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 structur

es----linear growth factor D(z)• Dynamical DE or w(z): measuring the geometry o

r DM dynamics at z=0—2

Power spectrum

Bispectrum

Reduced Bispectrum

Density Fluctuation

Definition of the bispectrum

Basics about the bispectrum method to measure the linear growth factor

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)

Bias Relation

2nd order Perturbation Theory

Q_m depends on the shape of P(k) only

Can measure D(z) through measuring b_1

On sufficiently large scale

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 10243 particles (PP-PM, Jing et al. 2007)

Box size

(Mpc/h)

M_p

(M_sun/h)

realizations

LCDM1 150 2.2E7 3

LCDM2 300 1.8 E9 4

LCDM3 600 1.5 E10 4

LCDM4 1200 1.2 E 11 4

LCDM5 1800 4.0 E 11 4

Distribution of dark matter and galaxies ---simulations

Density of dark matterGalaxy 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 l

imit 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

1200 Mpc/hMillennium Simulation

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 red

shift;• 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, da

rk energy and galaxy formation, promising• Feasibility study with ongoing redshift surveys, es

pecially at high redshifts, is being undertaken;• Accurate prediction for Q_m needs to be done (cf.

loop-corrections, Sccocimarro et al.)