Successful Supersymmetric Inflation

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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.