Feasibility of detecting dark energy using bispectrum

Yipeng Jing Shanghai Astronomical Observatory Hong Guo and YPJ, in preparation

Exploring Dark Energy ----Physical Principles

• Measuring the luminosity distance---standard candles • Measuring the angular distance---standard rulers • Measuring the shape of a known object • Measuring the dynamical evolution of the structures----linear growth factor D(z) • Dynamical DE or w(z): measuring the geometry or DM dynamics at z=0—2

Basics about the bispectrum method to measure the linear growth factor Definition of the bispectrum Density Fluctuation Power spectrum Bispectrum Reduced Bispectrum

General properties of bispectrum

• The quantity measures the correlation of the densities at three points in space; • It is vanished for Gaussian density fluctuation field; • But it is generated by gravitational clustering of matter; • It can be also induced by selecting the density field in a biased way (e.g. the galaxy density field)

On sufficiently large scale

2nd order Perturbation Theory Q_m depends on the shape of P(k) only Bias Relation Can measure D(z) through measuring b_1

Why Bispectrum

• In principle, one can measure the growth factor by measuring the power spectrum and the bispectrum since D(z) =1/b, without relying on the assumptions on bias and dynamics etc; measure sigma_8 and DE; • Bispectrum is of great use in its own right: non Gaussian features (inflation), bias factor (galaxy formation), nonlinear evolution

The key problems when measuring the growth factor • Nonlinear evolution of dark matter clustering; • Nonlinear coupling of galaxies to dark matter; • Is there any systematic bias in measuring D(z)? On which scales ?

• Feasibility to measure with next generation of galaxy surveys (especially for those at high redshift) ?

• Simulation requirement ： Large volume and high resolution

Cosmological N-body simulations at SHAO with 1024 3 particles (PP-PM, Jing et al. 2007) realizations LCDM1 LCDM2 Box size (Mpc/h) 150 300 LCDM3 600 LCDM4 LCDM5 1200 1800 M_p (M_sun/h) 2.2E7

1.8 E9 1.5 E10 1.2 E 11 4.0 E 11 4 4 3 4 4

Distribution of dark matter and galaxies ---simulations Density of dark matter Galaxy distribution based on a semi-analytical model (Kang et al. 2005). Red for E and blue for S galaxies

Test of the 2nd order Perturbation Theory Valid on scales larger than that of k=0.1 h/Mpc (less than 10%)

Halo model ： not perfect but helpful

Halo model ： understanding the nonlinear evolution (but two-halo term sensitive to upper limit in the integral)

Test of the bias model • Using Semi-Analytic Model of Millennium Simulation (Croton et al. 2006) to build Mock sample of “galaxies”.

• mock galaxies: 600 Mpc/h (3 realizations) and 1200 Mpc/h (4 realizations) 500 Mpc/h Millennium Simulation 1200 Mpc/h

Probability of galaxies in halos

Systematics: a few percent level; Non-linear Q_m used; Valid on slightly smaller scales (k<0.2 h/Mpc) Error bars need to be estimated carefully

b2: may tell about galaxy formation Positive for brightest galaxies (M_r<-22.5), negative for bright and faint galaxies

Error bars of bispectrumare comparable to the Gaussian fluctuation on large scales k<0.1 h/Mpc (Dark Matter)

Error bars of B_g comparable to the Gaussian case Mock galaxies

Preliminary conclusions

• 2nd perturbation theory for the bispectrum of dark matter is valid for k<0.1 Mpc/h at redshift 0 • Also valid for variance Delta^2(k)<0.3 at high redshift; • The bias expansion valid on slightly larger scales (about <0.1 Mpc/h) • The error is close to the Gaussian one • Unbiased measurement of b1 and b2, therefore, dark energy and galaxy formation, promising • Feasibility study with ongoing redshift surveys, especially at high redshifts, is being undertaken; • Accurate prediction for Q_m needs to be done (cf. loop-corrections, Sccocimarro et al.)