Classification of inflationary Einstein-scalar-field models via catastrophe theory

Various scenarios of the initial inflation of the Universe are distinguished by the choice of a scalar field potential U(φ) which simulates a temporarily nonvanishing cosmological term. Our new method, which involves a reparametrization in terms of the Hubble expansion parameter H, provides a classification of allowed inflationary potentials and of the instability of the critical points. It is broad enough to embody all known exact solutions involving one scalar field as special cases. Inflation corresponds to the evolution of critical points of some catastrophe manifold. The coalescence of its nondegenerate critical points with the creation of a degenerate critical point corresponds to the reheating phase of the Universe. This is illustrated by several examples.