  The temperature fluctuations in the cosmic microwave background observed by
COBE provide strong support for an inflationary phase in the early universe,
below the GUT scale. We argue that a singlet field in a hidden sector of an
effective supergravity theory yields the required inflationary potential
without fine tuning. Reheating occurs to a temperature low enough to avoid the
gravitino problem, but high enough to allow subsequent baryogenesis. Two
observational consequences are that gravitational waves contribute negligibly
to the microwave background anisotropy, and the spectrum of scalar density
perturbations is `tilted', improving the fit to large-scale structure in an
universe dominated by cold dark matter.
