INFLATIONARY DENSITY PERTURBATIONS WITH OMEGA LESS-THAN 1

Abstract

The inflationary scenario is considered, with omega-0 > 0.1 instead of the usual omega-0 = 1. The extent to which this is unnatural is quantified. On the hypothesis that the inflaton field perturbation is in the conformal vacuum state, it is found that the spectrum of the primeval curvature perturbation is still given by the usual formula in terms of the inflaton potential and its derivative, evaluated at the epoch when the observable universe leaves the horizon. The corresponding microwave background anisotropy is the same on small scales, and only a few times bigger on very large scales (quadrupole moment). The limit on the inflaton potential coming from present limits on the anisotropy is therefore about the same.