Inflation as a transient attractor inR2cosmology

Using the equivalence between the curvature-squared gravity theory and the Einstein theory with a scalar field, we show that the potential in the latter system has a very flat plateau. It turns out that inflation is quite natural but transient in the $R^2$ cosmology. All anisotropic Bianchi types of space-time except IX approach the de Sitter solution as an attractor, followed by the Friedmann universe after sufficient inflation. We find a similar behavior in higher- (4<D<10) dimensional theories, in which inflation is not exponential-type but power-law-type. The dilaton coupling to the $R^2$ term is also investigated. The coupling destroys the inflationary solution.