A Model to Explain Varying $\Lambda$, $G$ and $\sigma^2$ Simultaneously

Models with varying cosmical parameters, which were earlier regarded constant, are getting attention. However, different models are usually invoked to explain the evolution of different parameters. We argue that whatever physical process is responsible for the evolution of one parameter, should also be responsible for the evolution of others. This means that the different parameters are coupled together somehow. Based on this guiding principle, we investigate a Bianchi type I model with variable $\Lambda$ and $G$, in which $\Lambda$, $G$ and the shear parameter $\sigma^2$, all are coupled. It is interesting that the resulting model reduces to the FLRW model for large $t$ with $G$ approaching a constant.