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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
p
(EOS)
w:  x

x
z
w( z )  w0  w1
z 1
(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
Key cosmological factor:
H 0 dt
1

dz
(1  z ) E ( z )
H ( z)
E( z) 
  m 0 (1  z ) 3   x 0 X ( z )   k 0 (1  z ) 2
H0
( m 0   x 0   k 0  1)
 x ( z)
 z 3[1  w( z )] 
X ( z) 
 exp 
dz  
 x0
 0 1  z

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.
],
d L (z)
WMAP 3-year results: angular-diameter distance of the
sound horizon at zdec [inv.
]
d A (z)
SDSS luminous red galaxies: baryonic acoustic-peak
oscillations (BAO) [inv.
]
…..
d A (z)
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
Multiple-imaging (strong lensing)
probability:
H 0 dt
  RH  n( z ) s
Bdz
dz
dn
 d d 
n(z): number density, e.g.
s: cross section. B: magnification bias
Differential probability:
d
dz
d 2
dzd
dn
 dM dM
• 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
Theory: N-body simulations and analytical models
halo mass functions & mass profiles
baryonic physics:
cooling, star formation
& feedback, …
galaxy velocity functions & modified mass profiles
Observations: rotation velocities, gravitational lensing, etc
(Theory)
(observation)
(simulation)
dn
dM
dn
d
(simulation)
NFW(-like)
mass profile
Isothermal(like) profile
M
σ
(spectroscopic
survey; strong
lensing)
(rotation curves;
stellar dynamics;
strong lensing)
Linking M to σ:
recent N-body simulation results +
the SDSS VDF and strong lensing
-To study galaxy formation mechanisms
baryonic physics
involving
-To probe dark energy and galaxy formation together