Post on 19-Dec-2015
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
• 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