A bound on inflationary energy density from the isotropy of the microwave background

The following strong inequality is established in the inflationary scenario (units (h/2π)=c=8πG=1); rhosub(*)<<7(a2)2. Here rhosub(*) is the energy density of the universe at the beginning of the radiation dominated era, a2 is the quadrupole anisotropy of the microwave background. The present limit on a2 implies that psub(*)sup(1/4) is more than two orders of magnitude below the Planck mass. The limit arises from the effect of energy density perturbations, the effect of gravitational waves being small. (orig.)