Download Linear Growth Rate in Dynamic Dark Energy Models

in Dynamic Dark Energy Models
1. Accelerating expansion & interpretation
2. What is Dynamic dark energy model
3. recent observational results
Accelerating expansion
 observations revealed that our universe is not only just
expanding, but in a phase of accelerating expansion.(1998)
So let’s take a glance at type Ia supernova
Type Ia supernova
 What is it?
: Thermonuclear explosion of
white dwarf (WD) (identifying from spectra)
 WD is a remnant of a star and supported by electron degeneracy
pressure against gravity, and there is maximum mass limit that can
be supported by the pressure.
 when exceeding the mass limit (through mass accretion or
merging from companion star), WD collapses to explode as type Ia
supernova
-> so, all the type Ia release roughly same energy (luminosity)
=> we know the luminosity, whenever and wherever it explodes.
Type Ia supernova
we can exploit this homogeneity of luminosity of type Ia in
observation.
 Assuming constant energy density for the ‘unknown’
(i.e. non time-varying),
expansion history follows from the Friedmann eq. :
a 2
2
H ( z )  ( )  H 0 ( m , 0 (1  z )3    , 0 )
a
2
Accelerating expansion
..which means
- There is unknown
component which
make the universe
accelerate
(call it ‘dark energy’)
- and it began to domi
nate at the present
epoch
(but why now? )
QCDM proposal
 ΛCDM
- there are ‘dark energy’ term, which is constant with time.
( called ‘cosmological constant’ or denoted as Λ )
 Dynamic dark energy model (Quintessence-CDM)
- there are ‘dark energy’ term, which varies with time
- features are specified by ‘equation of state of dark energy’
- different QCDM model give different
, in turn, H(z)
Cosmic coincidence
Why QCDM models proposed,
if constant Λ is the simplest candidate which exerts
negative pressure and
seems consistent with observations ?
-> mostly to address ‘why now?’ problem
i.e. why necessarily did it become dominant at
the present epoch? Any earlier, would have
prevented structures to form in the universe.
equation of state - w
w defined as (for any energy component)
equation of state - w
w defined as (for any energy component)
for matter :
=>
equation of state - w
w defined as (for any energy component)
for radiation :
=>
equation of state - w
w defined as (for any energy component)
for Λ-component :
equation of state - w
 two branches of QCDM
- constant w (≠-1) QCDM models
- time-varying w(z) QCDM models
equation of state - w
 two branches of QCDM
- constant w (≠-1)
- w(z)
Constant w QCDM
- for constant w QCDM models,
only w < -1/3 considered,
since this range yields acceleration (
1
wQ  
3
)
w(z) QCDM models
generally, in w(z) QCDM models,
- the dark energy is described as a scalar field
slowly rolling down a potential V,
- in consequence, w(z) varies
with time
w(z) QCDM models
Rolling scalar field as in the inflation theory
extreme slow roll case : if V >> K, w-> -1
to yield negative pressure (w<0), slow roll is
needed. (the faster it rolls, the larger K, the larger w)
focus on one w(z) model..
“Tracker model”
Zlatev, Wang, & Steinhardt (1999)
 for example, for the potential
(where
are model parameters)
the equation of motion
has a solution
“Tracker model”
 ”tracker model” looses ‘why now’ problem
: solution extremely insensitive to initial conditions
- variations in the initial ratio of the Q-energy(dark energy)
density to the matter density by nearly 100 orders of
magnitude leads to the same final expansion.
i.e. the tracker models are similar to inflation in a
sense that they funnel a diverse range of initial
conditions into a common final state
“Tracker model”
 for
,
equation of state given like :
, where
is the equation-of-state of the
background , so when rad-dominated :
when matter-dominated :
when Q-dominated :
matter-dominated :
Q-dominated :
according to observations, the present epoch is between
matter-dominated and Q-dominated,
-> thus,
is expected.
peaks of CMB, d L ( z) , D( z) , ...


 luminosity distance at z
 linear growth rate D(z) - affects object formation
 for the case of
 for the case of varying w(z),
(Basilakos;2003)
with
dependent of
 from type Ia + CMB + BAO
for constant w QCDM :
 for w(z) QCDM :
- for the special case of
(Linder)
It is very hard to distinguish
observationally
Between constant w and w(z)
If
varies slowly with time (slow-roll)
then, observational predictions are well approximated
by treating w(a) as a constant with, (Wang et al.
2000)
 i.e. for w(a) models with diff. potential,
always there is effective constant w, which expects
nearly same observable quantities in value
Summary
observation (SN Ia, etc)
“dark energy”
constant
ΛCDM
time-varying
QCDM
constant w
w(z)
hard to distinguish observationally