Bianchi Type-I cosmological models containing perfect fluid with time varying G and Λ have been presented. The solutions obtained represent an expansion scalar θ bearing a constant ratio to the anisotropy in the direction of space-like unit vector λ i . Of the two models obtained, one has negative vacuum energy density, which decays numerically. In this model, we obtain Λ ∼ H 2 , Λ ∼ R44/R and Λ ∼ T −2 (T is the cosmic time) which is in accordance with the main dynamical laws for the decay of Λ. The second model reduces to a static solution with repulsive gravity.
Einstein field equations with variable gravitational and cosmological constants are considered in the presence of perfect fluid for Robertson-Walker universe by assuming the cosmological term proportional to the Hubble parameter. This variation law for vacuum density has recently been proposed by Schützhold on the basis of quantum field estimations in the curved and expanding background. The cosmological term tends asymptotically to a genuine cosmological constant and the model tends to a deSitter universe. We obtain that the present universe is accelerating with a large fraction of cosmological density in the form of cosmological term.
Einstein's field equations with variable gravitational and cosmological constants are considered in the presence of perfect fluid for the Bianchi type-I universe by assuming that the cosmological term is proportional to R −m (R is a scale factor and m is a constant). A variety of solutions are presented. The physical significance of the respective cosmological models are also discussed.
We have studied cosmological model generated by perfect fluid coupled with mass less scalar field for Kantowski-Sachs space-time in general theory of relativity. Two different physically viable models of the universe are obtained by using a special law of variation for Hubble's parameter that yields a constant value of deceleration parameter. Some physical consequences of the models have been discussed in case of Zel'dovich fluid.
Einstein field equations with variable gravitational and cosmological constants are considered in the presence of perfect fluid for the Bianchi type-III universe by assuming conservation law for the energy-momentum tensor. Exact solutions of the field equations are obtained by using the scalar of expansion proportional to the shear scalar θ ∝ σ, which leads to a relation between metric potential B = C n , where n is a constant. The corresponding physical interpretation of the cosmological solutions are also discussed.
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