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

Abstract

The following strong inequality is established in the inflationary scenario (units units h ̵ = c = 8πG = 1); ϱ ∗ ⪡ 7(a 2) 2 . Here ϱ ∗ is the energy density of the universe at the beginning of the radiation dominated era, a 2 is the quadrupole anisotropy of the microwave background. The present limit on a 2 implies that ϱ ∗ 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.