In this paper, bulk viscous Bianchi type V cosmological model with generalized Chaplygin gas, dynamical gravitational and cosmological constants has been investigated. We are assuming the condition on metric potential . To obtain deterministic model, we have considered physically plausible relations like , and the generalized Chaplygin gas is described by equation of state . A new set of exact solutions of Einstein’s field equations has been obtained in Eckart theory, truncated theory and full causal theory. Physical behavior of the models has been discussed.
Recent cosmology is on Fridman-Lemaitra-Robertson-Walkar (FLRW) which is completely homogeneous and isotropic. But it is widely believed that FLRW model does not give a correct matter description in the early stage of universe. The theoretical argument [
It has been widely discussed in the literature that during the evolution of the universe, bulk viscosity can arise in many circumstances and can lead to an effective mechanism of galaxy formation [
A wide range of observations strongly suggest that the universe possesses non zero cosmological term [
Time varying G has many interesting consequences in astrophysics. Cunuto and Narlikar [
According to recent observational evidence, the expansion of the universe is accelerated, which is dominated by a smooth component with negative pressure, the so called dark energy. To avoid problems associated with L and quintessence models, recently, it has been shown that Chaplygin gas may be useful. The unification of the dark matter and dark energy component creates a considerable theoretical interest, because on the one hand, model building becomes reasonably simpler, and on the other hand such unification implies existence of an era during which the energy densities of dark matter and dark energy are strikingly similar. For representation of such a
unification, the generalized Chaplygin gas (GCG) with exotic condition of state
constant B and
Motivated by above work we thought that it was worthwhile to study bulk viscous Bianchi type V space-time with generalized Chaplygin gas and dynamical G and L.
The spatially homogeneous and anisotropic space-time metric is given by
where
Einstein field equation with time dependent L and G may be written as
where G and L are time dependent gravitational and cosmological constants.
where p is equilibrium pressure,
Einstein’s field Equation (2) for the metric (1) takes form
By the divergence of Einstein’s tensor i.e.
The energy momentum conservation equation
For the full causal non-equilibrium thermodynamics the causal evolution equation for bulk viscosity is given by [
It can be easily seen that we have five Equations (5)-(9) with eight unknowns
For non causal solution
To find the complete solution of the system of equations, following relations are taken into consideration.
The power law relation for bulk viscosity is taken as
where
We consider an exotic background fluid, the Chaplygin gas, described by the equation of state
where B is constant and
To obtain the deterministic scenario of the universe, we assume the condition
From Equation (9) and (17), one can get
From Equations (17)-(18), one can easily calculate
Using Equations (17) and (18), Equation (11) yields
By solving Equation (20), we get
where
From
On differentiating Equation (21), we get
Now with the help of Equations (17)-(19) and (21), Equation (8) becomes
Which on differentiation yields
With the help of Equations (12), (14), (17)-(18) and (21), Equation (24) becomes
By use of Equations (15), (21) and (22) in Equation (25), we get
From
Now using Equations (21) and (26) in Equation (23) gives
On solving Equations (21) and (15) we can obtain the expression for bulk viscosity coefficient as
Thus the metric (1) reduces into the form
The deceleration parameter is given by
Expansion scalar, Shear coefficient, relative anisotropy for this model is given by
The critical energy density and the critical vacuum energy density are respectively given by
for the anisotropic Bianchi type V model can be expressed respectively as
Mass density parameter and the density parameter of the vacuum are given by
for the anisotropic Bianchi type V model can be expressed respectively as
The State finder parameters
For this model
In addition to physically plausible relations (15)-(17), in this case we assume
where H is Hubble parameter, given by
From Equation (17)-(19) and (41), the Hubble parameter is given by
Using equations (17)-(19), (40) and (42) in equation (8), we get
From Equations (21) and (43),
where
From
Substitute the values from Equations (17)-(19), (40) and (44) in Equation (5), we get
By use of Equation (21), Equation (44) gives
where
Now we study variation of bulk viscosity coefficient
In order to have exact solution of the system of equations one more physically plausible relation is required.
Thus, we consider the well known relation
Using Equations (17)-(19), (46) and (48) in Equation (47) one can obtain coefficient of bulk viscosity as
From
It has already been mentioned that for full causal theory
On the basis of Gibb’s inerrability condition, Maartens [
which with the help of Equation (21) gives
using Equations (21), (42), (48) and (52) in Equation (50) one can obtain
which on simplification yields the expression for bulk viscosity as
where
In this paper, we have studied bulk viscous Bianchi type V space-time geometry with generalized Chaplygin gas and varying gravitational and cosmological constants. We have obtained a new set of exact solutions of
Einstein’s equations by considering
When
have clear idea of variation in behavior of cosmological parameters, relevant graphs have been plotted; all
graphs are in fair agreement with cosmological observations.
Shubha S.Kotambkar,Gyan PrakashSingh,Rupali R.Kelkar, (2015) Bulk Viscous Bianchi Type V Space-Time with Generalized Chaplygin Gas and with Dynamical G and Λ. International Journal of Astronomy and Astrophysics,05,208-221. doi: 10.4236/ijaa.2015.53025