Phenomenological Varying Modified Chaplygin Gas with Variable $G$ and $\Lambda$: Toy Models for Our Universe

This article motivated by the recent articles and results of two authors. Recently, J. Sadeghi and H. Farahani presented a work [1], where they include viscosity and analyze general model, by this way they extended models considered by M. Khurshudyan [2] and [3]. In this article, We tempt to consider varying Modified Chaplygin gas model in case of variable $G$ and $\Lambda$. It is well known, that varying $G$ and $\Lambda$ gives rise to modified field equations and modified conservation laws. We will consider two different toy models. First model is a Universe with one component phenomenological gas of our consideration, while for the second model we assume existence of a composed fluid of gas and a matter with $P=\omega(t)\rho_{m}$. Sign changeable interaction between fluids is accepted. We will analyze important cosmological parameters like EoS parameter of a fluid, deceleration parameter $q$ of the model.