2014/12/10 CosPA2014@Auckland, New ZealandConstraining
primordial non-Gaussianity
via multitracer techniquewith Euclid and SKA
YAMAUCHI, Daisuke(RESCEU, U. Tokyo)
DY, K. Takahashi, M. Oguri, PRD90 083520 ,1407.5453

Plan
1.Brief introduction
 Primordial non-Gaussianity
 Scale-dependent bias

2.Multitracer technique
3.Results
4.(Future plan)

Main Message
We can test the extremely small primordial
non-Gaussianity at the level of σ(fNL)=O(0.1)
with Euclid and Square Kilometre Array (SKA).
EuclidSquare Kilometre ArrayWhat’s Primordial non-Gaussianity?
 Non-Gaussian initial fluctuations arise in several scenariosof inflation.

 Even the simplest model predicts small but non-vanishing fNL of O(0.01).

 PNG has primarily been constrained from the bispectrum in
CMB temperature fluctuations.

• WMAP : σ(fNL) < 100[Bennet+, 2013]• Planck : σ(fNL) < 10[Planck collaboration, 2014]• Ideal[Komatsu+Spergel, 2001]: σ(fNL) ~ 3

PNG in Large Scale Structure Luminous sources such as galaxies must be most obvious tracers of
the large scale structure.
 The galaxy density contrast δgal is linearly related to the underlying
dark matter density contrast δDM though the bias bh:

 In the Gaussian case, the bias is scale-invariant : bh=bh(M,z).

PNG in Large Scale Structure Primordial non-Gaussianity induces the scale dependent-biassuch that the effect dominates at very large scales:[Dalal+(2008), Desjacques+(2009)]

fNL=+100fNL=+500

fNL=-100fNL=-500[Dalal+(2008)]

 Galaxy surveys can effectively constrain fNL to the levelcomparable to CMB temp. anisotropies.

(amplitude)

Pgalaxy= (bG+Δb)2PDMΔbbG

Pgalaxy= (bG)2PDM

PDM

1/(scale)Accessing ultra-large scalesDifficulties in cosmology
 Nonlinear evolution of density perturbations
 Baryonic astrophysical process

Let us consider the ultra-large scales to avoid
these difficulties !
[Perturbations can be safely treated in linear-regime.
& There would be no baryonic process.]

Ultra-large scales v.s. cosmic variance Measuring large scales has the advantage ofaccessing the non-Gaussianity , but…
Constraints is limited due to cosmic variance (CV)[Due to the lack of enough independent measurements on large scales]

Multitracer technique [Seljak(2009)] :A method to reduce CV using multiple tracers
with different biases

[Seljak (2009)]

Multitracer technique：The availability of multiple tracers with the different biases allows
significantly improved statistical error in the measurement of ratioof biases.
All galaxy samples

Shot noise

Pgal,obs=(btot)2 P + 1/Ntot

Ntot, δgal = btot δLight gal.

Heavy gal.

Nlδgal,l = bl δNhδgal,h= bh δ・・・(bl)2 P + 1/Nl

bl bh Pbl bh P(bh)2 P + 1/Nh

[Seljak (2009)]

Multitracer technique：The availability of multiple tracers with the different biases allows
significantly improved statistical error in the measurement of ratioof biases.
σ(ln Pgal) ~ 1/2 = const.
All galaxy samples(Ntot→∞)

Ntot, δgal = btot δLight gal.

Heavy gal.

Nl
δgal,l = bl δNhδgal,h= bh δ

Limited due to CV!

・・・σ(bh/bl) ~ (Nl-1 + Nh-1)1/2(Nl, Nh→∞)
There is no fundamental limit!

amplitude

bhbh/blbl
Shape of CV noise is same…

Pgal,h= (bh)2PDM
Pgal,l= (bl)2PDM

PDM
wave number

Survey design
 Optical/infrared photometric survey : Euclid• Covers 15,000 [deg2].
• Provides redshift information via photometric redshifts.
• We use various galaxy properties to infer the halo mass.

 Radio continuum survey : SKA phase-1/2• Covers 30,000 [deg2] out to high-z.
• The redshift information is not available.
• Halo mass can be estimated from the galaxy type.
[Ferramacho+ (2014)]

 SKA+Euclid : 9,000 [deg2]

Number density of galaxies
SKA1

SKA2

But, estimates of halo mass for gal.
involves large uncertainties…
 Given Mest, the probability that the true mass is M is
assumed to be given by log-normal distributions with
[Lima+Hu (2004)]
the variance (σlnM)2 and the bias lnMbias:

14 nuisanceparameters foreach survey…We introduce a large number of parameters that model the uncertainty of thehalo mass estimate, which are fully marginalized over when deriving constraints.

Fisher matrix analysis• I, J run over the redshift and mass bin• Θα are model parameters

 To calculate the Fisher with several surveys,
we have to derive covariant matrix
generalized to multiple tracers withdifferent sky areas with some overlap:
Ωw(11)

Effect of different sky areas

Ωw(1122)

Ωw(22)[DY+Takahashi+Oguri (2014)]

 Nonvanishing overlap leads toimproved constraints on fNL,
which becomes smallest in
the case of maximal overlap.
 There is a critical value ofmass ratio which results in thetightest constraint.

Error on fNLEfficiency of mass-binning

Overlap region

The tightest constraint would be obtained when
the two shot noises become comparable.
[Changing the value of the mass ratio leads to the larger shot noisefor one of the mass-bins and smaller for the other.]Error on fNL[DY+Takahashi+Oguri (2014)]

 The constraining powerincreases with NM.
 Even 2-tracers drastically
improve the constraint.

PlanckEuclid12345Number of tracers NM

Error on fNL

 Combining multiple z-bins
improves substantially σ(fNL).
 Galaxy samples as far as z=3.2contribute to the constraint.
 Realistic:zmax=2.7 → σ(fNL)=0.66

PlanckEuclid
0.66
Maximal redshift

[DY+Takahashi+Oguri (2014)]

Error on fNL

Expected marginalized error

Euclid SKA1 Euclid+SKA1 SKA2 Euclid+SKA2

The constraints of σ(fNL)=O(1) can be obtained even witha single survey. Combining Euclid and SKA, even stronger
constraints of σ(fNL)=O(0.1) can be obtained.

SummarySplitting the galaxy samples into the subsamples by
the inferred halo mass and redshift, constraints on
fNL drastically improve.
The constraints of σ(fNL)=O(1) can be obtained evenwith a single survey. Combining Euclid and SKA,
even stronger constraints of σ(fNL)=O(0.1) can beobtained.

FutureConsistency relation
τNL≧(36/25)(fNL)2[Suyama+Yamaguchi (2010)]

fNL  Δb[fNL] ∝ 1/k2

gNL  Δb[gNL] ∝ 1/k2

∝k2

τNL  Δb[τNL] ∝ 1/k4

Non-local → weak dep.
[e.g. S.Yokoyama+Matsubara(2013)][Desjacques+2011]

Non-local fNL & higher-order non-Gaussianity can givethe stringent constraint on the inflationary paradigm!

Thank you!