  We study the homogeneous but anisotropic Bianchi type-V cosmological model
with time-dependent gravitational and cosmological "constants". Exact solutions
of the Einstein field equations (EFEs) are presented in terms of adjustable
parameters of quantum field theory in a spatially curved and expanding
background. It has been found that the general solution of the average scale
factor R as a function of time involved the hypergeometric function. Two
cosmological models are obtained from the general solution of the
hypergeometric function and the Emden-Fowler equation. The analysis of the
models shows that for a particular choice of parameters in our first model, the
cosmological "constant" decreases whereas the Newtonian gravitational
"constant" increases with time, and for another choice of parameters, the
opposite behaviour is observed. The models become isotropic at late times for
all parameter choices of the first model. In the second model of the general
solution, both the cosmological and gravitational "constants" decrease while
the model becomes more anisotropic over time. The exact dynamical and
kinematical quantities have been calculated analytically for each model.
