Interacting generalized chaplygin gas model in bianchi type-I universe

In this paper, we have studied the generalized chaplygin gas of interacting dark energy to obtain the equation of state for the generalized chaplygin gas energy density in anisotropic Bianchi type-I cosmological model. For negative value of B in equation of state of generalized chaplygin gas, we see that < 1 eff    , that corresponds to a universe dominated by phantom dark energy.


INTRODUCTION
One of the most important problems of cosmology, is the problem of so-called dark energy (DE).The type Ia supernova observations suggests that the universe is dominated by dark energy with negative pressure which provides the dynamical mechanism of the accelerating expansion of the universe [1][2][3].The strength of this acceleration is presently matter of debate, mainly because it depends on the theoretical model implied when interpreting the data.Most of these models are based on dynamics of a scalar or multi-scalar fields.Primary scalar field candidate for dark energy was quintessence scenario [4,5], a fluid with the parameter of the equation of state lying in the range, 1 < < 1 3    .In a very interesting paper Kamenshchik, Moschella and Pasquier [6] have studied a homogeneous model based on a single fluid obeying the Chaplygin gas equation of state where p and  are respectively pressure and energy density in comoving reference frame, with > 0


; A is a positive constant.This equation of state has raised a certain interest [7] because of its many interesting and, in some sense, intriguingly unique features.Some possi-ble motivations for this model from the field theory points of view are investigated in [8].The Chaplygin gas emerges as an effective fluid associated with d-branes [9] and can also be obtained from the Born-infield action [10].
Inserting the equation of state (1.1) into the relativistic energy conservation equation, leads to a density evolving as where B is an integration constant.
There exist a wide class of anisotropic cosmological models, which also often studying in cosmology [11].There are theoretical arguments that sustain the existence of an anisotropic phase that approaches an isotropic case [12].Also, anisotropic cosmological models are found a suitable candidate to avoid the assumption of specific initial conditions in FRW models.The early universe could also characterized by irregular expansion mechanism.Therefore, it would be useful to explore cosmological models in which anisotropic, existing at early stage of expansion, are damped out in the course of evolution.Interest in such models have been received much attention since 1978 [13].
Setare [14] has obtained the equation of state for the generalized Chaplygin gas energy density in non-flat universe.Chaubey [15] has obtained the role of modified chaplygin gas in Bianchi type -I universe.In the present paper, using the generalized Chaplygin gas model of dark energy, we obtain equation of state for interacting Chaplygin gas energy density in anisotropic Bianchi type-I cosmological model.For negative value of B in equation of state of generalized chaplygin gas, we see that  , that corresponds to a universe dominated by phantom dark energy.

INTERACTING GENERALIZED CHAPLYGIN GAS
In this section we obtain the equation of state for the generalized Chapligin gas when there is an interaction between generalized Chaplygin gas energy density   and a Cold Dark Matter (CDM) with = 0 m  .The continuity equations for dark energy and CDM are The interaction is given by the quality = Q    .This is a decaying of the generalized Chaplygin gas component into CDM with the decay rate  .Taking a ratio of two energy densities as = m r    , the above equations lead to Following [3], if we define Then, the continuity equations can be written in their standard form We consider the homogeneous anisotropic Bianchi type-I cosmological model with line element where 1 2 , a a and 3 a are function of t only.The Einstein field equations for the metric (2.1) are written in the form   where   8G/c 4 is constant.
We define (2.12) By using the method of Singh et al. [16-19], we obtain where i D (i = 1, 2, 3) and i X (i = 1, 2, 3) satisfy the relation 1 2 3 = 1 D D D and 1 2 3 = 0. X X X   Now, adding Eqs.2.9, 2.10 and 2.11 and three times Eq.2.8, we get   aa aa a a a a a a a a a a a a a p From Eqs.2.12 and 2.16, we have Define as usual From above, we obtain following relation for ratio of energy densities r as In the generalized Chaplygin gas approach [10], the equation of state to (1.1) is generalized to The above equation of state leads to a density evolution as Taking derivatives in both sides of above equation with respect to cosmic time, we obtain Substituting this relation into Eq.2.1 and using defini- Here as in Ref. [20], we choose the following relation for decay rate with the coupling constant 2 b .Using Eq.2.14, the above decay rate take following form Substituting this relation into Eq.2.23, one finds the generalized Chaplygin gas energy equation of state Now using the definition generalized Chaplygin gas energy   , and using   , we can rewrite the above equation as From Eqs.2.4,2.25 and 2.27, we have the effective equation of state as By choosing a negative value for B we see that < 1 eff    , that corresponds to a universe dominated by phantom dark energy, Eq.2.28, for = 1


, is the effective parameter of state for Chaplygin gas.In this case, in the expression for energy density (1.2), term under square root should be positive, i.e. 2 , then the minimal value of the volume factor is given by Now, from Eqs.2.13-2.15 and 2.29, we have find the minimal value of the scale factors are given by According to this model we have a bouncing universe.Generally for this model > 0, < 0 A B and 1 >0   .From Eq.2.21, we can realize that the cosmic scalar fac-tors take values in the interval < < (2.34) Using Eq.1.2,one can see that the Chaplygin gas interpolates between dust at small i a and a cosmological constant at large i a , but choosing a negative value of B , this quartessence idea lose.Following [6] The energy density and the pressure corresponding to the scalar field  are as respectively Therefore, the scalar field  is a phantom field.This implies that one can generate phantom-like equation of state from an interacting generalized Chaplygin gas dark energy model in anisotropic universe.

CONCLUSIONS
We have studied the generalized chaplygin gas of interacting dark energy to obtain the equation of state for the generalized chaplygin gas energy density in anisotropic Bianchi type-I cosmological model.By choosing a negative value for B we see that < 1 eff    , that cor-responds to a universe dominated by phantom dark energy.