1. 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

2. Outline Introduction Scale-dependent bias (from primordial non-Gaussianity) Cross-Correlation power spectrum Constraints on primordial non-Gaussianity Summary

3. Introduction 13.7 Gyr ©NASA WMAP TEAM CMBLSS (Large Scale Structure) WMAP Inflation Quantum fluctuations

4. Introduction N-body simulation –NG significantly influences the structure formation. –Rare objects are even more affected. Dalal+08 f NL = -5000 f NL = +5000 f NL = +500 f NL = -500 f NL = 0 Large-Scale Structure Primordial fluctuations ? particles: 512 3 box size: 800 h -1 Mpc mass: m p = 2.52x10 11 h -1 M sun 375h -1 Mpc 80h -1 Mpc Φ(x) = Φ G (x) + f NL (Φ G 2 (x) - )

5. Introduction Current constraints on NG (local type) –with scale-dependent bias from …. NVSS: f NL = 74 ± 40 SDSS (QSO): f NL = 59 ± 21 SDSS (LRG): f NL = 153 ± 95 –CMB bispectrum from WMAP-7yr Komatsu+10 fNL = 32 ± 21 –Planck will measure f NL with error level Δ f NL 〜 1-3. scale-dependent bias: b NG = b G + Δb combined result: f NL = 48 ± 20 Xia+11 Dalal+08, Slosar+08, Afshordi+08

6. 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 lensing previous works: TT, EE,TE, gg, Tg future survey: TT, EE,TE, gg, Tg + ψψ, Tψ, ψg + γγ, Tγ, γg

7. 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)

8. 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 where φis also maximum. relate the ▽ 2 Φ with the density field by Poisson equation. cubic type => Yokoyama-san’s talk

9. Scale-dependent bias relation between NG density field δ NG and Gaussina density field δ –density field is modified by –the number of the regions whose overdensity exceed δ c (halos) increase of decrease. if density field is Gaussian, the presence of ‘background’ density field boosts the ‘peak’ overdensity. Peacock (1990) background δ ： density field δcδc Kaiser 1984 modulatin of threshold δc by NG

10. Scale-dependent bias due to the NG, ‘peak’ height δ pk is enhanced by the long- wavelength curvature perturbation by If we focus on the peaks near threshold, δ pk 〜 δ c, the amount of enhancement becomes halo density: correction to the bias: –using: b = b L + 1

11. 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

12. mass function bias M th obs

13. 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] b eff (k, z) large scale small scale z =0 z =1 z =2 z =3 thin line ： f NL = 0 thick line: f NL = 100

14. 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. LSS CMB ©NASA WMAP TEAM

15. Future Survey Projects LSS (Large-Scale Structure) survey HSC (Hyper Suprime-Cam) survey area : 2,000 deg 2, mean redshift: z m ~1.0 While… L SST (Hyper Suprime-Cam) survey area : 20,000 deg 2, mean redshift: z m ~1.2 © Subaru HSC Team Δ f NL 〜 1-3

16. 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

17. Cross-correlation power spectrum galaxy-galaxy auto-correlation S/N: Signal-to-Noise ration signature of NG most of the contribution for constraing of f NL 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 f NL is wide survey area.

18. 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.

19. 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 lensing gψ: galaxy – CMB lensing

20. Constraints on primordial NG ■ Contribution of lensing information logM th obs : bias ■ Lensing information determines bias parameter. ＝＞ break degeneracy between f NL and M th obs. ■ Combing CMB lensing:ψ and galaxy lensing:γ improves the constraint. ■ Planck + ACTPol case constraints the parameters more tightly. Planck onlyPlanck + ACTPol Planck + HSC f NL Planck + ACTPol + HSC more sensitive to CMB (T, E, ψ) f NL logM th obs : bias

21. 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 + ψγ  Aqua ： CMB + gg + ψψ + γγ + γg  Yellow ： all information ■ galaxy lensing-galaxy( γg ) contributes the most !!  CMB lensing trace the high-z information of LSS, comparing with galaxy lensing. logM th obs : bias f NL HSC + Planck + ACTPol CMB = TT + EE + TE CMB lensing-galaxy CMB lensing-galaxy lensing galaxy lensing-galaxy + ψg + γg + ψγ

22. By tomography analysis, –similar behaviors to previous case (without tomography) can be seen. –the error will reach Δ f NL 〜 5

23. 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 f NL from power spectra, the contributions of the cross-correlations can not be negligible. Cross-correlations break the degeneracy between f NL & bias parameter. Not only future galaxy surveys but CMB experiments will improve the constraints on f NL.

24. For application for other Observations –Galaxy power spectrum v.s. Cluster counts effect of NG: Galaxy < Cluster. samples : Galaxy > Cluster. mass function bias