Bianchi type-I transit cosmological models with time dependent gravitational and cosmological constants

The present study deals with exact solutions of Einstein’s field equations with variable gravitational and cosmological constants for a spatially homogeneous and anisotropic Bianchi type-I space-time. To get deterministic solutions, we consider a law of variation of scale factor a(t)=tnet\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$a(t) = \sqrt{t^{n} e^{t}}$$\end{document}, which yields a time dependent deceleration parameter q=-1+2n(n+t)2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$q = - 1 + \frac{2n}{(n + t)^{2}}$$\end{document}, representing a class of models that generates a transition of the universe from early decelerated phase to the recent accelerating phase. We find that time dependent deceleration parameter is sensible for present day Universe and gives an earmark description of evolution of the universe. The gravitational constant G(t)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$G(t)$$\end{document} is permitted to follow a power-law expansion which is suitable for present evolution of the universe. The cosmological constant Λ(t)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Lambda (t)$$\end{document} 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. We also observed that our solution is stable. The physical significance of cosmological models has also been discussed.