Dynamical study of the empty Bianchi type I model in generalised scalar-tensor theory (Q1585777)

The paper is devoted to the study of the generalized scalar-tensor theory in the empty Bianchi type I model. The most general form of the action of the scalar-tensor theories is \(S=\int [F(\varphi)R-(1/2)(\nabla \varphi)^2-U(\varphi)]\sqrt {-g}d^4x\), where \(\varphi \) is a scalar field, and \(U(\varphi)\) is a potential. Here it is considered General Relativity with \(U=0\) (Newtonian limit for the weak fields), \(F(\varphi)=\varphi ^2/8\omega \), and \(\omega =const \). Using an original method, the author demonstrates how one can derive the sign of the first and second derivatives of the metric functions and examine three different theories. There exist important conditions such that the dynamic is in an expansion and decelerated at late time.