Nonminimal coupling of the inflaton field to the Ricci curvature of spacetime
is generally unavoidable, and the paradigm of inflation should be generalized
by including the corresponding term in the Lagrangian of the inflationary
theory. This paper reports on the status of the programme of generalizing
inflation. First, the problem of finding the correct value (or set of values)
of the coupling constant is analyzed; the result has important consequences for
the success or failure of inflationary scenarios. Then, the slow-roll
approximation to generalized inflation is studied. Both the unperturbed
inflating universe models and scalar/tensor perturbations are discussed, and
open problems are pointed out.Comment: 42 pages, LaTeX. Talk given at the conference ''Recent Developments
in Gravitation, Cosmology and Quantum Field Theory, Peyresq, France (June
2000
