Isotropization of the magnetic universe in the Horndeski theory with $G_3(X,\phi)$ and $G_5(X)$

Abstract

We study the isotropization process of Bianchi-I space-times in the Horndeski theory with $G_3(X,\phi)\neq 0$ and $G_5=\text{const}/X$. A global unidirectional electromagnetic field interacts with a scalar field according to the law $f^2(\phi)F_{\mu\nu}F^{\mu\nu}$. In the Horndeski theory, the anisotropy can develop in different ways. The proposed reconstruction method allowed us to build models with acceptable the anisotropy behavior. To analyze space-time anisotropy, we used the relations $a_i/a$ ($i=1,2,3$), where $a_i$ are metric functions and $a\equiv(a_1a_2a_3)^{1/3}$.