Statefinder parameters for interacting phantom energy with dark matter

Abstract

We apply in this paper the statefinder parameters to the interacting phantom energy with dark matter. There are two kinds of scaling solutions in this model. It is found that the evolving trajectories of these two scaling solutions in the statefinder parameter plane are quite different, and that are also different from the statefinder diagnostic of other dark energy models.PACS numbers: 98.80.Es Cosmic observations indicate that our universe is undergoing an accelerated expansion and the dominated component of the present universe is dark energy [1,2,3,4,5]. The Wilkinson Microwave Anisotropy Probe (WMAP) satellite experiment tells us that dark energy, dark matter, and the usual baryonic matter occupy about 73%, 23%, and 4% of the total energy of the universe, respectively. The accelerated expansion of the present universe is attributed to the dark energy whose essence is quite unusual and there is no justification for assuming that it resembles known forms of matter or energy. Candidates for dark energy have been widely studied and focus on the cosmological constant Λ [6,7] with W = −1, a dynamically evolving scalar field (quintessence) [8,9] with W > −1 and phantom [10] with W < −1. Recently, a study of high-Z (Z is redshift) SNe Ia [11] find that the equation of state of dark energy has a 99% probability of being W < −1 if no priors are placed on Ω 0 m . When these SNe results are combined with CMB and 2dFGRS the 95% confidence limits on an unevolving equation of state are −1.46 < W < −0.78 [3,11] which is consistent with estimates made by other groups [4,5]. In order to obtain W < −1, phantom field with reverse sign in its dynamical term may be a simplest way and can be regarded as one of interesting possibilities describing dark energy [12]. However, the other physical properties of phantom energy are rather weird, as they include violation of the dominant-energy condition, naive superluminal sound speed and increasing energy density with time. The latter property ultimately leads to unwanted future singularity called big rip which had been considered in [13]. This singularity is characterized by the divergence of the scale factor in a finite time in future [14].Many authors have discussed various kinds of phantom field models to avoid the cosmic doomsday [15], which require a special class of phantom field potentials with a local maximum. Moreover, the energy density of the phantom field increases with time, while the energy density of the matter fluid decreases as the universe expands. Why are the energy density of dark matter and the phantom energy density of the same order just at the present epoch? This coincidence problem becomes more difficult to solve in the phantom model without the suitable interaction [16]. But Guo et al. in Ref. [17,18] proposed a suitable interaction in the phantom field model, and the coincidence problem can be avoided. Moreover in Ref.[18], the universe also avoids the big rip. In Ref.[18], considering a universe model which contains phantom field φ and the dark matter ρ ...

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