The Pursuit of primordial non-Gaussianity in the

galaxy bispectrum and galaxy-galaxy, galaxy CMB weak lensing

Donghui JeongTexas Cosmology Center and Astronomy Department

University of Texas at Austin

The Almost Gaussian Universe, IPhT, CEA/Saclay, 11 June 2010

Bispectrum and non-Gaussianity• Bispectrum is the Fourier space counter part of three point

correlation function:

• CMB (z~1090) bispectrum is a traditional tool to test the non-Gaussianity, because it should vanish when density field is Gaussian.– The latest limit on fNL is (Komatsu et al. 2010) fNL= 32±21 (68% C.L.)

– Predicted 68% C.L. range of Planck satellite is ΔfNL~ 5.

What about galaxy bispectrum?• For the galaxy, there were previously three known sources for

galaxy bispectrum (Sefusatti & Komatsu 2007, SK07)

I. Matter bispectrum due to primordial non-GaussianityII. Matter bispectrum due to non-linear gravitational evolutionIII. Non-linear galaxy bias

I

II

III

Triangular configurations

Bispectrum of Gaussian Universe• We can measure bias parameters from Equilateral and Folded

triangles:Bispectrum from non-linear gravitational evolution

Bispectrum from non-linear galaxy bias

Jeong & Komatsu (2009)

Linearly evolved primordial bispectrum

• Notice the factor of k2 in the denominator.• Sharply peaks at the squeezed configuration!

Jeong & Komatsu (2009)

New terms (Jeong & Komatsu, 2009)

• It turns out that SK07 misses the dominant terms which comes from the statistics of “peaks”.

• Jeong & Komatsu (2009)“Primordial non-Gaussianity, scale dependent bias, and the bispectrum of galaxies”We present non-Gaussian bispectrum terms from the peak statistics on large scales and on squeezed configurations from MLB (Matarrese-Lucchin-Bonometto) formula!

Bispectrum from Pn

• Pn = Probability of finding n galaxies

• P2(x) is given by the two-point correlation function

• P3(r, s, t) is given by the two, and three-point correlation functions

• B(k,k’) is the Fourier transform of ζ(r,s).

• All we need are P1, P2, and P3!

dV1

dV2

r s

dV3

t

MLB formula gives P1, P2, P3

• Matarrese, Lucchin & Bonometto (1986)– Galaxies reside in the density peaks!– By analytically integrating following functional integration,

– We calculate P1, P2, and P3 as a function of density poly-spectra:

Threshold density

Non-Gaussian peak correlation terms

• The galaxy bispectrum also depends on trispectrum (four point function) of underlying mass distribution!!

Jeong & Komatsu (2009)

Matter trispectrum I. TΦ

• For local type non-Gaussianity,

• Primordial trispectrum is given by

• For more general multi-field inflation, trispectrum is

Shape of TΦ terms

• Both of TΦ terms peak at squeezed configurations.

• fNL2 term peaks more sharply than gNL term!!

Matter trispectrum II. T1112

• Trispectrum generated by non-linearly evolved primordial non-Gaussianity.

Shape of T1112 terms

• T1112 terms also peak at squeezed configurations.

• T1112 terms peak almost as sharp as gNL term.

fNL terms : SK07 vs. JK09

SK07

Jeong & Komatsu (2009b)

Are new terms important? (z=0)Jeong & Komatsu (2009)

Even more important at high-z!! (z=3)Jeong & Komatsu (2009)

Prediction for galaxy surveys• Predicted 1-sigma marginalized (bias) error of non-linearity

parameter (fNL) from the galaxy bispectrum alone

• Note that we do not include survey geometry and covariance.z V

[Gpc/h]3ng

10-5[h/Mpc]3b1 ΔfNL

(SK07)ΔfNL

(JK09)

SDSS-LRG0.315 1.48 136 2.17 60.38 5.43

BOSS0.35 5.66 26.6 1.97 31.96 3.13

HETDEX2.7 2.96 27 4.10 20.39 2.35

CIP2.25 6.54 500 2.44 8.96 0.99

ADEPT1.5 107.3 93.7 2.48 5.65 0.92

EUCLID1.0 102.9 156 1.93 5.56 0.77

Conclusion - bispectrum• The galaxy bispectrum, especially in its squeezed limit, is a sen-

sitive probe of the primordial non-Gaussianity.• Also, it is safe from the contaminations from non-linear gravity

and non-linear bias.• With new terms induced by the peak correlation provide about

a factor of 15 higher signal than the previous calculation, and the uncertainty on measuring fNL decrease about a factor of 10.

• But, this is a first step! (like Kaiser 1984 for the linear bias)• Tension between MLB/peak-background split method• BBKS-like calculation for non-Gaussian PDF may help?• Need to compare to N-body simulations to guide the the-

ory!

fNL from Weak gravitational lensing

Picture from M. Takada (IPMU)

Jeong, Komatsu, Jain (2009)

• Mean tangential shear is given by

It is often written as

where, Σc is the “critical surface density”

Mean tangential shear

G

R

Mean tangential shear, status

Mean tangential shear from SDSS Sheldon et al. (2009)

What about larger scales?

fNL in mean tangential shear (LRG)Jeong, Komatsu, Jain (2009)

Full sky survey with Million lens galaxies, and ns=30 arcmin-2

fNL in mean tangential shear (LSST)Jeong, Komatsu, Jain (2009)

Statistics will accumulate as we include more lens redshits.

CMB anisotropy as a backlight

Picture from Hu & Okamoto (2001)

Unlensed

Lensed

Galaxy-CMB lensing, z=0.3Jeong, Komatsu, Jain (2009)

Full sky, Million lens galaxies and “nearly perfect” CMB experiment

Galaxy-CMB lensing, z=0.8Jeong, Komatsu, Jain (2009)

Cluster-CMB lensing, z=5High-z population provide a better chance of finding fNL.

Jeong, Komatsu, Jain (2009)

Conclusion – weak lensing• Weak gravitational lensing can be yet another probe of primor-

dial non-Gaussianity.• In order to get a high signal-to-noise ratio from weak lensing

method, we need to use high redshift lens galaxies.