Degree of scale invariance of inflationary perturbations - art. no. 063503

Most inflationary models predict that the power-law index of the spectrum o f density perturbations is close to 1, though nor precisely equal to 1, \n- 1\similar to O(0.1), implying that the spectrum of density perturbations is nearly, but not exactly, scale invariant. However, there are models where it is significantly less than 1 (n similar to 0.7); a spectral index signif icantly greater than 1 is more difficult to achieve. Without recourse to sp ecific models, we show very generally and very explicitly that n approximat e to 1 is a consequence of the slow-roll conditions for inflation and "natu ralness," and thus, that near scale invariance is a generic prediction of i nflation and a test of the inflationary framework. We derive the conditions needed to deviate significantly from scale invariance, and then show, by e xplicit construction, the existence of smooth potentials that satisfy all t he conditions for successful inflation and give n as large as 2.