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

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.

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

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

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

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

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

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

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

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

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,

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

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

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

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,

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 70.2+1.3-1.4 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

Derived parameters in the same level WMAP7+BAO+H0 WMAP7 β -6.51+0.24-0.25 6.5±0.4 ρm0 2.52+0.25-0.24×10-27 kg/m3 2.50+0.48-0.42×10-27 kg/m3 ρc0 9.3+0.3-0.4×10-27 kg/m3 9.58+0.68-0.66×10-27 kg/m3 ts 104.5+1.9-2.0Gyr[(3.30±0.06)×1018 sec] 102.3±3.5Gyr[(3.23±0.11)×1018 sec]

Potential plotted against time

The EOS plotted against time

Square of kinetic energy plotted Against time

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.