1. The role of potential in the ghost-condensate dark energy model
TCGC(ER)
IIT KHARAGPUR
Anirban Saha,
Department of Physics, West Bengal State University, Barasat
Collaboration :
Gour Bhattacharya,
Department of Physics, Presidency University
&
Pradip Mukherjee, Amit Singha Roy,
Department of Physics, Barasat Govt. College 1

2. Motivation:
Dynamical Models of DE - Quintessence (canonical scalar field models), k-essence (noncanonical kinetic terms) –Phantom, Ghost-condensate [GC] .
Observations do not rule out the Phantom (ω < -1) evolutionary scenario.
But Phantom model has unbounded energy density, leads to instabilities.
Ghost-condensate (GC) models can achieve phantom evolution and yet can evade instabilities.
Though Phantom model must have a self-interaction to achieve accelerated expansion, for GC models it is not essential
however !!!
We show that presence of self-interaction helps to realize phantom evolution for a certain range of KE.
Consistency with the field dynamics with a generic potential.
For GC models the generic potential can be expressed in terms of geometric quantities.

3. THE MODEL The action for our ghost-condensate model is:
We choose the metric to be of FLRW form:

4. The set of Friedmann equations are:
The energy-momentum tensor
Due to the isotropy of FLRW universe the eqn of motion for the scalar field reduces to

5. The pressure and energy densities are
The conservation condition
leads to
The evolution of matter density is

6. The solution of the above mentioned eqn is
where
and we assume

7. CRITERIA FOR REALISING PHANTOM REGIME
The phantom regime is demarcated by
The dark energy EOS parameter is given in terms of field is

8. Define, The EOS can now be cast in the form Consider the case when
The positive energy condition leads to

9. So to realise phantom regime we need to have
This leads to following bounds on the parameter
'M'

10. Other case is, Again positive energy condition leads to
The restriction imposed is,
Since time derivative of scalar field is real, we simply require,

11. POTENTIAL FROM GEOMETRIC QUANTITIES
We next define
In terms of scalar field potential and time derivative of scalar field A and B takes the following form,

12. leads to quadratic eqn in V,
We got the above ones by inverting previous eqns.
Algebric identity
leads to quadratic eqn in V,

13. Solution of above eqn is,
Reality condition gives
In terms of
the reality condition becomes

14. Assuming phantom power law,
potential and scalar field kinetic energy takes the form,

15. Input from observational data
We take into account of WMAP7+BAO+H0 and WMAP7 dataset separately.
From phantom power law,
Assuming flat geometry and at late times dark energy will dominate universe,the big Rip time can be expressed as,

16. Maximum likelihood values for observed cosmological parameters in level
WMAP7+BAO+H0
WMAP7 t0
13.78±0.11Gyr[(4.33±0.04)×1017 sec]
13.71±0.13Gyr[(4.32±0.04)×1017 sec] H0
km/sec/Mpc
71.4±2.5 km/sec/Mpc
Wb0
0.0455±0.0016
0.0445±0.0028
WCDM0
0.227±0.014
0.217±0.026

17. Derived parameters in the same level
WMAP7+BAO+H0
WMAP7 β
6.5±0.4
ρm0
×10-27 kg/m3
×10-27 kg/m3
ρc0
×10-27 kg/m3
×10-27 kg/m3 ts
Gyr[(3.30±0.06)×1018 sec]
102.3±3.5Gyr[(3.23±0.11)×1018 sec]

18. Potential plotted against time

19. The EOS plotted against time

20. Square of kinetic energy plotted Against time

21. Summary
Recent observations indicate there is possibility of late time universe to follow phantom evolution.
The GC model realizes the same eradicating some problems of original phantom model.
Presence of a potential widens the range of values the KE can take to realize the phantom evolution.
The generic potential can be expressed in terms of the geometric objects.
The theoretically derived conditions are in conformity with observational data throughout the late time evolution.