Anisotropic inflation in Brans-Dicke gravity with a non-Abelian gauge field

Abstract

We study anisotropic inflation in the Brans-Dicke gravity in the presence of a non-Abelian gauge field where the gauge field is nonminimally coupled to the inflaton. We consider the displaced quadratic potential for the inflation. We find out that the solution of equations of motion is an attractor in the phase space. Moreover, anisotropy grows with the number of $e$-folds. It may become either positive or negative in contradiction to the Abelian gauge field coupling. The anisotropy depends on the Brans-Dicke parameter and constant parameter of the coupling function of the scalar field and the non-Abelian gauge field.