On the degree of scale invariance of inflationary perturbations

Details On the degree of scale invariance of inflationary perturbations On the degree of scale invariance of inflationary perturbations

1999-08-14

arxiv.org/abs/astro-ph/9908157v1

Phys.Rev. D62 (2000) 063503

Astronomy and Astrophysics

Astrophysics

7 pages, 2 figures, submitted to Phys. Rev. D

Scientific paper

10.1103/PhysRevD.62.063503

Many, if not most, inflationary models predict the power-law index of the spectrum of density perturbations is close to one, though not precisely equal to one, |n-1| \sim O(0.1), implying that the spectrum of density perturbations is nearly, but not exactly, scale invariant. Some models allow n to be significantly less than one (n \sim 0.7); a spectral index significantly greater than one is more difficult to achieve. We show that n \approx 1 is a consequence of the slow-roll conditions for inflation and ``naturalness,'' and thus is a generic prediction of inflation. We discuss what is required to deviate significantly from scale invariance, and then show, by explicit construction, the existence of smooth potentials that satisfy all the conditions for successful inflation and give $n$ as large as 2.

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