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We investigate anisotropic and homogeneous cosmological models in the scalar-tensor theory of gravity with non-minimal kinetic coupling of a scalar field to the curvature given by the function (/2) G_\, ^ ^ in the Lagrangian. We assume that the space-times are filled a global unidirectional electromagnetic field that minimally interacts with the scalar field. The Horndeski theory allows anisotropy to grow over time. The question arises about isotropization. In the theory under consideration, a zero scalar charge imposes a condition on the anisotropy level, namely its dynamics develops in a limited region. This condition uniquely determines a viable branch of solutions of the field equations. The magnetic energy density that corresponds to this branch is a bounded function of time. The sign of parameter l=1+8 determines the properties of cosmological models, where is the cosmological constant. The sign = 1 defines the canonical scalar field and the phantom field, respectively. An inequality />0 is a necessary condition for isotropization of models, but not sufficient. Three cases were considered: l=0, the isotropization does not occur; l>0, there is isotropization; l<0, there are two branches, one of which has the property of isotropization, and the other describes the Universe with collapse. The model with l<0 has an anisotropic bounce and the Universe evolution begins with a non-zero volume value. Models of an infinitely expanding Universe eventually go into inflation mode with the scale factor a (t) e^h_ t, h_={3}.
Muharlyamov et al. (Thu,) studied this question.