We present new exact solutions to Einstein's equations that describe the evolution of inflationary universe models. The inflation is driven by the evolution of scalar fields in potentials which possess minima. One solution describes double inflation and the other displays a Mexican-hat potential. The spectral indices of the scalar density and gravitational wave fluctuations are computed. One of the solutions displays the limitations of attempts to reconstruct the inflationary potential from present-day observations via an expansion in the slow-roll parameters.

• Received 27 September 1993

DOI:https://doi.org/10.1103/PhysRevD.49.3055