Bianchi {VI}${}_0$ in Scalar and Scalar-Tensor Cosmologies

We study several cosmological models with Bianchi $\text{VI}$${}_0$ symmetries under the self-similar approach. In order to study how the \textquotedblleft constants\textquotedblright\ $G$ and $\mathrm{\Lambda }$ may vary, we propose three scenarios where such constants are considered as time functions. The first model is a perfect fluid. We find that the behavior of $G$ and $\mathrm{\Lambda }$ are related. If $G$ behaves as a growing time function then $\mathrm{\Lambda }$ is a positive decreasing time function but if $G$ is decreasing then $\mathrm{\Lambda }$ is negative. For this model we have found a new solution. The second model is a scalar field, where in a phenomenological way, we consider a modification of the Klein-Gordon equation in order to take into account the variation of $G$. Our third scenario is a scalar-tensor model. We find three solutions for this models where $G$ is growing, constant or decreasing and $\mathrm{\Lambda }$ is a positive decreasing function or vanishes. We put special emphasis on calculating the curvature invariants in order to see if the solutions isotropize.