2014/11/13 JGRG24@IPMU

Constraining
primordial non-Gaussianity
via multi-tracer techniquewith Euclid and SKA
YAMAUCHI, Daisuke(RESCEU, U. Tokyo)
DY, K. Takahashi, M. Oguri, PRD90 083520 ,1407.5453

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, 2013]• Ideal[Komatsu+Spergel, 2001]: σ(fNL) ~ 3

PNG in Large Scale Structure Luminous sources such as galaxies must be most obvious tracers ofthe 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)2PDM
ΔbbG

Pgalaxy= (bG)2PDM

PDM

1/(scale)Accessing ultra-large scales Clustering analysis at large scales are limited due tocosmic variance.

MULTI-TRACER TECHNIQUE[Seljak (2009)]• a method to reduce the cosmic variance using multiple
tracers with different biases.
• The availability of multiple tracers allows significantly
improved statistical error in the measurement of fNL.

Multi-tracer technique [Seljak (2009)]
 If we treat the data as the single group, the galaxy survey canconstrain fNL to the level comparable to CMB:σ(fNL) = O(10)Full galaxy samples
Splitting the data into subsamples…

Group 1 Group 2 Group 3・・・

σ(fNL) < 1 !

Multi-tracer technique [Seljak (2009)]
 Angular power spectraGroup1

Group2

Shot noiseGroup1Group2
 Accuracy for b2/b1

We can make a measurement of the ratio of two biases that is
only limited by shot noise and hence beats cosmic variance!

The accuracy of the amplitude itself is limited by CV, but for
the ratio between the powers there is NO fundamental limit!

b2b2/b1

b1

Pgal,2= (b2)2PDM
Pgal,1= (b1)2PDM

PDM

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]

Fisher matrix analysis

 Covariant matrix generalized to multiple tracers withdifferent sky areas with some overlap:[DY+Takahashi+Oguri (2014)]Effect of different
sky areasError on fNL[DY+Takahashi+Oguri (2014)]

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

PlanckEuclid12345

Number of tracers NM
Error on fNL

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

PlanckEuclid0.66

Maximal redshift

[DY+Takahashi+Oguri (2014)]

Error on fNL

Expected marginalized error

Number of mass bin = 5Euclid 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.

Thank you!

 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 fNL

Efficiency of mass-binning

Overlap region

The tightest constraint would be obtained when the two
shot noises becomes comparable.
(Changing the value of the mass ratio leads to the larger shotnoise for one of the mass-bins and smaller for the other.)Number density of galaxies
SKA1

SKA2

Angular power spectra Wi(b) : window fn
 Ni(b) : number density Si(b) : selection fn

Gray-bodyfactor

Redshift binning

Mass-observable relation

Fisher matrix formalismFisher matrix
Covariance matrix

Estimated angular power spectrum
Cosmic variance Shot noise

N~108 (SKA1,Euclid),
109 (SKA2)

Mass-observable relation
 Probability of assigning the observable mass Mobs tothe true mass M : log-normal distribution [Lima+Hu(2004)]

withSystematicerrors