Bianchi VI h with variable gravitational and cosmological constants

In order to study how the gravitational and the cosmological constants, G, Λ may vary, we consider two theoretical frameworks which are, a modification of the General Relativity and several scalar models (the standard, non-interacting and interacting models and their respective modifications to allow a G varying). We find exact self-similar solutions for the geometry Bianchi VI _h , (that is, the models: III, VI₀, and VI _h ,). Some physical and geometrical properties of the models are also discussed and we compare the obtained theoretical results with the current observational data. In the first of the theoretical models, we reach the conclusion that, from the structure of the field equations, the behaviour of Λ and G are related, but taking into account the observational data, we conclude that the Λ behaves as a positive decreasing time function while G is growing but in the long time regimen it tends to a constant value. In the scalar models, our solutions predict a “positive” dynamical cosmological constant in all the obtained solutions while the behaviour of G yields indeterminate, since its depends on a free parameter, G≈t ^2α , so it may be growing or decreasing as in the scalar-tensor theories.