From the spectrum to inflation: an inverse formula for the general slow-roll spectrum

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Abstract
We propose a general inverse formula for extracting inflationary parameters from the observed power spectrum of cosmological perturbations. Under the general slow-roll scheme, which helps to probe the properties of inflation in a model independent way, we invert the leading order, single field, power spectrum formula. We also give some physically interesting examples to demonstrate its wide applicability and illuminate its properties.