Successful Supersymmetric Inflation

The temperature uctuations in the cosmic microwave background observed by COBE provide strong support for an innationary phase in the early universe, below the GUT scale. We argue that a singlet eld in a hidden sector of an eeective supergravity theory yields the required innationary potential without ne 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 t to large-scale structure in an universe dominated by cold dark matter.