Dark Energy, Halo Mass Functions and Lens Statistics

채규현 (Kyu-Hyun Chae)세종대학교 천문우주학과

1. Dark Energy (DE)

• Theoretical possibility invoked to explain the observed accelerating expansion of the Universe

• Alternatively, modified gravity theories • An evolving dark energy or a cosmological

constant? • Whether dark energy evolution crosses (has

crossed) the phantom divide line (PDL)?• Present cosmological observational results do

not appear to converge.

• Consider the following parameterization for the evolution of the DE equation of state (EOS) :

(Linder 2003) w0 =-1 & w1 =0

: Einstein’s cosmological constant w0 = present-epoch EOS

w0 + w1 = EOS right after the big bang

w1 = evolution parameter

x

xpw

1)( 10

z

zwwzw

Key cosmological factor:

zdz

zwzzX

zzXzH

zHzE

zEzdz

dtH

z

x

x

kxm

kxm

00

000

200

30

0

0

1

)](1[3exp

)()(

)1(

)1()()1()(

)(

)()1(

1

Cosmological distances [dL(z), dA(z)] depend on this factor.

2. Recent Constraints on DE Evolution

Type Ia supernovae observations [in particular, Gold data set, Supernova Legacy Survey (SNLS) data set, ESSENCE data set]: luminosity distance-redshift relation [inv. ],

WMAP 3-year results: angular-diameter distance of the sound horizon at zdec [inv. ]

SDSS luminous red galaxies: baryonic acoustic-peak oscillations (BAO) [inv. ]

…..

)(zdL

)(zdA

)(zdA

Nesseris & Perivolaropoulos (2007)

Wu & Yu (2007)

• Based on current results: DE Evolving or Not?

- The current results are inconclusive: Different data sets produce different results.

- Some results suggest an evolving DE that has only recently crossed the PDL.

- Further independent cosmological tests are warranted.

3. Lens Statistics Test of DE

dMdM

dn

Bdzdz

dtHsznRH

0)(

d

d

dn

Multiple-imaging (strong lensing) probability:

n(z): number density, e.g.

s: cross section. B: magnification bias

Differential probability:

dz

d

dzd

d 2

• For the distribution of the number density, we use the velocity dispersion function dn/dσ of early-type galaxies based on the SDSS DR5 data (Choi, Park, & Vogeley 2007).

• For the lensing potential, we use the singular isothermal ellipsoid mass model.

• Use CLASS + other radio-selected lens sample of 26 lenses.

Ωm0=0.2 Ωm0=0.25

Strong Lensing appears to slightly favor an evolving DE EOS that has crossed the PDL at a recent epoch!

Larger data sets are required for improving precision (e.g. SKA).

4. Dark Halo vs Galaxy

halo mass functions & mass profiles

Theory: N-body simulations and analytical models

baryonic physics: cooling, star formation & feedback, …

galaxy velocity functions & modified mass profiles

Observations: rotation velocities, gravitational lensing, etc

dM

dn

ddn

(Theory) (observation)

(simulation)(spectroscopic survey; strong lensing)

NFW(-like) mass profile

Isothermal(-like) profile

(simulation)(rotation curves; stellar dynamics; strong lensing)

M σ

Linking M to σ: recent N-body simulation results + the SDSS VDF and strong lensing

-To study galaxy formation mechanisms involving baryonic physics

-To probe dark energy and galaxy formation together