COSMOLOGICAL N-BODY SIMULATIONS WITH NON-GAUSSIAN INITIAL CONDITIONS

Transcription

1 COSMOLOGICAL N-BODY SIMULATIONS WITH NON-GAUSSIAN INITIAL CONDITIONS Takahiro Nishimichi (Univ. of Tokyo IPMU from Apr.) Atsushi Taruya (Univ. of Tokyo) Kazuya Koyama, Cristiano Sabiu (ICG, Portsmouth) The Non-Gaussian Auditorium, Yukawa Hall, Mar. 2010

2 Cosmology from Upcoming Galaxy Redshift Surveys 3D map of millions of galaxies by spectroscopy statistical analyses to extract cosmological information Features of upcoming surveys deep (z~1 or z~3) large volume (10 ~ 100h -3 Gpc 3 ) SDSS final data release c.f., Sloan Digital Sky Survey: current biggest z ~ 0.35 (Luminous Red Galaxies) volume ~ 1h -3 Gpc 3

3 Not only BAOs!! advantage of huge surveys: detection/measurement of small signals at large scale BAOs standard -1 Mpc for dark energy SDSS final data release Primordial NG examine the statistical -1 Gpc for inflation Huge surveys designed for BAOs are also good opportunities for studies of Primordial NG!!

4 Not only power spectrum!! Everybody measures the power spectrum, but... δ k = δ k e iθ P (k) = δ k 2 same power spectra randomize the phase Structure dissapeared!! Tegmark+04 limitation of 2pt statistics

5 Bispectrum? the lowest-order statistic for NG δ k1 δ k2 δ k3 (2π) 3 B(k 1, k 2, k 3 )δ D (k 1 + k 2 + k 3 ) triangles in Fourier space Which configuration is more important for NG study? Accurate modeling for ``important configurations! many practical difficulties I focus on the local-type primordial non-gaussianity (thus squeezed triangles)

6 Difficulties in Large Scale Structure contaminations nonlinear gravitational growth redshift-space distortion galaxy biasing

7 Local-type NG and Large Scale Structure nonlinear gravitational growth local-type primordial Non-Gaussianity power spectrum (Taruya,Koyama,Matsubara08) Φ(x) =Φ G (x)+f NL [Φ 2 G(x) Φ 2 G(x) ] Gaussian 10 <f NL < 74 (95% CL) WMAP7(Komatsu+10) Φ 10 5 Probability 2nd term is at most ~0.1% of 1st term (Sefusatti,Komatsu07) z=4 z=1 bispectrum Q B123/[P1P2+cyc.] Non-Gaussian (fnl>0) Gaussian z=0 fnl=+100 perturbation fnl=-100

8 Local-type NG and Large Scale Structure nonlinear gravitational growth + galaxy biasing We do observe ``galaxy, not ``matter density fluctuations biasing changes things dramatically! halo mass function halo power spectrum halo bispectrum Probability Non-Gaussian fnl>0 Gaussian A big change in the high density tail leads to the formation of massive haloes. Understanding of the halo/galaxy biasing is the key! perturbation

9 Halo power spectrum galaxy (or halo) biasing Assuming local bias model δ g (x) =b 1 δ m (x)+ 1 2 b 2δm(x)+ 2 d P g (k) =b 2 3 q 1P m (k)+b 1 b 2 (2π) 3 B m(k, q, q k) Measure the bispectrum through the power spectrum! Taruya,Koyama,Matsubara08 P g (k; f NL ) P g (k; f NL = 0) Desjacques+09 initial final (matter) final (galaxy) PowS PowS PowS BiS BiS Bispectrum term dominates at large scales ``scale-dependent bias theory N-body

10 Halo power spectrum galaxy (or halo) biasing scale-dependent bias: many authors reached similar conclusions using different methods Dalal+07 (peak bias) Matarrese+Verde08 (peak bias) Slosar+08 (peak-background split) Afshordi+Tolley08 (halo bias) McDonald08 (renormalization of bias parameters) Afshordi+Tolley08 ex.) correlation between modes Φ(x) =Φ G (x)+f NL [Φ 2 G(x) Φ 2 G(x) ] d 3 q Φ(k) =Φ G (k)+f NL (2π 3 ) Φ G(q)Φ G (k q) Then, what about bispectrum??

11 N-body simulations with fnl Author fnl volume/run [h -3 Gpc 3 ] run/model particle/run mass/particle [h -1 Msun] Kang , (2) 128^3 ~10 12 Grossi+07 0,±100,±500,± ^3 2.0x10 10 Dalal+08 0,±5,±50,±500 (±5000) ^3 2.5x10 11 Pillepich+08 0,±27,±80,250,500, (2) 1024^3 1.2x10 11 Desjacques+08 0,±100 (±10,±30) (2) 1024^3 3.0x10 11 Grossi+09 0,±100,± ^3 1.4x10 11 This work 0,±100,±300,± ^3 4.6x10 12 examine the clustering of massive haloes at large scale

12 Our halo catalog Mass function Power spectrum fnl>0 fnl<0 Consistent with previous works!!

13 Matter bispectrum Halo bispectrum Result large scale squeezed fnl fnl

14 Interpretation Local bias model again... Jeong,Komatsu09 Asymptotic behavior at ``squeezed limit (α ) fnlα 2 3 k 2 c.f. matter BS: fnlα 1 1 k 0 k 1 = k 2 αk 3 k k2 k3 k1 initial final (matter) final (galaxy) P P B B B T T New term! fnl 0 fnl fnl 2

15 Dependence on the halo mass Halo bispectrum for different minimum halo masses fnl 2 term is more important for more massive haloes

16 Dependence on redshift halo bispectrum at different epochs h 1 M fnl 2 term is more important at higher redshift

17 Detectability detectability when using only limited configurations of k1=k2=0.042h/mpc k2 Preliminary k3 k2 k1 k3 k1 constraints like f NL <10 will be obtainable from ultimate future surveys!

18 Summary We have examined the effects of local-type primordial non-gaussianity on the halo bispectrum: Big difference between the matter and halo bispectra fnl 2 term is important for squeezed configurations at large scale Especially for massive haloes at high z The trend can be explained by analytical model assuming local bias new term f 2 NLα 3 k 2

19 Future plans We need more accurate modeling... higher resolution runs to resolve less massive haloes keeping accuracy at large scales (>100~1000h -1 Mpc) need a wider dynamic range make mock catalogs for future surveys running N=2048^3 simulations now!