Nonminimal Derivative Couplings and Inflation in Generalized Theories of Gravity

We study extended theories of gravity where nonminimal derivative couplings of the form Rᵏˡϕ, kϕ, l are present in the Lagrangian. We show how and why the other couplings of similar structure may be ruled out and then deduce the field equations and the related cosmological models. Finally, we get inflationary solutions which do follow neither from any effective scalar field potential nor from a cosmological constant introduced ``by hand'', and we show the de Sitter space--time to be an attractor solution.