de Sitter attractors in generalized gravity

We obtain conditions for the existence and stability of de Sitter attractors in the phase space of spatially homogeneous and isotropic cosmology in generalized theories of gravity (including non-linear and scalar-tensor theories). These conditions are valid for any form of the coupling functions of the theory. Stability with respect to inhomogeneous perturbations is analyzed using a covariant and gauge-invariant formalism. The relevance for inflationary scenarios of the early universe and for quintessence models of the present era is discussed.