Consequences of the COBE satellite results for the inflationary scenario

The discovery of the microwave background anisotropy by the Cosmic Background Explorer (COBE) satellite is in accord with the inflationary scenario. For five promising models involving a single scalar field, the coupling constants and the fluctuation spectra are calculated including a correction for gravitational radiation. The primordial density fluctuation spectrum computed from these models is not exactly scale-invariant; the spectral index is constrained to be n≳0.8 for inflation with an exponential potential (assuming that the biasing parameter for galaxies ${\mathit{b}}_{\mathrm{\rho }}$<2). The implications for biased galaxy formation scenarios are discussed.