Scalar-tensor theory and the anisotropic perturbations of the inflationary universe

Inflationary higher derivative scalar-tensor theory is analyzed in this paper in a de Sitter background space. A useful model-independent formula of the Friedmann equation is derived and used to study the stability problem associated with the anisotropic perturbations of the inflationary solution. The stability conditions of the de Sitter solution are derived for a general class of models. For a simple demonstration, an induced gravity model is considered in this paper for the effects of the higher derivative interactions including a cubic term.