1. in Dynamic Dark Energy Models

2. 1. Accelerating expansion & interpretation 2. What is Dynamic dark energy model 3. recent observational results

3.  observations revealed that our universe is not only just expanding, but in a phase of accelerating expansion.(1998)

4. So let’s take a glance at type Ia supernova

5.  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.

6. we can exploit this homogeneity of luminosity of type Ia in observation.

8.  Assuming constant energy density for the ‘unknown’ (i.e. non time-varying), expansion history follows from the Friedmann eq. :

9. ..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? )

11.  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)

12. 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.

13. w defined as (for any energy component)

14. w defined as (for any energy component) for matter : =>

15. w defined as (for any energy component) for radiation : =>

16. w defined as (for any energy component) for Λ-component :

17.  two branches of QCDM - constant w (≠-1) QCDM models - time-varying w(z) QCDM models

18.  two branches of QCDM - constant w (≠-1) - w(z)

19. - for constant w QCDM models, only w < -1/3 considered, since this range yields acceleration ( )

21. 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

22. 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)

23. “Tracker model”

24. Zlatev, Wang, & Steinhardt (1999)

25.  for example, for the potential (where are model parameters) the equation of motion has a solution

26.  ”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

27.  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 :

28. matter-dominated : Q-dominated : according to observations, the present epoch is between matter-dominated and Q-dominated, -> thus, is expected.

31.    

32.  luminosity distance at z  linear growth rate D(z) - affects object formation

33.  for the case of

34.  for the case of varying w(z), (Basilakos;2003) with dependent of

35.  from type Ia + CMB + BAO for constant w QCDM :

36.  for w(z) QCDM : - for the special case of (Linder)

37. Between constant w and w(z)

38. 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)

39.  i.e. for w(a) models with diff. potential, always there is effective constant w, which expects nearly same observable quantities in value

40. observation (SN Ia, etc) “dark energy” constant time-varying ΛCDM QCDM constant w w(z) hard to distinguish observationally