Title:Phenomenological models of Universe with varying $G$ and $Λ$

Abstract:In this article we will consider several phenomenological models for the Universe with varying $G$ and $\Lambda(t)$, where $G$ is the gravitational "constant" and $\Lambda(t)$ is a varying cosmological "constant". Two-component fluid model taken into account. An interaction of the phenomenological form between a barotropic fluid and a quintessence DE is supposed. Three different forms of $\Lambda(t)$ will be considered. The problem is analysed numerically and behavior of different cosmological parameters investigated graphically. Conclusion and discussions are given at the end of the work. In an Appendix an information concerning to the other cosmological parameters is presented.