BIANCHI TYPE-I COSMOLOGICAL MODELS WITH TIME DEPENDENT GRAVITATIONAL AND COSMOLOGICAL CONSTANTS: AN ALTERNATIVE APPROACH

The present study deals with the exact solutions of the Einstein's field equations with variable gravitational and cosmological "constants" for a spatially homogeneous and anisotropic Bianchi type-I space-time. We assume that the conservation law for the matter is fulfilled. Hence giving rise to separate equations one for the perfect fluid and other connecting gravitational and cosmological constants. Assuming that G be a function of volume scale V. the metric functions, A-term, energy density and pressure are found to be functions of V. The equation for V is found through Einstein's field equations and solved both analytically and numerically. The present study also allows a time dependent deceleration parameter (DP). It is found that for empty universe, the derived model is accelerating whereas for radiating dominated and stiff fluid universes, we obtain models that depict a transition of the universe from the early decelerated phase to the recent accelerating phase. The cosmological constant A is obtained as a decreasing function of time and approaching a small positive value at present epoch which is corroborated by consequences from recent supernovae Ia observations. The physical significances of the cosmological models have also been discussed.