A model-independent expression for the Friedmann equation in Bianchi type spaces is derived. In addition, a model-independent stability analysis of the higher curvature de Sitter solution is discussed. Stability conditions of the de Sitter solution are derived explicitly for a cubic model with interesting effects. It is known that quadratic terms do not contribute to this de Sitter background solution. Higher curvature terms are all critical to the stability of the de Sitter space.