Isotropization of generalized scalar-tensor theory plus a massive scalar field in the Bianchi type I model (Q2752500)

The isotropization of Bianchi type I cosmological models is studied within a generalized scalar-tensor theory defined by the Lagrangian NEWLINE\[NEWLINE{\mathcal L}=[R-({3\over 2}+\omega (\phi)) \phi^{|\mu} \phi_{|\mu} \phi^2-U (\phi)] \sqrt{-g}.NEWLINE\]NEWLINE The important result is: A necessary condition for isotropization will be that the quantity \(\varphi U_\varphi U^{-1} (3+2\omega)^{-1/2}\) tends toward a constant \(l\) with \(l^2<3\). It arises at late times if the Hamiltonian is positive, and at early times otherwise. If \(l\neq 0\) the metric functions tend toward \(t^{l-2}\). The Universe is expanding and will be inflationary if \(l^2<1\). If \(l=0\), the Universe tends toward a de Sitter model. The value of the scalar field \(\phi\) when the Universe reaches an isotropic equilibrium state is given by a differential equation.