Magnetic Bianchi-I cosmology in the Horndeski theory

In this paper, we study the evolution of Bianchi-I spacetimes within the framework of the Horndeski theory with G5=const./X. The spacetimes are filled a global unidirectional electromagnetic field interacting with a scalar field. We consider the minimal interaction and the non-minimal interaction by the law f2(phi)F mu nu F mu nu. The Horndeski theory allows anisotropy to grow over time, so the question arises of regulating the anisotropic level in this theory. Using the designer method, we build models in which the anisotropic level tends to a small value as the Universe expands. One of the results is a model with a anisotropic bounce.