NG.

• One of the key-points for the tighter constraint:– How do we break down the uncertainty of bias?

⇒ gravitational lensing is good tracer of the matter distribution.

• CMB: T, E, ψ• Galaxy distribution: g• Galaxy lensing: γ

CMB lensingprevious works: TT, EE,TE, gg, Tg

future survey: TT, EE,TE, gg, Tg + ψψ, Tψ, ψg + γγ, Tγ, γg

Introduction• CMB lensing

– good trace of large-scale structure (matter distribution).– 4σ detection by ACT. Das+11– more precise observation can be expected by Planck,

ACTPol, etc.

ACT (Atacama Cosmology Telescope)

Scale-dependent bias• Let’s derive the bias parameter in the presence of

the local type NG. Dalal+08

• Local type NG

• Laplacian of Φ

• ▽φ = 0: we are interested in the density peak region whereφis also maximum.

• relate the ▽2Φ with the density field by Poisson equation.

cubic type => Yokoyama-san’s talk

Scale-dependent bias• relation between NG density field δNG and Gaussina

density field δ

– density field is modified by – the number of the regions whose overdensity exceed δc (halos)

increase of decrease.

• if density field is Gaussian, the presence of ‘background’ density field boosts the ‘peak’ overdensity.

Peacock (1990)background

δ ：density fieldδc

Kaiser 1984

modulatin of threshold δc by NG

Scale-dependent bias• due to the NG, ‘peak’ height δpk is enhanced by the long-

wavelength curvature perturbation by

• If we focus on the peaks near threshold, δpk 〜 δc, the amount of enhancement becomes

• halo density:

• correction to the bias:

– using: b = bL + 1

• NG mass function– NG-pdf can be constructed from the cumulants with

Edgeworth Expansion:

NG-pdf = Gaussian-pdf × (1 + deviation)

• Effective bias– From galaxy imaging survey, we can not know mass for

each galaxy. – We know only averaged bias.

LoVerde+08, Desjacques+09

mass function

bias

Mthobs

• Effective bias– the scale-dependence appear in large scale: Δb 1/k∝ 2

– NG correction has redshift dependence: Δb 1/D(z)∝

wave number ： k [h /Mpc]

beff (

k, z

)

large scale small scale

z =0

z =1

z =2z =3

thin line ： fNL = 0

thick line: fNL = 100

Cross-correlation power spectrum• T: CMB Temperature• E: E-mode Polarization • ψ: CMB lensing potensial

• g: Galaxy distribution

• γ: Weak lensing (cosmic shear)

γ

• We think that gravitational lensing may be good tracer of dark matter halo without uncertainty of galaxy bias.• Our analysis includes all auto- & cross-correlations.

LSSCMB

©NASA WMAP TEAM

Future Survey Projects• LSS (Large-Scale Structure) survey

HSC (Hyper Suprime-Cam) survey area: 2,000 deg2, mean redshift: zm~1.0

While…LSST (Hyper Suprime-Cam)

survey area: 20,000 deg2, mean redshift: zm~1.2

© Subaru HSC Team

ΔfNL 〜 1-3

Future Survey Project• CMB experiments

ACTPol: (2012? 〜 )upgrading ACT for observation of polarization

PLANCK: on observing just now

■There are overlap regions between grand-base observations. cross-correlation between HSC & ACTPol

■Current results: the improvements by combining CMB experiments WMAP + ACT (Dunkley et al. 2010), WMAP + ACBAR (Reichardt et al. 2009)

© ESA, ACT Team

Cross-correlation power spectrum• galaxy-galaxy auto-correlation

S/N: Signal-to-Noise ration

signature

of NG

• most of the contribution for constraing of fNL comes from gg auto-correlation.

• the effect of NG through scale-dependent bias appears on small-l region(large-scale).

• The key point of putting strict constraint on fNL is wide survey area.

Cross-correlation power spectrum• Tg: CMB T-galaxy cross-correlation

S/N: Signal-to-Noise ration

• The signature of NG is dominated by error, which almost comes from cosmic variance.

• Improvement by CMB experiment does not expected.• The key point is galaxy survey region.

• We can not expect large S/N value.

Cross-correlation power spectrum• For galaxy-CMB lensing cross-correlation, some

improvement by more sensitive CMB experiments can be expected.

• Both cases, larger S/N value can be expected then Temperature-galaxy cross-correlation.

gγ: galaxy – weak lensinggψ: galaxy – CMB lensing

Constraints on primordial NG■Contribution of lensing information

logM

thob

s: b

ias

■Lensing information determines bias parameter.

＝＞ break degeneracy between fNLand Mthobs .

■Combing CMB lensing:ψ and galaxy lensing:γ improves the constraint.

■Planck + ACTPol case constraints the parameters more tightly.

Planck only Planck + ACTPol

Planck + HSC

fNL

Planck + ACTPol + HSC

more sensitive to CMB (T, E, ψ)

fNLlo

gMth

obs:

bia

s

Constraints on primordial NG■Contribution from each cross-correlations.

Red ：

CMB + gg + ψψ + γγ Green ：

CMB + gg + ψψ + γγ + ψg Blue ：

CMB + gg + ψψ + γγ + ψγAqua ：

CMB + gg + ψψ + γγ + γgYellow ： all information

■galaxy lensing-galaxy(γg) contributes the most !! CMB lensing trace the high-z information of LSS, comparing with galaxy

lensing.

logM

thob

s: b

ias

fNL

HSC + Planck + ACTPolCMB = TT + EE + TE

CMB lensing-galaxy

CMB lensing-galaxy lensing

galaxy lensing-galaxy + ψg

+ γg

+ ψγ

• By tomography analysis,

– similar behaviors to previous case (without tomography) can be seen.

– the error will reach

ΔfNL 〜 5

Summary• Primordial NG of the local type predicts the scale-

dependent bias.

• We estimate the accuracy of parameter determination including all cross-correlations.

• On the constraint of fNL from power spectra, the contributions of the cross-correlations can not be negligible.

• Cross-correlations break the degeneracy between fNL & bias parameter.

• Not only future galaxy surveys but CMB experiments will improve the constraints on fNL.

• For application for other Observations– Galaxy power spectrum v.s. Cluster counts

• effect of NG:

Galaxy < Cluster.• samples :

Galaxy > Cluster.

mass function

bias