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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