The Pursuit of primordial non-Gaussianity in the galaxy bispectrum and galaxy-galaxy, galaxy CMB weak lensing Donghui Jeong Texas 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 f NL is (Komatsu et al. 2010) f NL = 32±21 (68% C.L.) – Predicted 68% C.L. range of Planck satellite is Δf NL ~ 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-Gaussianity II. Matter bispectrum due to non-linear gravitational evolution III. 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 k 2 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 P n P n = Probability of finding n galaxies P 2 (x) is given by the two-point correlation function P 3 (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 P 1, P 2, and P 3 ! dV 1 dV 2 r s dV 3 t

MLB formula gives P 1, P 2, P 3 Matarrese, Lucchin & Bonometto (1986) –Galaxies reside in the density peaks! –By analytically integrating following functional integration, –We calculate P 1, P 2, and P 3 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. T Φ For local type non-Gaussianity, Primordial trispectrum is given by For more general multi-field inflation, trispectrum is

Shape of T Φ terms Both of T Φ terms peak at squeezed configurations. f NL 2 term peaks more sharply than g NL term!!

Matter trispectrum II. T 1112 Trispectrum generated by non-linearly evolved primordial non-Gaussianity.

Shape of T 1112 terms T 1112 terms also peak at squeezed configurations. T 1112 terms peak almost as sharp as g NL term.

f NL 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 (f NL ) from the galaxy bispectrum alone Note that we do not include survey geometry and covariance. zV [Gpc/h] 3 n g [h/Mpc] 3 b1Δf NL (SK07) Δf NL (JK09) SDSS-LRG BOSS HETDEX CIP ADEPT EUCLID

Conclusion - bispectrum The galaxy bispectrum, especially in its squeezed limit, is a sensitive 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 f NL 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 theory!

f NL 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, Σ c 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?

f NL in mean tangential shear (LRG) Jeong, Komatsu, Jain (2009) Full sky survey with Million lens galaxies, and n s =30 arcmin -2

f NL 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=0.3 Jeong, Komatsu, Jain (2009) Full sky, Million lens galaxies and “nearly perfect” CMB experiment

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

Cluster-CMB lensing, z=5 High-z population provide a better chance of finding f NL. Jeong, Komatsu, Jain (2009)

Conclusion – weak lensing Weak gravitational lensing can be yet another probe of primordial non-Gaussianity. In order to get a high signal-to-noise ratio from weak lensing method, we need to use high redshift lens galaxies.